+publisher:"University of Kansas" +contributor:("Surana, Karan S.")

1. Quiros Fonseca, Luis Alonso. Mathematical Models and Numerical Simulations of phase change in Lagrangian and Eulerian descriptions.

Degree: MS, Mechanical Engineering, 2012, University of Kansas

URL: http://hdl.handle.net/1808/8779

► This thesis presents development of mathematical models for liquid-solid and solid-liquid phase change phenomena in Lagrangian and Eulerian descriptions. The mathematical models are derived by… (more)

▼ This thesis presents development of mathematical models for liquid-solid and solid-liquid phase change phenomena in Lagrangian and Eulerian descriptions. The mathematical models are derived by assuming a smooth interface (or transition region) between the solid and liquid phases in which the specific heat, thermal conductivity, density and latent heat are continuous and differentiable functions of temperature. The width of the interface region can be as large or as small as desired by a specific application. The derivations assume the matter to be homogeneous and isotropic. In case of Lagrangian description we assume zero velocity field i.e. no flow with free boundaries i.e. stress free medium. Under these assumptions the mathematical model reduces to the first law of thermodynamics i.e. energy equation. The derivation is based on specific total energy and the heat vector. The constitutive theory for heat vector is assumed to be Fourier heat conduction law. The specific total energy incorporates the physics of phase change in the transition region between the solid and the liquid phases. This results in a time dependent non-linear diffusion equation in temperature. The physics of initiation of the phase change as well as formation and propagation of the transition region (front) is intrinsic in the mathematical model and hence no other means of front tracking are required. For the purposes of numerical simulation, the mathematical model can also be recast as a system of first order partial differential equations. In case of Eulerian description, the mathematical model consists of the continuity equation, momentum equations, energy equation, constitutive theories for stress tensor and heat vector in the liquid phase, solid phase and as well in the transition region. In the liquid phase we assume the matter to be Newtonian fluid, hence the details of the mathematical model are straight forward. In the solid region we assume the solid to be hypoelastic, hence the rate constitutive theory is valid for the stress tensor. We also assume Fourier heat conduction law for the solid phase. In the transition region containing a mixture of solid and liquid phases, use of mixture theory is most appropriate for conservation laws as well as the constitutive theory. Such mathematical models are beyond the scope of the work considered in this thesis. Instead, we present a simple model that is based on representative volume fractions in the transition region. Eulerian descriptions are necessitated when phase change occurs in a flowing medium. Regardless of whether the mathematical models utilize Lagrangian or Eulerian description, the resulting mathematical models consist of a system of non-linear partial differential equation in space and time, i.e. they constitute initial value problems. Numerical solutions of these mathematical models are obtained using space-time least squares finite element process based on minimization of residual functional. This approach results in space-time variationally consistent integral forms that yield… Advisors/Committee Members: Surana, Karan S. (advisor), Romkes, Albert (cmtemember), TenPas, Peter W. (cmtemember).

Subjects/Keywords: Mechanical engineering; Finite elements; Lagrangian and eulerian; Melting; Phase change; Solidification

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APA (6^th Edition):

Quiros Fonseca, L. A. (2012). Mathematical Models and Numerical Simulations of phase change in Lagrangian and Eulerian descriptions. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/8779

Chicago Manual of Style (16^th Edition):

Quiros Fonseca, Luis Alonso. “Mathematical Models and Numerical Simulations of phase change in Lagrangian and Eulerian descriptions.” 2012. Masters Thesis, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/8779.

MLA Handbook (7^th Edition):

Quiros Fonseca, Luis Alonso. “Mathematical Models and Numerical Simulations of phase change in Lagrangian and Eulerian descriptions.” 2012. Web. 15 Jan 2021.

Vancouver:

Quiros Fonseca LA. Mathematical Models and Numerical Simulations of phase change in Lagrangian and Eulerian descriptions. [Internet] [Masters thesis]. University of Kansas; 2012. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/8779.

Council of Science Editors:

Quiros Fonseca LA. Mathematical Models and Numerical Simulations of phase change in Lagrangian and Eulerian descriptions. [Masters Thesis]. University of Kansas; 2012. Available from: http://hdl.handle.net/1808/8779

University of Kansas

2. Knight, Jason. Nonlinear Waves in Solid Continua with Finite Deformation.

Degree: MS, Mechanical Engineering, 2015, University of Kansas

URL: http://hdl.handle.net/1808/19389

► This work considers initiation of nonlinear waves, their propagation, reflection, and their interactions in thermoelastic solids and thermoviscoelastic solids with and without memory. The conservation… (more)

▼ This work considers initiation of nonlinear waves, their propagation, reflection, and their interactions in thermoelastic solids and thermoviscoelastic solids with and without memory. The conservation and balance laws constituting the mathematical models are derived for finite deformation and finite strain using second Piola-Kirchoff stress tensor and Green's strain tensor. The constitutive theories for thermoelastic solids express the second Piola-Kirchoff stress tensor as a linear function of the Green's strain tensor. In the case of thermoviscoelastic solids without memory, the constitutive theory for deviatoric second Piola-Kirchoff stress tensor consists of a first order rate theory in which the deviatoric second Piola-Kirchoff stress tensor is a linear function of the Green's strain tensor and its material derivative. For thermoviscoelastic solids with memory, the constitutive theory for deviatoric second Piola-Kirchoff stress tensor consists of a first order rate theory in which the material derivative of the deviatoric second Piola-Kirchoff stress is expressed as a linear function of the deviatoric second Piola-Kirchoff stress, Green's strain tensor, and its material derivative. For thermoviscoelastic solids with memory, the constitutive theory for deviatoric second Piola-Kirchoff stress tensor consists of a first order rate theory in which the material derivative of the deviatoric second Piola-Kirchoff stress is expressed as a linear function of the deviatoric second Piola-Kirchoff stress, Green's strain tensor, and its material derivative. Fourier heat conduction law with constant conductivity is used as the constitutive theory for heat vector. The mathematical models are derived using conservation and balance laws. Alternate forms of the mathematical models are presented and their usefulness is illustrated in the numerical studies of the model problems with different boundary conditions. Nondimensionalized mathematical models are used in the computations of the numerical solutions of the model problems. All numerical studies are performed using space-time variationally consistent finite element formulations derived using space-time residual functionals in which the second variation of the residuals is neglected in the second variation of the residual functional and the non-linear equations resulting from the first variation of the residual functional are solved using Newton's Linear Method (Newton-Raphson method) with line search. Space-time local approximations are considered in higher order scalar product spaces that permit desired order of global differentiability in space and time. Extensive numerical studies are presented for different boundary conditions. Computed results for non-linear wave propagation, reflection, and interaction are compared with linear wave propagation to demonstrate significant differences between the two, the importance of the nonlinear wave propagation over linear wave propagation as well as to illustrate the meritorious features of the mathematical models and the space-time… Advisors/Committee Members: Surana, Karan S (advisor), Sorem, Robert M (cmtemember), Tenpas, Peter W (cmtemember).

Subjects/Keywords: Mechanical engineering; Constitutive Theories; Finite Strain; Green's Strain; Linear and Nonlinear Waves; Second Piola-Kirchoff Stress

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APA (6^th Edition):

Knight, J. (2015). Nonlinear Waves in Solid Continua with Finite Deformation. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/19389

Chicago Manual of Style (16^th Edition):

Knight, Jason. “Nonlinear Waves in Solid Continua with Finite Deformation.” 2015. Masters Thesis, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/19389.

MLA Handbook (7^th Edition):

Knight, Jason. “Nonlinear Waves in Solid Continua with Finite Deformation.” 2015. Web. 15 Jan 2021.

Vancouver:

Knight J. Nonlinear Waves in Solid Continua with Finite Deformation. [Internet] [Masters thesis]. University of Kansas; 2015. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/19389.

