“Homogenization with non‐homogeneous plastic flow”

Abstract This paper provides the solution of a homogenization model that simultaneously considers the plastic and elastic strain fields in a single analytical formulation. In addition, the authors aim to decouple plastic flows triggered in the inclusions, in the matrix at the interfaces with the inclusions, and in the matrix at a large distance from the inclusions. The authors propose an admissible displacement field containing elastic and anelastic contributions in series. This field provides a new strain homogenization formula in which the plastic deformations in the inclusions, at the interface between the matrix and the inclusions, and in the matrix far from the inclusions appear explicitly. Applications allow to evaluate the pertinence of the approximation provided by this field, and show that this new formulation is able to create macroscopic work hardening while all the elementary phases have elastic‐perfectly plastic behaviour without resorting to expensive numerical simulations (such as mesoscopic finite element modelling). This is the consequence of the simultaneous presence of elasticity and plasticity on the one hand and, on the other, the possibility of triggering plastic flows independently on the surface of each type of inclusion and in the matrix at a large distance from the inclusions.