An elasto-plastic constitutive model with plastic strain rate potentials for anisotropic cubic metals

Abstract

An elasto-plastic constitutive model with the plastic strain rate potential was developed for finite element analysis. In the model, isotropic-kinematic hardening was incorporated under the plane stress condition for anisotropic sheet cubic metal forming analysis. The formulation is general enough for any homogeneous plastic strain rate potential (with the first-order homogeneous effective strain rate) but the plastic strain rate potential Srp2004-18p was considered here. Attention was focused on the development of the elasto-plastic transition criterion and the effective stress update algorithm. Also, to assure the quadratic convergence rate in Newton’s method, the elasto-plastic tangent modulus was analytically derived. Accuracy and convergence of the stress update algorithm were assessed by the iso-error maps, whereas stability of the algorithm was confirmed by analytical procedure. Validations were performed for the examples of the circular cup drawing, 2D draw-bending and unconstrained cylindrical bending tests, utilizing aluminum sheet alloys.