Council of Science Editors:

Knight J. Nonlinear Waves in Solid Continua with Finite Deformation. [Masters Thesis]. University of Kansas; 2015. Available from: http://hdl.handle.net/1808/19389

University of Kansas

3. Joy, Aaron D. Non-Classical Continuum Theories for Solid and Fluent Continua.

Degree: PhD, Mechanical Engineering, 2017, University of Kansas

URL: http://hdl.handle.net/1808/26353

► This dissertation presents non-classical continuum theories for solid and fluent con- tinua. In these theories additional physics due to internal rotations and rotation rates arising… (more)

▼ This dissertation presents non-classical continuum theories for solid and fluent con- tinua. In these theories additional physics due to internal rotations and rotation rates arising from the Jacobian of deformation and the velocity gradient tensor as well as Cosserat rotations and rotation rates are considered. While the internal rotations and rotation rates are completely defined by the deformation physics, the Cosserat rota- tions and Cosserat rotation rates are additional degrees of freedom at a material point. The non-classical theories that only consider the internal rotations and the internal ro- tation rates are referred to as internal polar theories, while those that consider both are called polar or non-classical theories. The conservation and balance laws and the constitutive theories are derived for non- classical continuum theories. It is shown that these non-classical theories require mod- ifications of the balance laws used in classical continuum theories. In the presence of additional rotation and rotation rate physics in non-classical theories, the modifica- tions of the balance laws used in classical continuum theories are not sufficient to ensure equilibrium of the deforming matter. It is shown that these theories require the balance of moments of moments as an additional balance law. The constitutive theories for solid and fluent continua are derived using the conditions resulting from the entropy inequality and the representation theorem. Use of integrity in their deriva- tions ensures completeness of the resulting constitutive theories. Specific derivations and details of the constitutive theories for thermoelastic and thermoviscoelastic solids with and without memory are presented for small deformation, small strain physics. Detailed derivations of the constitutive theories for compressible as well as incom- iiipressible thermoviscous and thermoviscoelastic fluent continua are also presented. Retardation and/or memory moduli are derived for polymeric solids and fluids. The present theories are compared with published works, particularly with the microp- olar theories of Eringen, to highlight the significance and the thermodynamic consis- tency of the present work, as well as to contrast the differences. Advisors/Committee Members: Surana, Karan S. (advisor), TenPas, Peter (cmtemember), Sorem, Robert (cmtemember), Parr, Alfred (cmtemember), Taghavi, Ray (cmtemember).

Subjects/Keywords: Mechanics; Cosserat; Polar continua; rotations

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APA (6^th Edition):

Joy, A. D. (2017). Non-Classical Continuum Theories for Solid and Fluent Continua. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/26353

Chicago Manual of Style (16^th Edition):

Joy, Aaron D. “Non-Classical Continuum Theories for Solid and Fluent Continua.” 2017. Doctoral Dissertation, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/26353.

MLA Handbook (7^th Edition):

Joy, Aaron D. “Non-Classical Continuum Theories for Solid and Fluent Continua.” 2017. Web. 15 Jan 2021.

Vancouver:

Joy AD. Non-Classical Continuum Theories for Solid and Fluent Continua. [Internet] [Doctoral dissertation]. University of Kansas; 2017. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/26353.

Council of Science Editors:

Joy AD. Non-Classical Continuum Theories for Solid and Fluent Continua. [Doctoral Dissertation]. University of Kansas; 2017. Available from: http://hdl.handle.net/1808/26353

4. Klein, Kayla. Flows of Incompressible Newtonian and Generalized Newtonian Fluids over a Circular Cylinder.

Degree: MS, Mechanical Engineering, 2012, University of Kansas

URL: http://hdl.handle.net/1808/9831

► max <= O(10^-6) always ensures that Newton's linear method with line search yields an accurate solution of the system of non-linear algebraic equations resulting from… (more)

Subjects/Keywords: Mechanical engineering; Mathematics; Circular cylinder; Computational; Finite element method; Incompressible; Least squares processes; Shear thinning

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APA (6^th Edition):

Klein, K. (2012). Flows of Incompressible Newtonian and Generalized Newtonian Fluids over a Circular Cylinder. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/9831

Chicago Manual of Style (16^th Edition):

Klein, Kayla. “Flows of Incompressible Newtonian and Generalized Newtonian Fluids over a Circular Cylinder.” 2012. Masters Thesis, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/9831.

MLA Handbook (7^th Edition):

Klein, Kayla. “Flows of Incompressible Newtonian and Generalized Newtonian Fluids over a Circular Cylinder.” 2012. Web. 15 Jan 2021.

Vancouver:

Klein K. Flows of Incompressible Newtonian and Generalized Newtonian Fluids over a Circular Cylinder. [Internet] [Masters thesis]. University of Kansas; 2012. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/9831.

Council of Science Editors:

Klein K. Flows of Incompressible Newtonian and Generalized Newtonian Fluids over a Circular Cylinder. [Masters Thesis]. University of Kansas; 2012. Available from: http://hdl.handle.net/1808/9831

5. Mendoza, Yusshy. Constitutive Theories for Thermoelastic Solids in Lagrangian Description Using Gibbs Potential.

Degree: MS, Mechanical Engineering, 2012, University of Kansas

URL: http://hdl.handle.net/1808/10186

► This thesis presents constitutive theories for finite deformation of homogeneous, isotropic thermoelastic solids in Lagrangian description using Gibbs potential. Since conservation of mass, balance of… (more)

▼ This thesis presents constitutive theories for finite deformation of homogeneous, isotropic thermoelastic solids in Lagrangian description using Gibbs potential. Since conservation of mass, balance of momenta and the energy equation are independent of the constitution of the matter, the second law of thermodynamics, i.e. entropy inequality, must form the basis for all constitutive theories of the deforming matter to ensure thermodynamic equilibrium during the evolution [1, 2]. The entropy inequality expressed in terms of Helmholtz free energy is recast in terms of Gibbs potential. The conditions resulting from the entropy inequality expressed in terms of Gibbs potential permit the derivation of constitutive theory for strain tensor in terms of conjugate stress tensor and the constitutive theory for the heat vector. In the work presented here, it is shown that using the conditions resulting from the entropy inequality, the constitutive theory for the strain tensor can be derived using three different approaches: (i) assuming the Gibbs potential to be a function of the invariants of the conjugate stress tensor and then using the conditions resulting from the entropy inequality, (ii) using theory of generators and invariants, and (iii) expanding Gibbs potential in conjugate stress tensor using Taylor series about a known configuration and then using the conditions resulting from the entropy inequality. The constitutive theories resulting from these three approaches are compared for equivalence between them as well as their merits and shortcomings. The constitutive theory for the heat vector can also be derived either directly using the conditions resulting from the entropy inequality or using the theory of generators and invariants. The derivation of constitutive theory for heat vector using the theory of generators and invariants with complete set of argument tensors yields a more comprehensive constitutive theory for heat vector. In the work we consider both approaches. Summaries of the constitutive theories using parallel approaches (as described above) resulting from the entropy inequality expressed in terms of Helmholtz free energy density are also presented and compared for equivalence with the constitutive theories derived using Gibbs potential. Advisors/Committee Members: Surana, Karan S. (advisor), TenPas, Peter W. (cmtemember), Yimer, Bedru (cmtemember).

Subjects/Keywords: Mechanical engineering; Constitutive theory; Entropy inequality; Generators and invariants; Gibbs potential; Thermoelastic solids

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mendoza, Y. (2012). Constitutive Theories for Thermoelastic Solids in Lagrangian Description Using Gibbs Potential. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/10186

Chicago Manual of Style (16^th Edition):

Mendoza, Yusshy. “Constitutive Theories for Thermoelastic Solids in Lagrangian Description Using Gibbs Potential.” 2012. Masters Thesis, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/10186.

MLA Handbook (7^th Edition):

Mendoza, Yusshy. “Constitutive Theories for Thermoelastic Solids in Lagrangian Description Using Gibbs Potential.” 2012. Web. 15 Jan 2021.

Vancouver:

Mendoza Y. Constitutive Theories for Thermoelastic Solids in Lagrangian Description Using Gibbs Potential. [Internet] [Masters thesis]. University of Kansas; 2012. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/10186.

