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

In this paper, we develop a model to characterize the deterioration of mechanical responses of microheterogeneous solids due to progressive microstructural failure with increased loading. In the approach, the effects of microscopic failure, so-called “relaxation”, are described by a variational boundary value problem with constraints on the microfields. The extent of the relaxation, which is induced by reducing the eigenvalues of the elasticity tensor at a point in the heterogeneous body, is dictated by the condition that the solution must satisfy the equations of equilibrium, and simultaneously the constraints at that point. Theoretical properties of the model are determined and a computational algorithm is developed to simulate the deterioration of the material microstructure. Numerical simulations involving the finite element method are given to illustrate various aspects of the model.