Thermo-Plastic Materials with Memory

A theory of thermoplastically simple materials with memory is developed. The response functionals are assumed to depend on the histories of the strain tensor, inelastic strain tensor, temperature, θ, and the current value of the temperature gradient. Thermodynamical restrictions on the forms of the constitutive equations are explored, and it is shown that the stress tensor and specific entropy are derivable from the free energy functional which is independent of temperature gradient. It is also shown that the internal dissipation can be computed directly from the free energy and the constitutive equation for the inelastic strain rate. Under additional restrictions, special forms of the constitutive equations are developed. Furthermore, the present theory does not make use of the idea of yield functions. Examples are included.