Council of Science Editors:

Mendoza Y. Constitutive Theories for Thermoelastic Solids in Lagrangian Description Using Gibbs Potential. [Masters Thesis]. University of Kansas; 2012. Available from: http://hdl.handle.net/1808/10186

6. Powell, Michael J. A Simple Mixture Theory for ν Newtonian and Generalized Newtonian Constituents.

Degree: MS, Mechanical Engineering, 2012, University of Kansas

URL: http://hdl.handle.net/1808/10208

► This work presents development of mathematical models based on conservation laws for a saturated mixture of ν homogeneous, isotropic, and incompressible constituents for isothermal flows.… (more)

▼ This work presents development of mathematical models based on conservation laws for a saturated mixture of ν homogeneous, isotropic, and incompressible constituents for isothermal flows. The constituents and the mixture are assumed to be Newtonian or gen- eralized Newtonian fluids. Power law and Carreau-Yasuda models are considered for gen- eralized Newtonian shear thinning fluids. The mathematical model is derived for a ν con- stituent mixture with volume fractions φα using principles of continuum mechanics: con- servation of mass, balance of momenta, first and second laws of thermodynamics, and principles of mixture theory yielding continuity equations, momentum equations, energy equation, and constitutive theories for mechanical pressures and deviatoric Cauchy stress tensors in terms of the dependent variables related to the constituents. It is shown that for Newtonian fluids with constant transport properties, the mathematical models for con- stituents are decoupled. In this case one could use individual constituent models to obtain constituent deformation fields, and then use mixture theory to obtain the deformation field for the mixture. In the case of generalized Newtonian fluids, the dependence of viscosities on deformation field does not permit decoupling. Numerical studies are also presented to demonstrate this aspect. Using fully developed flow of Newtonian and generalized Newto- nian fluids between parallel plates as a model problem, it is shown that partial pressures pα of the constituents must be expressed in terms of the mixture pressure p. In this work we propose pα = φα p and ν α pα = p which implies ν α φα = 1 which obviously holds. This rule for partial pressure is shown to be valid for a mixture of Newtonian and generalized Newtonian constituents yielding Newtonian and generalized Newtonian mixture. Modifi- cations of the currently used constitutive theories for deviatoric Cauchy stress tensor are proposed. These modifications are demonstrated to be essential in order for the mixture theory for ν constituents to yield a valid mathematical model when the constituents are the same. Dimensionless form of the mathematical models are derived and used to present numerical studies for boundary value problems using finite element processes based on a residual functional i.e. least squares finite element processes in which local approximations are considered in H k,p Ωe scalar product spaces. Fully developed flow between parallel plates and 1:2 asymmetric backward facing step are used as model problems for a mixture of two constituents. Advisors/Committee Members: Surana, Karan S. (advisor), TenPas, Peter W. (cmtemember), Yimer, Bedru (cmtemember).

Subjects/Keywords: Mechanical engineering; Continuum mechanics; Finite element method; Fluids; Mechanics; Mixture theory

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APA (6^th Edition):

Powell, M. J. (2012). A Simple Mixture Theory for ν Newtonian and Generalized Newtonian Constituents. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/10208

Chicago Manual of Style (16^th Edition):

Powell, Michael J. “A Simple Mixture Theory for ν Newtonian and Generalized Newtonian Constituents.” 2012. Masters Thesis, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/10208.

MLA Handbook (7^th Edition):

Powell, Michael J. “A Simple Mixture Theory for ν Newtonian and Generalized Newtonian Constituents.” 2012. Web. 15 Jan 2021.

Vancouver:

Powell MJ. A Simple Mixture Theory for ν Newtonian and Generalized Newtonian Constituents. [Internet] [Masters thesis]. University of Kansas; 2012. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/10208.

Council of Science Editors:

Powell MJ. A Simple Mixture Theory for ν Newtonian and Generalized Newtonian Constituents. [Masters Thesis]. University of Kansas; 2012. Available from: http://hdl.handle.net/1808/10208

7. Hirst, Thomas Thayer. A Simple Mixture Theory for Isothermal and Non-isothermal Flows of n Newtonian and Generalized Newtonian Constituents including Interaction Effects.

Degree: MS, Mechanical Engineering, 2013, University of Kansas

URL: http://hdl.handle.net/1808/12962

► Development of mathematical models based on conservation and balance laws including constitutive theories are presented for a saturated mixture of n homogeneous, isotropic, and incompressible… (more)

▼ Development of mathematical models based on conservation and balance laws including constitutive theories are presented for a saturated mixture of n homogeneous, isotropic, and incompressible constituents for isothermal and non-isothermal flows. The constituents and the mixture are assumed to be Newtonian or generalized Newtonian fluids. Power law and Carreau-Yasuda models are considered for generalized Newtonian shear thinning fluids. The mathematical model is derived for a n constituent mixture with volume fractions using principles of continuum mechanics: conservation of mass, balance of momenta, first and second laws of thermodynamics, and principles of mixture theory yielding continuity equations, momentum equations, energy equation, and constitutive theories for mechanical pressures, deviatoric Cauchy stress tensors, and heat vector in terms of the dependent variables related to the constituents and their material coefficients. In the derivation of the mathematical model effects of the interaction forces are accounted in the momentum and energy equations. In the development of the constitutive theories two approaches are considered. In the first approach we assume that the mixture stress is the sum of the constituent stresses. This approach requires derivation of the bulk properties of the constituents based on the constituent volume fractions and their properties which are then utilized in the constitutive theories for the constituents forming the mixture. In the second approach the mixture stress is assumed not to be the sum of the constituent stress. For a homogenous isotropic mixture we begin with its own constitutive theory for the deviatoric mixture stress defined using mixture material coefficients and the symmetric part of the velocity gradient tensor for the mixture. Mixture material coefficients are derived using volume and mole fractions of the constituents and a mixing rule. The mutual parameter in the mixing rule is described using arithmetic mean, geometric mean, and harmonic mean. The validity of the proposed models are demonstrated for degenerated cases of same constituents i.e., two of the constituents same etc. Dimensionless forms of the mathematical models are derived and used to present numerical studies for boundary value problems using finite element processes based on a residual functional, that is, least squares processes in which local approximations are considered in H(k,p) scalar product spaces. Fully developed flow between parallel plates and 1:2 asymmetric backward facing step are used as model problems for a mixture of two constituents. Advisors/Committee Members: Surana, Karan S. (advisor), TenPas, Peter W. (cmtemember), Yimer, Bedru (cmtemember).

Subjects/Keywords: Mechanical engineering; Computational mechanics; Continuum mechanics; Mixture theory

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APA (6^th Edition):

Hirst, T. T. (2013). A Simple Mixture Theory for Isothermal and Non-isothermal Flows of n Newtonian and Generalized Newtonian Constituents including Interaction Effects. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/12962

Chicago Manual of Style (16^th Edition):

Hirst, Thomas Thayer. “A Simple Mixture Theory for Isothermal and Non-isothermal Flows of n Newtonian and Generalized Newtonian Constituents including Interaction Effects.” 2013. Masters Thesis, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/12962.

MLA Handbook (7^th Edition):

Hirst, Thomas Thayer. “A Simple Mixture Theory for Isothermal and Non-isothermal Flows of n Newtonian and Generalized Newtonian Constituents including Interaction Effects.” 2013. Web. 15 Jan 2021.

Vancouver:

Hirst TT. A Simple Mixture Theory for Isothermal and Non-isothermal Flows of n Newtonian and Generalized Newtonian Constituents including Interaction Effects. [Internet] [Masters thesis]. University of Kansas; 2013. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/12962.

Council of Science Editors:

Hirst TT. A Simple Mixture Theory for Isothermal and Non-isothermal Flows of n Newtonian and Generalized Newtonian Constituents including Interaction Effects. [Masters Thesis]. University of Kansas; 2013. Available from: http://hdl.handle.net/1808/12962

8. Selvaraj, Deeptesh. Wave Propagation in Solids with Finite Deformation and Finite Strain.

Degree: MS, Mechanical Engineering, 2017, University of Kansas

URL: http://hdl.handle.net/1808/24142

► This work investigates one dimensional wave propagation in thermoelastic and ther- moviscoelastic solids with and without memory. The work considers the solid matter to be… (more)

Subjects/Keywords: Mechanical engineering; Compressible solid; Continuum Mechanics; Finite Element Analysis; Large deformation; Space time coupled; Wave Propagation

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APA (6^th Edition):

Selvaraj, D. (2017). Wave Propagation in Solids with Finite Deformation and Finite Strain. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/24142

Chicago Manual of Style (16^th Edition):

Selvaraj, Deeptesh. “Wave Propagation in Solids with Finite Deformation and Finite Strain.” 2017. Masters Thesis, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/24142.

MLA Handbook (7^th Edition):

Selvaraj, Deeptesh. “Wave Propagation in Solids with Finite Deformation and Finite Strain.” 2017. Web. 15 Jan 2021.

Vancouver:

Selvaraj D. Wave Propagation in Solids with Finite Deformation and Finite Strain. [Internet] [Masters thesis]. University of Kansas; 2017. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/24142.

