Anisotropic yield criterion based on microplane effective stress vector

In this paper, based on microplane model, the damagevariable is defined as the reduction of loading area on microplanes, whichis an scalar-valued ODF(Orientation Distribution Function). Kachanov'seffective stress in one dimension is generalized to three dimension byintroducing the concept of effective stress vector on microplanes. Accordingto the concept of microplane effective stress vector, the integral relationsbetween macro stress tensor, its invariants and stress vector onmicroplances for virgin material are generalized to damaged material byreplacing invariants of macro stress tensor as its effective counterparts.For damaged material, macro effective stress tensor and its invariants canbe expressed as the functions of macro nominal stress tensor and fabrictensors of microplane damage. An anisotropic yield criterion is obtained fordamaged materials by extending Drucker-Prager yield criterion. It is shownthat macro effective stress tensor has the same form with Murakami'seffective stress tensor and the anisotropic yield criterion has the sameform with the phenomenological yield criterion proposed by Liu et al. Whenhydrostatic stress has no influence on material yield such as metals, theanisotropic yield criterion has the same form with Hill's anisotropic yieldcriterion.