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1.
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 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

…configuration
ix
Chapter 1
Introduction
For homogeneous and isotropic *thermoelastic* *solids*… …Gibbs potential, then the constitutive theories for *thermoelastic* *solids* result in strain… …theories for homogeneous, isotropic *thermoelastic*
*solids* experiencing finite deformation using… …homogeneous, isotropic *thermoelastic* *solids* undergoing finite deformations based on the second law… …possible choice of dependent variables in the
constitutive theories. For *thermoelastic* *solids*…

Record Details Similar Records

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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

2.
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 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

…*Thermoelastic* *Solids*
2.1
Introduction
The classical Fourier heat conduction law [5–7] used… …thermal conductivity. For *thermoelastic* *solids* that are continuous media, the Fourier heat… …constitutive theories. In case of
*thermoelastic* *solids*, the entropy inequality expressed in terms of… …List of Figures
2.1
Schematic of 1-D heat conduction in a *thermoelastic* solid… …Schematic of 1-D heat conduction in a *thermoelastic* solid . . . . . . . . . . . . . 14
2.13…

Record Details Similar Records

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

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