Council of Science Editors:

Selvaraj D. Wave Propagation in Solids with Finite Deformation and Finite Strain. [Masters Thesis]. University of Kansas; 2017. Available from: http://hdl.handle.net/1808/24142

9. Khadka, Dipin. Numerical Solutions of Boundary Value Problems for Incompressible Internal Polar Viscous Fluids.

Degree: MS, Mechanical Engineering, 2016, University of Kansas

URL: http://hdl.handle.net/1808/22350

► The work presented here considers conservation and balance laws and constitutive theories for internal polar non-classical isotropic, homogeneous incompressible thermofluids presented by Surana et.al to… (more)

▼ The work presented here considers conservation and balance laws and constitutive theories for internal polar non-classical isotropic, homogeneous incompressible thermofluids presented by Surana et.al to present numerical studies and comparison with the results obtained using classical thermodynamic frame and standard constitutive theories. The internal polar continuum theories are based on the fact that if the velocity gradient tensor is a fundamental measure of deformation physics in fluids then the thermodynamic framework for such fluids must incorporate the velocity gradient tensor in its entirety. Polar decomposition of the velocity gradient tensor into stretch rates and the rotation rates shows that only the stretch rates are incorporated in the currently used thermodynamic framework and the rotation rates are completely neglected. If the velocity gradient tensor varies from a material point to the neighboring material points, then so do the rates of rotations which, when resisted by the fluid result in conjugate moment tensor. Rates of rotations and conjugate moment tensor can result in additional resistance to fluid motion and additional dissipation i.e. entropy production. Due to the fact that the internal polar non-classical continuum theory incorporates internal rotations and conjugate moment tensor, the theory is called internal polar non-classical continuum theory. The thermodynamic framework for internal polar thermofluids has been presented by Surana et.al. The constitutive theory for internal polar incompressible thermofluids has also been presented by Surana et.al. These are utilized in this work to present numerical studies for model problems. Boundary value problems consisting of fully developed flow between parallel plates, square and rectangular lid driven cavities and asymmetric sudden expansion with three different expansion ratios are used as model problems. Numerical solutions are computed using least squares finite element processes based on residual functional in which p-version hierarchical local approximations are considered in scalar product spaces that permit higher order global differentiability local approximations. Nonlinear algebraic equations resulting from the finite element formulation are solved using Newton’s linear method with line search. Numerical solutions obtained from internal polar mathematical models are compared with those obtained using classical continuum theory. Advisors/Committee Members: Surana, Karan S (advisor), TenPas, Peter W (cmtemember), Sorem, Robert M (cmtemember).

Subjects/Keywords: Mechanical engineering; Classical continuum theory; Constitutive theory; Continuum mechanics; Incompressible viscous fluids; Internal polar non-classical continuum theory

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APA (6^th Edition):

Khadka, D. (2016). Numerical Solutions of Boundary Value Problems for Incompressible Internal Polar Viscous Fluids. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/22350

Chicago Manual of Style (16^th Edition):

Khadka, Dipin. “Numerical Solutions of Boundary Value Problems for Incompressible Internal Polar Viscous Fluids.” 2016. Masters Thesis, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/22350.

MLA Handbook (7^th Edition):

Khadka, Dipin. “Numerical Solutions of Boundary Value Problems for Incompressible Internal Polar Viscous Fluids.” 2016. Web. 15 Jan 2021.

Vancouver:

Khadka D. Numerical Solutions of Boundary Value Problems for Incompressible Internal Polar Viscous Fluids. [Internet] [Masters thesis]. University of Kansas; 2016. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/22350.

Council of Science Editors:

Khadka D. Numerical Solutions of Boundary Value Problems for Incompressible Internal Polar Viscous Fluids. [Masters Thesis]. University of Kansas; 2016. Available from: http://hdl.handle.net/1808/22350

10. Kedari, Sayali Ravindra. Investigation of More Complete Constitutive Theories for Heat Conduction in Solids and for Deviatoric Stress Tensor in Incompressible Fluids.

Degree: MS, Mechanical Engineering, 2016, University of Kansas

URL: http://hdl.handle.net/1808/24136

► This thesis presents numerical studies utilizing more complete constitutive theories for: (i) Heat vector in isotropic, homogeneous, incompressible, elastic solid continua and (ii) Deviatoric stress… (more)

▼ This thesis presents numerical studies utilizing more complete constitutive theories for: (i) Heat vector in isotropic, homogeneous, incompressible, elastic solid continua and (ii) Deviatoric stress tensor for isotropic, homogeneous, incompressible, viscous fluids without memory. The derivation of the constitutive theories for heat vector in Lagrangian description for solid continua and for deviatoric stress tensor for incompressible fluent continua without memory in Eulerian description, using theory of generators and invariants, have been presented by Surana, Reddy, Eringen. These theories utilize integrity i.e. complete basis, hence are complete. A serious shortcoming of these theories is that they require too many material coefficients that must be determined experimentally. Due to the lack of availability of the material coefficients, these theories have not been used commonly in applications, instead their simplified forms requiring fewer material coefficients are currently being used. The purpose of this investigation is to study the influence of additional terms in the more complete constitutive theories derived using integrity that are routinely neglected to examine the influence of the additional physics that is introduced in the constitutive theories by their presence and their impact in applications. In specific, the first study focuses on constitutive theory for heat conduction in Lagrangian description for solid continua in which the argument tensors of heat vector are temperature gradient and temperature and the constitutive theory for heat vector is based on integrity and is derived using theory of generators and invariants. The second study considers incompressible, viscous fluids without memory in which the constitutive theory for the deviatoric Cauchy stress tensor is also based on theory of generators and invariants in which symmetric part of velocity gradient tensor and its square are combined generators of its argument tensors. 1D transient heat conduction in a rod, fully developed flow between parallel plates, square lid driven cavity and asymmetric expansion are used as model problems to illustrate the significance of the newer constitutive theories considered here. Advisors/Committee Members: Surana, Karan S. (advisor), TenPas, Peter W. (cmtemember), Sorem, Robert M. (cmtemember).

Subjects/Keywords: Mechanical engineering; Constitutive theory; Deviatoric Cauchy stress tensor; Heat vector; Thermoelastic Solids; Viscous Fluids without Memory

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APA (6^th Edition):

Kedari, S. R. (2016). Investigation of More Complete Constitutive Theories for Heat Conduction in Solids and for Deviatoric Stress Tensor in Incompressible Fluids. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/24136

Chicago Manual of Style (16^th Edition):

Kedari, Sayali Ravindra. “Investigation of More Complete Constitutive Theories for Heat Conduction in Solids and for Deviatoric Stress Tensor in Incompressible Fluids.” 2016. Masters Thesis, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/24136.

MLA Handbook (7^th Edition):

Kedari, Sayali Ravindra. “Investigation of More Complete Constitutive Theories for Heat Conduction in Solids and for Deviatoric Stress Tensor in Incompressible Fluids.” 2016. Web. 15 Jan 2021.

Vancouver:

Kedari SR. Investigation of More Complete Constitutive Theories for Heat Conduction in Solids and for Deviatoric Stress Tensor in Incompressible Fluids. [Internet] [Masters thesis]. University of Kansas; 2016. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/24136.

