Deformation Behavior of Ductile Solids Containing Anisotropic Damage

Abstract

Many materials of interest contain initial crack‐like defects. Often these cracks are oriented more or less regularly and hence, they contribute to an anisotropic material behavior. We have applied a second‐order tensorial representation of damage, and treat the cracks as a continuum phenomenon on a suitable macroscopic scale. Our model accounts for the progressive failure of damaging materials due to the growth of these defects. The main emphasis of the presented work is put on the propagation of sets of cracks in mode II. This case occurs when the loading axis does not coincide with the plane of the initial cracks. Thus, our model is not restricted to proportional loading. Assuming the existence of a Helmholz free‐energy function and a dissipation potential in the space of affinities we have derived a constitutive equation and a damage propagation law by means of the thermodynamic principles of irreversible processes. Within the framework of the small deformation theory, the proposed formulation considers both brittle and ductile materials.