Mechanical Modeling of Material Damage

A systematic theory to describe the anisotropic damage states of materials and a consistent definition of effective stress tensors are developed within the framework of continuum damage mechanics. By introducing a fictitious undamaged configuration, mechanically equivalent to the real damaged configuration, the classical creep damage theory is extended to the general three-dimensional states of material damage; it is shown that the damage state can be described in terms of a symmetric second rank tensor. The physical implications, mathematical restrictions, and the limitations of this damage tensor, as well as the effects of finite deformation on the damage state, are discussed in some detail. The notion of the fictitious undamaged configuration is then applied also to the definition of effective stresses. Finally, the extension of the effective stresses incorporating the effects of crack closure is discussed. The resulting effective stress tensor is employed to analyze the stress-path dependence of the elastic behavior of a cracked elastic-brittle material.