Frame-Free Continuum Thermomechanics

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.