A large anisotropic damage theory based on an incremental complementary energy equivalence model

Abstract

This paper presents a large anisotropic damage theory of continuum damage mechanics. It is developed via a new hypothesis of incremental complementary elastic energy equivalence. This hypothesis is more versatile and accurate if compared to the original hypothesis of total complementary energy equivalence. To model the large damage, we assumed that it occurs as a series of incremental small damage. An expression for the damage effect tensor M(D) for large damage is derived. It is shown that when the damage is small, that is, D _i≪1, the proposed large damage theory reduces to the small damage model of Chow and Wang [1]. To demonstrate this large damage theory, it is applied to model the following cases: (a) uniaxial tension, (b) pure torsion and (c) elastic perfectly-plastic material behavior. In all three cases, the results clearly show that when the damage is small, Chow and Wang's model is recovered. However, for large damage, there are significant differences in predictions. Since this large damage theory is formulated on the basis of the incremental complementary energy, it is applicable to a wider range of problems.