A model for simulating the deterioration of structural-scale material responses of microheterogeneous solids

In this paper, we develop a model to characterize the deterioration of mech anical responses of microheterogeneous solids due to progressive microstruc tural failure with increased loading. In the approach, the effects of micro scopic failure, so-called "relaxation", are described by a variational boun dary value problem with constraints on the microfields. The extent of the r elaxation, which is induced by reducing the eigenvalues of the elasticity t ensor at a point in the heterogeneous body, is dictated by the condition th at the solution must satisfy the equations of equilibrium, and simultaneous ly the constraints at that point. Theoretical properties of the model are d etermined and a computational algorithm is developed to simulate the deteri oration of the material microstructure. Numerical simulations involving the finite element method are given to illustrate various aspects of the model . (C) 2001 Elsevier Science B.V. All rights reserved.