A description of macroscopic damage through microstructural relaxation

In this paper a exible model for the description of damage in heterogeneous structural materials is presented. The approach involves solving the equations of equilibrium, with unilateral constraints on the maximum attainable values of selected internal variables. Due to the unilateral constraints, the problem is non-linear. Accordingly, a simple iterative algorithm is developed to solve this problem by (1) computing the internal elds with the initial undamaged microstructure and (2) reducing the material sti ness at locations where the constraints are violated. This process is repeated until a solution, with a corresponding microstructure, that satis es the equations of equilibrium and the constraints, is found. The corresponding microstructure is the nal `damagedʹ material. As an application, the method is used in an incremental fashion to generate response curves describing the progressive macroscopic damage for a sample of commonly used bre-reinforced Aluminum=Boron composite. The results are compared to laboratory experiments published by Kyono et al.1 and computational results using standard numerical methods, published by Brockenbrough et al.2