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You searched for subject:(Classical continuum theory). Showing records 1 – 3 of 3 total matches.

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Texas A&M University

1. Powell, Michael Joseph. Internal Polar Continuum Theories for Solid and Fluent Continua.

Degree: PhD, Civil Engineering, 2016, Texas A&M University

Classical continuum theories are useful in the study of a variety of problems of engineering and applied sciences. However, the emergence of new materials has provided the need for refined theories that account for certain features that are not accounted for in the classical continuum theories. Polar decomposition of the deformation gradient tensor into pure stretch and pure rotation tensors shows that the rotation tensor will in general vary from point to point. Similarly, polar decomposition of the velocity gradient tensor shows that the rate of rotation tensor will vary from point to point. It can also be shown that the strain and strain rate tensors used in classical theories of continuum mechanics do not depend on the rotation tensor or its gradients and therefore neglect the effect of changing rotations and rates of rotations between neighboring material points in Lagrangian description, and between neighboring locations in Eulerian description. Varying rotations and rates of rotations between neighboring material points will, if resisted by the continua, result in internal moments which are conjugate to these rotations and rates of rotations. These internal moments along with the conjugate rotations and rates of rotations will result in energy storage and dissipation, in addition to the energy storage and dissipation resulting from stress and its conjugate strain and strain rate. Based on this observation, it is necessary to modify the existing conservation and balance laws to include internal moments, which results in a more complete thermodynamic framework for solid and fluent continua. In this work, new conservation and balance laws are derived for solid and fluent continua that include internal moments which result from varying rotations and rotation rates. Also, constitutive theories are derived for the stress tensor, moment tensor, and heat vector, resulting in a complete mathematical model internal polar thermoelastic solids and internal polar thermoviscous fluids. This derivation does not rely on the introduction of external micro-rotations or stress couples as is done in the so called micro-polar or couple-stress theories. The theories presented here are therefore referred to as “internal polar continuum theories”, as they are derived using only internal measures of deformation and do not require introduction of external degrees of freedom. We also present a framework for obtaining approximate solutions to the mathematical models resulting from the new continuum theories. Numeric results are presented to show the affect of the internal polar theories presented here. Advisors/Committee Members: Reddy, JN (advisor), Fry, Gary (committee member), Hueste, Mary Beth (committee member), Hogan, Harry (committee member).

Subjects/Keywords: Continuum Mechanics; Non-classical continuum mechanics; polar theory; rotations; rates of rotations

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APA (6th Edition):

Powell, M. J. (2016). Internal Polar Continuum Theories for Solid and Fluent Continua. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/159102

Chicago Manual of Style (16th Edition):

Powell, Michael Joseph. “Internal Polar Continuum Theories for Solid and Fluent Continua.” 2016. Doctoral Dissertation, Texas A&M University. Accessed January 15, 2021. http://hdl.handle.net/1969.1/159102.

MLA Handbook (7th Edition):

Powell, Michael Joseph. “Internal Polar Continuum Theories for Solid and Fluent Continua.” 2016. Web. 15 Jan 2021.

Vancouver:

Powell MJ. Internal Polar Continuum Theories for Solid and Fluent Continua. [Internet] [Doctoral dissertation]. Texas A&M University; 2016. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/1969.1/159102.

Council of Science Editors:

Powell MJ. Internal Polar Continuum Theories for Solid and Fluent Continua. [Doctoral Dissertation]. Texas A&M University; 2016. Available from: http://hdl.handle.net/1969.1/159102

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

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

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

classical continuum theory obviously are different than the classical continuum framework for… …obtained using the mathematical models based on classical continuum theory. The intent is to… …model for internal polar non-classical continuum theory described by (2.11)… …incompressible viscous fluid in R2 based on classical continuum theory This mathematical model… …following mathematical model based on classical continuum theory for fully developed flow between… 

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

APA (6th 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 (16th 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 (7th 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

3. Motevaselian, Mohammad Hossein. A multiscale theory to determine thermodynamic properties of confined fluids.

Degree: MS, Mechanical Engineering, 2015, University of Illinois – Urbana-Champaign

Empirical potential-based quasi-continuum theory (EQT) provides a route to incorporate atomistic detail into a continuum framework such as the Nernst- Planck equation. EQT is a simple and fast approach to predict inhomogeneous density and potential profiles of confined fluids. EQT potentials can be used to construct a grand potential functional for classical density functional theory (cDFT). The combination of EQT and cDFT provides a robust and accurate approach to predict the structure and thermodynamic properties of confined fluids at multiple length-scales, ranging from few Angstroms to macro meters. In this work, first, we demonstrate the EQT-cDFT approach by simulating sin- gle component Lennard-Jones (LJ) fluids, namely, methane and argon, confined inside slit-like channels of graphene. For these systems, we show that the EQT- cDFT can accurately predict the structure and thermodynamic properties, such as density profiles, adsorption, local pressure tensor, surface tension, and solva- tion force of confined fluids as compared to the MD simulation results. Next, we extend the EQT-cDFT approach to confined fluid mixtures and demonstrate it by simulating a mixture of methane and hydrogen inside slit-like channels of graphene. We show that the EQT-cDFT predictions for the structure of the confined fluid mixture compare well with the MD simulations results. In addi- tion, our results show that graphene slit nanopores exhibit a selective adsorption of methane over hydrogen. Advisors/Committee Members: Aluru, Narayana R. (advisor).

Subjects/Keywords: confined nanofluids; Empirical potential-based quasi-continuum theory (EQT); classical density functional theory (cDFT); molecular dynamics (MD); confined mixture; thermodynamic properties

…fluid-solid in- 2 terfaces, classical continuum descriptions fail to accurately capture… …is not only as accurate as molecular simulations, but also as fast as classical continuum… …classical density functional theory (cDFT) in order to obtain thermodynamic properties… …POTENTIAL-BASED MULTISCALE THEORY 3.1 Empirical Potential-Based Quasi-Continuum Theory (EQT… …x29; An empirical potential-based quasi-continuum theory (EQT) is a multiscale… 

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

APA (6th Edition):

Motevaselian, M. H. (2015). A multiscale theory to determine thermodynamic properties of confined fluids. (Thesis). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/88082

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Motevaselian, Mohammad Hossein. “A multiscale theory to determine thermodynamic properties of confined fluids.” 2015. Thesis, University of Illinois – Urbana-Champaign. Accessed January 15, 2021. http://hdl.handle.net/2142/88082.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Motevaselian, Mohammad Hossein. “A multiscale theory to determine thermodynamic properties of confined fluids.” 2015. Web. 15 Jan 2021.

Vancouver:

Motevaselian MH. A multiscale theory to determine thermodynamic properties of confined fluids. [Internet] [Thesis]. University of Illinois – Urbana-Champaign; 2015. [cited 2021 Jan 15]. Available from: http://hdl.handle.net/2142/88082.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Motevaselian MH. A multiscale theory to determine thermodynamic properties of confined fluids. [Thesis]. University of Illinois – Urbana-Champaign; 2015. Available from: http://hdl.handle.net/2142/88082

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.