Non-associated flow rule with symmetric stiffness modulus for isotropic-kinematic hardening and its application for earing in circular cup drawing

Under a standard derivation, the stiffness modulus for the non-associated flow rule is asymmetric since its plastic potential (for the plastic strain increment under the normality rule) differs from the plastic yield stress function (to define the elastic range). A new formulation was developed in this work, which leads to the symmetric stiffness modulus for the non-associated flow rule, under the framework of the combined isotropic-kinematic hardening law for generalization purposes. As for its application, the non-quadratic Yld2000-2d (Barlat et al., 2003) function (and Hill’s (1948) function for comparison) was utilized to validate the formulation for earing in circular cup drawing of AA2090-T3 and AA5042 sheets, which successfully represented 6 and 8 ears, respectively.