Council of Science Editors:

Kedari SR. Investigation of More Complete Constitutive Theories for Heat Conduction in Solids and for Deviatoric Stress Tensor in Incompressible Fluids. [Masters Thesis]. University of Kansas; 2016. Available from: http://hdl.handle.net/1808/24136

11. Joy, Aaron D. Mathematical Modeling and Numerical Simulation of Liquid-Solid and Solid-Liquid Phase Change.

Degree: MS, Mechanical Engineering, 2013, University of Kansas

URL: http://hdl.handle.net/1808/12181

► This thesis presents numerical simulations of liquid-solid and solid-liquid phase change processes using mathematical models in Lagrangian and Eulerian descriptions. The mathematical models are derived… (more)

▼ This thesis presents numerical simulations of liquid-solid and solid-liquid phase change processes using mathematical models in Lagrangian and Eulerian descriptions. The mathematical models are derived by assuming a smooth interface (or transition region) between the solid and liquid phases in which the specific heat, density, thermal conductivity, and latent heat of fusion are continuous and differentiable functions of temperature. In the derivations of the mathematical models we assume the matter to be homogeneous, isotropic, and incompressible in all phases. The change in volume due to change in density during phase transition is neglected in all mathematical models considered in this thesis. In one class of mathematical models we assume the velocity field to be zero i.e. no flow assumption, and free boundaries i.e. zero stress field. Under these assumptions the mathematical models reduce to first law of thermodynamics i.e. the energy equation, a nonlinear diffusion equation in temperature if we assume Fourier heat conduction law relating temperature gradient to the heat vector. These mathematical models are invariant of the type of description i.e. Lagrangian or Eulerian. In the second group it is shown that when the stress field and the velocity field are assumed nonzero in all three phases, then the resulting mathematical model from the conservation and balance laws in Lagrangian description for solid phase, Eulerian description for liquid phase, and mixed descriptions in the transition region are inadequate in describing the interaction between the media. Validity and usefulness of these models from the point of view of continuum mechanics as well as computational mathematics are considered and discussed. The third group of mathematical models are derived using conservation and balance laws with the assumption that stress field and velocity field are nonzero in the fluid region but are assumed zero in the solid region. In the transition zone the stress field and the velocity field transition from nonzero at the liquid state to zero at the solid state based on temperature in the transition zone. These models are consistent based on principles of continuum mechanics, hence provide correct interaction between the media and are shown to work well in the numerical simulations of phase transition applications with flow. Numerical solutions of the nonlinear diffusion equation in R1 and R2 resulting from the first group of models (zero stress and zero velocity field in all phases) and the nonlinear partial differential equations resulting from the third group of mathematical models are obtained using space-time hpk finite element processes based on spacetime residual functional in which the space-time integral forms are space-time variationally consistent, hence the resulting computations remain unconditionally stable during the entire evolution regardless of the choices of h, p, and k and the dimensionless parameters in the mathematical model. Numerical studies are presented in R1 and R2 for liquid-solid and… Advisors/Committee Members: Surana, Karan S. (advisor), TenPas, Peter W. (cmtemember), Sorem, Robert (cmtemember).

Subjects/Keywords: Mechanical engineering; Mechanics; Eulerian description; Lagrangian description; Phase change

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APA (6^th Edition):

Joy, A. D. (2013). Mathematical Modeling and Numerical Simulation of Liquid-Solid and Solid-Liquid Phase Change. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/12181

Chicago Manual of Style (16^th Edition):

Joy, Aaron D. “Mathematical Modeling and Numerical Simulation of Liquid-Solid and Solid-Liquid Phase Change.” 2013. Masters Thesis, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/12181.

MLA Handbook (7^th Edition):

Joy, Aaron D. “Mathematical Modeling and Numerical Simulation of Liquid-Solid and Solid-Liquid Phase Change.” 2013. Web. 15 Jan 2021.

Vancouver:

Joy AD. Mathematical Modeling and Numerical Simulation of Liquid-Solid and Solid-Liquid Phase Change. [Internet] [Masters thesis]. University of Kansas; 2013. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/12181.

Council of Science Editors:

Joy AD. Mathematical Modeling and Numerical Simulation of Liquid-Solid and Solid-Liquid Phase Change. [Masters Thesis]. University of Kansas; 2013. Available from: http://hdl.handle.net/1808/12181

12. Nunez, Daniel. Ordered Rate Constitutive Theories in Eulerian Description.

Degree: PhD, Mechanical Engineering, 2012, University of Kansas

URL: http://hdl.handle.net/1808/10627

► This research work presents development of ordered rate constitutive theories in Eulerian description for homogeneous, isotropic, compressible and incompressible matter experiencing finite deformation using contravariant,… (more)

▼ This research work presents development of ordered rate constitutive theories in Eulerian description for homogeneous, isotropic, compressible and incompressible matter experiencing finite deformation using contravariant, covariant and Jaumann bases. The constitutive theories presented here are applicable to thermoelastic solids, thermofluids and thermoviscoelastic fluids. Due to the inability to monitor material point displacements, and hence strain measures in Eulerian descriptions, the constitutive theories for Cauchy stress tensor utilizing strain measures in Eulerian description are not useful, hence the need for ordered rate constitutive theories presented in this work. Covariant, contravariant and Jaumann bases identify deformed material lines in the current configuration, thus these bases are possible choices for the development of constitutive theories. Covariant Cauchy stress tensor, contravariant Cauchy stress tensor and Jaumann stress tensor are measures of stress in these bases while Green's strain tensor, Almansi strain tensor and Jaumann strain tensor are conjugate measures of finite strain. Even though strain measures are not defined in Eulerian description, their convected time derivatives in their respective bases are defined. Thus, convected time derivatives of various orders of the Green's strain tensor in covariant basis, convected time derivatives of various orders of the Almansi strain tensor in contravariant basis and likewise, Jaumann strain tensor in Jaumann basis are defined and measurable in Eulerian description. These convected time derivatives in their respective bases are symmetric tensors of rank two and are fundamental kinematic tensors, and hence they can be utilized in the derivations of the constitutive theories for the Cauchy stress tensors in the chosen bases. In addition, we also have convected time derivatives of various orders of the contravariant Cauchy stress tensor in contravariant basis, convected time derivatives of various orders of the covariant Cauchy stress tensor in covariant basis and convected time derivatives of various orders of the Jaumann stress tensor in Jaumann basis. These are also fundamental symmetric tensors of rank two. The ordered rate constitutive theories presented in this work utilize convected time derivatives of upto orders n and m of the strain and stress tensors (i.e. rates) in their respective bases. Thus, there are many possibilities for various rate theories depending upon the choices of the dependent variables in the constitutive theories and their argument tensors. Specific choices of these are made to address specific physics. In this work we consider homogeneous, isotropic, compressible and incompressible matter with finite deformation, that is in thermodynamic equilibrium during evolution. Thus, conservation laws and thermodynamic principles provide the basis for deriving mathematical models and constitutive theories. Conservation of mass, balance of momenta and the first law of thermodynamics yielding continuity equation, momentum… Advisors/Committee Members: Surana, Karan S. (advisor), TenPas, Peter W. (cmtemember), Yimer, Bedru (cmtemember), Taghavi, Ray (cmtemember), Parr, David (cmtemember).

Subjects/Keywords: Mechanical engineering; Entropy inequality; Eulerian description; Giesekus model; Generators and invariants; Least squares processes; Rate constitutive theories

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Nunez, D. (2012). Ordered Rate Constitutive Theories in Eulerian Description. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/10627

Chicago Manual of Style (16^th Edition):

Nunez, Daniel. “Ordered Rate Constitutive Theories in Eulerian Description.” 2012. Doctoral Dissertation, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/10627.

MLA Handbook (7^th Edition):

Nunez, Daniel. “Ordered Rate Constitutive Theories in Eulerian Description.” 2012. Web. 15 Jan 2021.

Vancouver:

Nunez D. Ordered Rate Constitutive Theories in Eulerian Description. [Internet] [Doctoral dissertation]. University of Kansas; 2012. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/10627.

Council of Science Editors:

Nunez D. Ordered Rate Constitutive Theories in Eulerian Description. [Doctoral Dissertation]. University of Kansas; 2012. Available from: http://hdl.handle.net/1808/10627

13. Moody, Tristan. Ordered rate constitutive theories in Lagrangian description for thermoelastic solids and thermoviscoelastic solids with and without memory using Helmholtz free energy density.

