On macroscopic effects of heterogeneity in elastoplastic media at finite strain

Abstract

For elastic or plastic media the linkages between basic properties at two levels of description are rigorously analysed. At one level the material is structurally heterogeneous, while at the other it behaves macroscopically as if homogeneous. The deformation is unrestricted as to magnitude, but is treated incrementally. Full account is taken of coupling between stresses and rotations within a representative volume. Theorems on spatial averages of tensor variables and their products are reviewed and extended. Relations between constitutively significant quantities at both levels are developed by means of tensor influence functions associated with auxiliary elastic fields. The analysis is conducted primarily in terms of non-objective variables and a Lagrangian reference configuration. A final transformation to intrinsic variables is effected with the help of some novel operators.