Study on the definition of equivalent plastic strain under non-associated flow rule for finite element formulation

As opposed to associated flow rule (AFR) in which yield function and plastic potential are equal, the different definitions for them is an inherent characteristic of non-associated flow rule (non-AFR). This imposes a specific relation (but not equality) between equivalent plastic strain and plastic compliance factor. Unavoidably, this leads to a laborious effort for FE implementation of non-associated constitutive model specifically when several internal variables (such as kinematic hardening or damage parameters) are involved. This paper is mainly devoted to studying the conditions at which the non-AFR approach can be simplified so that the numerical implementation scheme is more convenient without loss of accuracy. It will be shown that by scaling the plastic potential function, the equality of equivalent plastic strain and compliance factor can be reserved. The effect of scaling of the non-AFR based on Barlat et al.'s (2003) anisotropic model (called Yld2000-2d) is comprehensively studied with FE simulation of tensile loading under uniaxial tensions along the different orientations as well as balanced biaxial stress condition. A fully implicit return-mapping scheme was introduced for stress integration of the constitutive model in a User-defined MATerial subroutine (UMAT). Cup drawing simulations of a highly textured aluminum alloy 2090-T3 were performed using simplified and original approaches. The results prove that the proposed simplified technique is a reliable alternative for the full expression.