Degree: PhD, Mechanical Engineering, 2013, University of Kansas

URL: http://hdl.handle.net/1808/11456

► The research work presented here considers development of constitutive theories in Lagrangian description for homogeneous, isotropic, compressible and incompressible thermoelastic solids, thermoviscoelastic solids without memory,… (more)

▼ The research work presented here considers development of constitutive theories in Lagrangian description for homogeneous, isotropic, compressible and incompressible thermoelastic solids, thermoviscoelastic solids without memory, and thermoviscoelastic solids with memory. Since conservation of mass, balance of momenta, and the first law of thermodynamics assume the existence of a stress field and heat vector without regard to how they are arrived at, the constitutive theories for the stress field and heat vector must be derived using the second law of thermodynamics to ensure thermodynamic equilibrium in the deforming matter during evolution. In the present work, we use the entropy inequality resulting from the second law of thermodynamics expressed in terms of the Helmholtz free energy density φ. The initial choice of dependent variables is directly from the entropy inequality: φ, second Piola-Kirchhoff stress tensor σ[0], entropy density η, and heat vector q. The argument tensors are established based on desired physics, i.e., choices are made depending on whether the solid matter is thermoelastic, thermoviscoelastic without memory, or thermoviscoelastic with memory. The use of the entropy inequality with the desired choices of argument tensors of the dependent variables allows us to determine the final choice of dependent variables in the constitutive theories as φ, σ[0], and q as well as their argument tensors (depending on the desired physics). In the case of thermoelastic solids, the entropy inequality provides conditions from which the constitutive theories for σ[0] and q can be derived. For thermoviscoelastic solids with and without memory, the conditions resulting from the entropy inequality do not permit derivation of a constitutive theory for σ[0]. Using a decomposition of σ[0] into eσ[0] and dσ[0] (equilibrium and deviatoric second Piola-Kirchhoff stress tensors), the constitutive theories for eσ[0] can be derived using the conditions resulting from the entropy inequality. However, the entropy inequality provides no mechanism to derive constitutive theories for dσ[0]. In the present work, we use the theory of generators and invariants to derive constitutive theories for dσ[0]. The constitutive theories for \heat consistent with σ[0] or dσ[0] in the sense of argument tensors are also derived using the theory of generators and invariants. It is shown that for thermoelastic solids, the constitutive theory for σ[0] and q are of rate zero in the Green's strain tensor ε (ε[0]), the constitutive theories for thermoviscoelastic solids without memory for dσ[0] and q are up to orders n in the Green's strain tensor, and the constitutive theories for thermoviscoelastic solids with memory for dσ[0] and q are of orders m and n in the second Piola-Kirchhoff stress tensor and Green's strain tensor. Many simplified forms of the rate theories are presented and compared with those used currently to demonstrate the merits of this research and severe limitations and shortcomings of the constitutive theories used currently for… Advisors/Committee Members: Surana, Karan S. (advisor), TenPas, Peter W. (cmtemember), Yimer, Bedru (cmtemember), Taghavi, Ray (cmtemember), Parr, Alfred D (cmtemember).

Subjects/Keywords: Mechanical engineering; Constitutive theory; Continuum mechanics; Lagrangian description; Theory of generators and invariants; Viscoelastic solid

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APA (6^th Edition):

Moody, T. (2013). Ordered rate constitutive theories in Lagrangian description for thermoelastic solids and thermoviscoelastic solids with and without memory using Helmholtz free energy density. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/11456

Chicago Manual of Style (16^th Edition):

Moody, Tristan. “Ordered rate constitutive theories in Lagrangian description for thermoelastic solids and thermoviscoelastic solids with and without memory using Helmholtz free energy density.” 2013. Doctoral Dissertation, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/11456.

MLA Handbook (7^th Edition):

Moody, Tristan. “Ordered rate constitutive theories in Lagrangian description for thermoelastic solids and thermoviscoelastic solids with and without memory using Helmholtz free energy density.” 2013. Web. 15 Jan 2021.

Vancouver:

Moody T. Ordered rate constitutive theories in Lagrangian description for thermoelastic solids and thermoviscoelastic solids with and without memory using Helmholtz free energy density. [Internet] [Doctoral dissertation]. University of Kansas; 2013. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/11456.

Council of Science Editors:

Moody T. Ordered rate constitutive theories in Lagrangian description for thermoelastic solids and thermoviscoelastic solids with and without memory using Helmholtz free energy density. [Doctoral Dissertation]. University of Kansas; 2013. Available from: http://hdl.handle.net/1808/11456

University of Kansas

14. Truex, Michael. Numerical Simulation of Liquid-Solid, Solid-Liquid Phase Change Using Finite Element Method in h,p,k Framework with Space-Time Variationally Consistent Integral Forms.

Degree: MS, Mechanical Engineering, 2010, University of Kansas

URL: http://hdl.handle.net/1808/6956

► This thesis presents development of mathematical models for liquid-solid phase change phenomena using Lagrangian description with continuous and differentiable smooth interface (transition region) between the… (more)

▼ This thesis presents development of mathematical models for liquid-solid phase change phenomena using Lagrangian description with continuous and differentiable smooth interface (transition region) between the solid and the liquid phases in which specific heat, thermal conductivity, and latent heat of fusion are a function of temperature. The width of the interface region can be as small or as large as desired in specific applications. The mathematical models presented in the thesis assume homogeneous and isotropic medium, zero velocity field (no flow) with free boundaries i.e. stress free domain. With these assumptions the mathematical model reduces to the first law of thermodynamics i.e. energy equation. The mathematical models presented here are neither labeled as enthalpy models or others, instead these are based on a simple statement of the first law of thermodynamics using specific total energy and heat vector augmented by the constitutive equation for heat vector i.e. Fourier heat conduction law and the statement of total specific energy incorporating the physics of phase change in the smooth interface region between solid and liquid phases. This results in a time dependent non-linear convection diffusion in temperature in which physics of interface initiation and propagation is intrinsic and thus avoids front tracking methods. This can also be cast as a system of first order PDEs using auxiliary variables and auxiliary equations if so desired due to the use of specific methods of approximation as done in the present work. The numerical solutions of the initial value problems resulting from the mathematical models are obtained using space-time least squares finite element process based on minimization of the residual functional. This results in space-time variationally consistent integral forms that yield symmetric algebraic systems with positive definite coefficient matrices that ensure unconditionally stable computations during the entire evolution. The local approximations for the space-time finite elements are considered in h,p,k framework which permits higher degree as well as higher order local approximations in space and time. Computations of the evolution are performed using a space-time strip or slab corresponding to an increment of time with time marching procedure. 1D numerical studies are presented and the results are compared with sharp interface and phase field methods. Numerical studies also presented for 1D and 2D model problems in which initiation as well as propagation of the interface is demonstrated. These studies cannot be performed using sharp interface and phase field models. The significant aspects of the present work are: (i) the smooth interface permits desired physics and avoids singular fronts that are non physical (ii) the mathematical model resulting from the present approach is a non-linear diffusion equation, hence intrinsically containing the ability to initiate as well as locate the front during evolution and hence no special front tracking methods are needed. (iii) This… Advisors/Committee Members: Surana, Karan S. (advisor), Romkes, Albert (cmtemember), TenPas, Peter W. (cmtemember), Yimer, Bedru (cmtemember).

Subjects/Keywords: Mechanical engineering; Mathematics; Physics; Finite element; Ivp; Phase change

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APA (6^th Edition):

Truex, M. (2010). Numerical Simulation of Liquid-Solid, Solid-Liquid Phase Change Using Finite Element Method in h,p,k Framework with Space-Time Variationally Consistent Integral Forms. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/6956

Chicago Manual of Style (16^th Edition):

Truex, Michael. “Numerical Simulation of Liquid-Solid, Solid-Liquid Phase Change Using Finite Element Method in h,p,k Framework with Space-Time Variationally Consistent Integral Forms.” 2010. Masters Thesis, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/6956.

MLA Handbook (7^th Edition):

Truex, Michael. “Numerical Simulation of Liquid-Solid, Solid-Liquid Phase Change Using Finite Element Method in h,p,k Framework with Space-Time Variationally Consistent Integral Forms.” 2010. Web. 15 Jan 2021.

Vancouver:

Truex M. Numerical Simulation of Liquid-Solid, Solid-Liquid Phase Change Using Finite Element Method in h,p,k Framework with Space-Time Variationally Consistent Integral Forms. [Internet] [Masters thesis]. University of Kansas; 2010. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/6956.

Council of Science Editors:

Truex M. Numerical Simulation of Liquid-Solid, Solid-Liquid Phase Change Using Finite Element Method in h,p,k Framework with Space-Time Variationally Consistent Integral Forms. [Masters Thesis]. University of Kansas; 2010. Available from: http://hdl.handle.net/1808/6956

University of Kansas

15. Nunez, Daniel. J-integral Computations for Linear Elastic Fracture Mechanics in h,p,k Mathematical and Computational Framework.

