Crystalline Materials with Thermo-inelastic Memory

The objective of this chapter is to consider a relation between inelastic materials with internal variables and damaged inelastic materials with memory. If an evolution equation for plastic strain rate is given for the first class of materials, then its integration leads to the description represented by integrals whose kernels are responsible for the plastic memory. Here the opposite and more difficult way is taken: to see how functionals appearing in a description of damaged inelastic materials with memory may be transformed into the corresponding evolution equations.

For a correct constitutive theory a geometric description, able to describe properly the most important microstructural changes during an inelastic deformation process, is indispensable. Here only slight amendments to considerations of the first chapter are made, whereas the last section of this chapter is reserved for formulation of the theory.