Anisotropic yield criterion based on microplane effective stress vector
基于微面有效应力矢量的各向异性屈服准则

In this paper,based on the microplane model,a damage variable is defined as the reduction of the loading area on microplanes,which is an scalar-valued ODF(Orientation Distribution Function).Kachanov's effective stress in one dimension is generalized to three dimensions by introducing the concept of the effective stress vector on microplanes.According to the concept of the microplane effective stress vector,the integral relations between the macro stress tensor,its invariants and the stress vector on microplances for the virgin material are generalized to the damaged material by replacing them by their effective counterparts.For the damaged material,the macro effective stress tensor and its invariants can be expressed as the hmctions of macro nominal stress tensor and fabric tensors of microplane damage.An anisotropic yield criterion is obtained for the damaged materials by extending Drucker-Prager yield criterion.It is shown that the macro effective stress tensor has the same form as Murakami's effective stress tensor and the anisotropic yield criterion has the same form as the phenomenological yield criterion proposed by Liu et al.If the hydrostatic stress has no influence on material yielding as for metals,the anisotropic yield criterion has the same form as Hill's anisotropic yield criterion.