AN ANISOTROPIC STRESS RESULTANT CONSTITUTIVE LAW FOR SHEET METAL FORMING

Based on Hillʹs quadratic orthotropic yield function, a yield function in the stress resultant space is approximated in quadratic form for sheets with planar isotropy and normal anisotropy. An equivalent stress resultant is defined and the equivalent work-conjugate generalized plastic strain rate is then derived. A power-law hardening rule between the equivalent stress resultant and generalized plastic strain is obtained under proportional straining conditions. A hemispherical punch stretching operation and a plane-strain draw operation are simulated by finite element methods based on the stress resultant constitutive law. The results of these finite element simulations are in good agreement with those using the through-the-thickness integration method. The results also indicate that the computational time of the simulations based on the stress resultant constitutive law is much shorter than that based on the through-the-thickness integration method