Degree: MS, Aerospace Engineering, 2008, University of Kansas

URL: http://hdl.handle.net/1808/4045

► This thesis presents an infrastructure for computations of the J-integral for mode I linear elastic fracture mechanics in h,p,k mathematical and computational framework using finite… (more)

▼ This thesis presents an infrastructure for computations of the J-integral for mode I linear elastic fracture mechanics in h,p,k mathematical and computational framework using finite element formulations based on the Galerkin method with weak form and the least squares process. Since the differential operators in this case are self-adjoint, both the Galerkin method with weak form and the least square processes yield unconditionally stable computational processes. The use of h,p,k frameworks permits higher order global differentiability approximations in the finite element processes which are necessitated by physics, calculus of continuous and differentiable functions and higher order global differentiability features of the theoretical solutions. The significant aspect of this research is that with the proposed methodology very accurate J-integral computations are possible for all paths including those in very close proximity of the crack without use of special crack tip or quarter point elements at the crack tip. A center crack panel under isotropic homogeneous plane strain linear elastic behavior, subjected to uniaxial tension (mode I) is used as model problem for all numerical studies. The investigations presented in this thesis are summarized here: (i) J-integral expression is derived and it is shown that its path independence requires the governing differential equations (GDEs) to be satisfied in the numerical process used for its computations (ii) It has been shown that the J-integral path must be continuous and differentiable (iii) The integrand in the J-integral must be continuous along the path as well as normal to the path (iv) Influence of the higher order global differentiability approximations on the accuracy of the J-integral is demonstrated (v) Stress intensity correction factors are computed and compared with published data. The work presented here is a straight-forward finite element methodology in h,p,k framework is presented in which all mathematical requirements for J-integral computations are satisfied in the computational process and as a result very accurate computations of J-integral are possible for any path surrounding the crack tip without using any special treatments. Both the Galerkin method with weak form and the least square processes perform equally well. Advisors/Committee Members: Surana, Karan S. (advisor), Ewing, Mark (advisor), Taghavi, Ray (cmtemember), Hale, Richard (cmtemember).

Subjects/Keywords: Aerospace engineering; Mechanical engineering; J-integral; Galerkin method with weak form; Least squares processes; Linear elastic fracture mechanics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Nunez, D. (2008). J-integral Computations for Linear Elastic Fracture Mechanics in h,p,k Mathematical and Computational Framework. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/4045

Chicago Manual of Style (16^th Edition):

Nunez, Daniel. “J-integral Computations for Linear Elastic Fracture Mechanics in h,p,k Mathematical and Computational Framework.” 2008. Masters Thesis, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/4045.

MLA Handbook (7^th Edition):

Nunez, Daniel. “J-integral Computations for Linear Elastic Fracture Mechanics in h,p,k Mathematical and Computational Framework.” 2008. Web. 15 Jan 2021.

Vancouver:

Nunez D. J-integral Computations for Linear Elastic Fracture Mechanics in h,p,k Mathematical and Computational Framework. [Internet] [Masters thesis]. University of Kansas; 2008. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/4045.

Council of Science Editors:

Nunez D. J-integral Computations for Linear Elastic Fracture Mechanics in h,p,k Mathematical and Computational Framework. [Masters Thesis]. University of Kansas; 2008. Available from: http://hdl.handle.net/1808/4045

University of Kansas

16. Maduri, Rajesh Kumar. Higher order global differentiability local approximations for 2-D and 3-D distorted element geometries.

Degree: PH.D., Mechanical Engineering, 2008, University of Kansas

URL: http://hdl.handle.net/1808/4006

► The primary focus of this thesis is to present a framework to develop higher order global differentiability local approximations for 2-D and 3-D distorted element… (more)

▼ The primary focus of this thesis is to present a framework to develop higher order global differentiability local approximations for 2-D and 3-D distorted element geometries. The necessity and superiority of higher order global differentiability approximations in designing finite element computational processes has been demonstrated by Surana and co-workers [1-4]. It has been shown by Surana et al. [5] that when the element geometry is rectangular, higher order global differentiability approximations can be easily derived using tensor product of 1-D higher order continuity approximations. When the element geometries are distorted, the tensor product approach cannot be utilized in deriving these approximation functions. This thesis presents a systematic procedure for deriving desired order global differentiability approximations for 2-D and 3-D elements of distorted geometries. The curved element in 2-D or 3-D physical coordinate space is mapped to a master element in 2-D or 3-D natural coordinate space. The master elements considered for 2-D quadrilateral, 2-D triangular and 3-D hexahedral elements are a 2 unit square, a 2 unit equilateral triangle and a 2 unit cube respectively. For the master element, 2-D C00 or 3-D C000 p-version local approximations are considered and appropriate degrees of freedom and the corresponding approximation functions from appropriate nodes are borrowed to derive the higher order approximations and the corresponding derivative degrees of freedom at the corner nodes. These degrees of freedom can be transformed from natural coordinate space to the physical coordinate space by using Jacobians of transformations for the derivatives of various orders. The choice of these degrees of freedom and the corresponding functions being borrowed in deriving these desired functions for the derivative dofs is not arbitrary and must be made in such a way that all lower degree admissible functions and the corresponding dofs are borrowed before considering the higher degree functions and the corresponding dofs. Pascal's rectangle, Pascal's triangle and Pascal's pyramid provide a systematic selection process for accomplishing this selection process for 2-D quadrilateral, 2-D triangular and 3-D hexahedral geometries respectively. Numerical studies are presented to illustrate the behavior and performance of the approximations developed. The applicability of the developed approximation functions to all physical problems is demonstrated by solving model problems which are described by self-adjoint, non self-adjoint and non-linear differential operators. In all cases, various finite element quantities of interest (error or residual functional, error norms) are computed and a study of their convergence rates with h, p and k refinement is made. Advisors/Committee Members: Surana, Karan S. (advisor), TenPas, Peter W. (cmtemember), Sorem, Robert (cmtemember), Taghavi, Ray (cmtemember), Romkes, Albert (cmtemember).

Subjects/Keywords: Mechanical engineering; Finite element method; Higher order global differentiability; Hpk framework; Distorted elements

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Maduri, R. K. (2008). Higher order global differentiability local approximations for 2-D and 3-D distorted element geometries. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/4006

Chicago Manual of Style (16^th Edition):

Maduri, Rajesh Kumar. “Higher order global differentiability local approximations for 2-D and 3-D distorted element geometries.” 2008. Doctoral Dissertation, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/4006.

MLA Handbook (7^th Edition):

Maduri, Rajesh Kumar. “Higher order global differentiability local approximations for 2-D and 3-D distorted element geometries.” 2008. Web. 15 Jan 2021.

Vancouver:

Maduri RK. Higher order global differentiability local approximations for 2-D and 3-D distorted element geometries. [Internet] [Doctoral dissertation]. University of Kansas; 2008. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/4006.

Council of Science Editors:

Maduri RK. Higher order global differentiability local approximations for 2-D and 3-D distorted element geometries. [Doctoral Dissertation]. University of Kansas; 2008. Available from: http://hdl.handle.net/1808/4006

University of Kansas

17. Allu, Srikanth. Computations of Viscous Compressible Flows in h, p, k Finite Element Framework with Variationally Consistent Integral Forms.

Degree: PH.D., Mechanical Engineering, 2008, University of Kansas

URL: http://hdl.handle.net/1808/3943

► This thesis presents mathematical models for time dependent and stationary viscous compressible flows based on conservation laws, constitutive equations and equations of state using Eulerian… (more)

