Anisotropic damage model for brittle materials with different tensile-compressive response

A micromechanics-based constitutive equation for brittle materials having different tensile-compressive response is developed. The material is modelled as a linear elastic isotropic matrix containing a distribution of plane microcracks growing in the loading process. As a consequence, the material response evolves from isotropy at the natural state to anisotropy in damaged states. Under the simplifying assumption of non-interacting and self-similar propagating cracks, the analysis builds on a previous work by the first author, who proposed a coupled damage-friction model based on two internal variables, representing damage and frictional contact tractions, as orientation fields. In the present paper it is shown how simplifying assumptions on the orientation fields permit a convenient description for damage and contact tractions in terms of two second-order tensors. The evolution equations of damage and sliding are deduced from damage and frictional limit conditions and corresponding flow rules. Thus, an anisotropic damage model exhibiting different response to tensile, compressive and mixed stress states is obtained. The constitutive equations are applied to analyse the material response to meaningful loading paths. Limit strength domains for biaxial and triaxial stress states are also derived in order to verify the validity of the model.