On the micro-to-macro transition in constitutive analyses of elastoplastic response at finite strain

Abstract

AbstractThe theoretical transition between basic properties of elastoplastic media at two levels of description is examined rigorously. At the micro-level the material response is heterogeneous, whereas at the macro-level it appears homogeneous. A broad class of constitutive relations is envisaged, and no restriction is placed on the magnitude of deformations and rotations at the micro-level. The investigation is concerned with quadratic differential forms that feature prominently in constitutive analyses, and is complementary to a previous study of bilinear differential forms. A principal objective is to access the transmissibility of measure-invariant inequalities from one level to the other.