Date of Award

5-2010

Embargo Period

1-27-2012

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

Advisor(s)

Walter Noll

Second Advisor

Juan Schaffer

Third Advisor

David Owen

Fourth Advisor

Eliot Fried

Abstract

The principle of material frame-indifference is a fundamental concept in classical physics. In 1972 Walter Noll showed that one can formulate constitutive laws without using any external frames of reference. Constitutive laws formulated in this way vacuously satisfy the principle of material frame-indifference. This thesis describes the basic concepts involved in formulating frame-free continuum thermomechanics and presents a framework for formulating constitutive laws for simple materials that take into account thermal effects. The restrictions coming from the second law of thermodynamics on the constitutive laws for materials with fading memory are found using the Coleman{Noll procedure. Also, it is shown that materials with fading memory, when subjected to slow processes, can be approximated by what I call thermoelasto-viscous materials, which are also studied in detail.

Included in

Mathematics Commons

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