Microplane-damage-based Effective Stress and Invariants

This paper addresses some issues of the application of the effective stress tensor to coupled damage-plasticity from the point of view of a microplane. In this paper, damage and effective stress are defined on microplanes. The effective stress tensor of Murakami (1988) can be recovered as the second-order fabric tensor of the effective stress vector. The effective second invariant J ₂ is defined as the integration of the square of the effective shear stress over the unit sphere. It is revealed that the J ₂ possesses the form of the Hill (1950) anisotropic yield function based on the definition. Therefore, one can also use the Hill (1950) model to describe coupled anisotropic-damage-plasticity except for the conventional approach of effective stress.