▼ This thesis presents mathematical models for time dependent and stationary viscous compressible flows based on conservation laws, constitutive equations and equations of state using Eulerian description. In the presence of physical viscosity, conductivity and other transport properties, the mathematical models are well recognized Navier-Stokes equations. Variable transport properties as well as ideal and real gas models are considered for equations of state. The mathematical models are a highly non-linear coupled partial differential equations in space and time. The mathematical and computational infrastructure using finite element method is presented for obtaining numerical solutions of the Boundary Value Problems and Initial Value Problems associated with the mathematical models. This infrastructure is based on h, p, k (h-characteristic length, p-degree of local approximation, k-order of approximation space) as independent computational parameters with an additional requirement that the integral form be variationally consistent in case of Boundary Value Problems and space-time variationally consistent in case of Initial Value Problems. All methods of approximation except Least Squares and Space-Time Least Squares Processes are Variationally Inconsistent. Variational Consistency and Space-Time Variational Consistency of integral forms ensure unconditionally stable computational processes. A variety of numerical studies are presented for Initial Value Problems as well as Boundary Value Problems. 1-D transient viscous form of Burgers equation, 1-D Riemann shock tube with ideal and real gas models and Boundary Value Problems in 2-D compressible flow : Carter's plate with Mach 1, 2, 3 and 5 flows and Mach 1 flow past a circular cylinder are used as model problems. Shock evolution, propagation, interactions and reflection are quantified based on the rate of entropy production using Air as a medium for 1-D Riemann shock tube. It is clearly established that rarefaction shocks are not possible for FC70 for any choice of initial conditions. In all studies evolution of a shock is presented (unlike the published work). Its existence and sustained propagation is established based on Sr, the rate of entropy production per unit volume. In case of transient Burgers equation it is demonstrated that time accurate evolutions can be computed for any finite Reynolds number. Contrary to the common belief, the work presented here shows that solutions of Boundary Value Problems in compressible flows present no special problems. In Summary : (i) the mathematical models for the compressible flow are based on Navier-Stokes equations. (ii) computational infrastructure is based on hpk and unconditionally stable integral forms with higher order global differentiability in space and time. (iii) All numerical studies utilize actual transport properties of the medium. (iv) Up-winding methods such as SUPG, SUPG/DC, SUPG/DC/LS are neither needed nor used. (v) existence of shocks is established through evolution and not using Rankine-Hugoniot… Advisors/Committee Members: Surana, Karan S. (advisor), TenPas, Peter W. (cmtemember), Yimer, Bedru (cmtemember), Romkes, Albert (cmtemember), Taghavi, Ray (cmtemember).

Subjects/Keywords: Mechanical engineering; Applied mechanics; Finite element method; Variational consistency; Viscous compressible flows; Gas dynamics; H, p, k framework; K-version of finite element method

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Allu, S. (2008). Computations of Viscous Compressible Flows in h, p, k Finite Element Framework with Variationally Consistent Integral Forms. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/3943

Chicago Manual of Style (16^th Edition):

Allu, Srikanth. “Computations of Viscous Compressible Flows in h, p, k Finite Element Framework with Variationally Consistent Integral Forms.” 2008. Doctoral Dissertation, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/3943.

MLA Handbook (7^th Edition):

Allu, Srikanth. “Computations of Viscous Compressible Flows in h, p, k Finite Element Framework with Variationally Consistent Integral Forms.” 2008. Web. 15 Jan 2021.

Vancouver:

Allu S. Computations of Viscous Compressible Flows in h, p, k Finite Element Framework with Variationally Consistent Integral Forms. [Internet] [Doctoral dissertation]. University of Kansas; 2008. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/3943.

Council of Science Editors:

Allu S. Computations of Viscous Compressible Flows in h, p, k Finite Element Framework with Variationally Consistent Integral Forms. [Doctoral Dissertation]. University of Kansas; 2008. Available from: http://hdl.handle.net/1808/3943

University of Kansas

18. Basaran, Salahi. Lagrangian and Eulerian Descriptions in Solid Mechanics and Their Numerical Solutions in hpk Framework.

Degree: PH.D., Mechanical Engineering, 2008, University of Kansas

URL: http://hdl.handle.net/1808/3946

► In this thesis mathematical models for a deforming solid medium are derived using conservation laws in Lagrangian as well as Eulerian descriptions. First, most general… (more)

Subjects/Keywords: Mechanical engineering; Finite element; Hpk; Eulerian; Solid mechanics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Basaran, S. (2008). Lagrangian and Eulerian Descriptions in Solid Mechanics and Their Numerical Solutions in hpk Framework. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/3946

Chicago Manual of Style (16^th Edition):

Basaran, Salahi. “Lagrangian and Eulerian Descriptions in Solid Mechanics and Their Numerical Solutions in hpk Framework.” 2008. Doctoral Dissertation, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/3946.

MLA Handbook (7^th Edition):

Basaran, Salahi. “Lagrangian and Eulerian Descriptions in Solid Mechanics and Their Numerical Solutions in hpk Framework.” 2008. Web. 15 Jan 2021.

Vancouver:

Basaran S. Lagrangian and Eulerian Descriptions in Solid Mechanics and Their Numerical Solutions in hpk Framework. [Internet] [Doctoral dissertation]. University of Kansas; 2008. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/3946.

Council of Science Editors:

Basaran S. Lagrangian and Eulerian Descriptions in Solid Mechanics and Their Numerical Solutions in hpk Framework. [Doctoral Dissertation]. University of Kansas; 2008. Available from: http://hdl.handle.net/1808/3946

University of Kansas

19. Deshpande, Kedar M. k - Version of Finite Element Method for Polymer flows using Giesekus Constitutive Model.

Degree: PH.D., Mechanical Engineering, 2008, University of Kansas

URL: http://hdl.handle.net/1808/4039

► One of the fundamental differences in the polymer flows compared to Newtonian or generalized Newtonian flow is the presence of elasticity due to polymer in… (more)

▼ One of the fundamental differences in the polymer flows compared to Newtonian or generalized Newtonian flow is the presence of elasticity due to polymer in addition to the viscosities of the solvent and the polymer. While for Newtonian and generalized Newtonian fluids viscous stresses are explicitly defined in terms of strain rates and transport properties, and thus can be completely eliminated from the governing differential equations (GDEs) by their substitution in the momentum and energy equations. This however is not possible in the case of polymer flows. The mathematical models for polymer flows are derived using conservation laws in which many different choices of stresses as dependent variables are possible. In the published works it is generally accepted that GDEs in elastic stresses are meritorious in Galerkin method with weak form over other choices. However, regardless of the choices of stresses the GDEs always remain non-linear and hence, the Galerkin method with weak form yields variationally inconsistent integral forms for all possible choices of the stresses. Thus, one of the investigation in this study is to show the influence of the choices of stresses in the mathematical models on the computational processes when the integral forms are variationally consistent (VC). Another significant issue in polymer flows is the issue of numerical solutions for higher Deborah numbers. For a given fluid and a given geometric configuration the choices of length ( Lo ) and relaxation time are generally fixed and hence high Deborah number flows are invariably associated with higher flow rates and thus higher velocities. In many standard model problems such as couette flow, lid driven cavity, expansion, contraction etc, severe deborah number (De) limitations are reported in the computational processes based on Galerkin method with weak form while there appears to be no such apparent limitation in the constitutive model such as Giesekus model. In this work we investigate if such Deborah number limitations exist in hpk framework or are such limitations a consequence of VIC integral form and C0 local approximations. The work presented here considers boundary value problems ( BVPs ) as well as initial value problems ( IVPs ) using Giesekus constitutive model. For BVPs, numerical studies are presented for (i) One dimensional fully developed flow between parallel plates (ii)developing flow between parallel plates and (iii) lid driven square cavity. In case of one dimensional fully developed flow solutions are reported for Deborah numbers up to 6514.52 and there does not seem to be any limit of deborah number in 'hpk' framework. Solutions are reported for developing flow between parallel plates upto deborah number of 20.13. Excellent agreement is obtained between for one dimensional fully developed flow between parallel plates and developing flow between parallel plates. For lid driven square cavity, mathematical idealization of the physics at the corners where stationary walls intersect the lid is presented. It is shown… Advisors/Committee Members: Surana, Karan S. (advisor), TenPas, Peter W. (cmtemember), Taghavi, Ray (cmtemember), Sorem, Robert (cmtemember), Romkes, Albert (cmtemember).

Subjects/Keywords: Mechanical engineering; K-version; Finite element method; Polymer flows; Giesekus

Record Details Similar Records Cite « Share

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Deshpande, K. M. (2008). k - Version of Finite Element Method for Polymer flows using Giesekus Constitutive Model. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/4039

Chicago Manual of Style (16^th Edition):

Deshpande, Kedar M. “k - Version of Finite Element Method for Polymer flows using Giesekus Constitutive Model.” 2008. Doctoral Dissertation, University of Kansas. Accessed January 15, 2021. http://hdl.handle.net/1808/4039.

MLA Handbook (7^th Edition):

Deshpande, Kedar M. “k - Version of Finite Element Method for Polymer flows using Giesekus Constitutive Model.” 2008. Web. 15 Jan 2021.

Vancouver:

Deshpande KM. k - Version of Finite Element Method for Polymer flows using Giesekus Constitutive Model. [Internet] [Doctoral dissertation]. University of Kansas; 2008. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1808/4039.

Council of Science Editors:

Deshpande KM. k - Version of Finite Element Method for Polymer flows using Giesekus Constitutive Model. [Doctoral Dissertation]. University of Kansas; 2008. Available from: http://hdl.handle.net/1808/4039

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