Equivalence principles in continuum damage mechanics

In this paper, as usual in continuum damage mechanics, an effective continuum is introduced, but this continuum is here considered as an auxiliary body. The main purpose is then to connect together these two materials for a possible comparison, i.e. to propose geometrical and mechanical constraints between these materials. In this paper, we recall briefly the three-terms multiplicative decomposition of the deformation gradient by using a natural geometrical constraint, and we propose a new theoretical method available for obtaining mechanical constraints between the two materials. The proposed approach is then applied to generalize the hypothesis of strain equivalence and the hypothesis of energy equivalence. In this approach, new equivalence principles are obtained, and a new mechanical constraint based on reciprocity is analysed. This paper is restricted to mechanical processes and time-independant plasticity, but large strains are considered.