AN ANISOTROPIC STRESS RESULTANT CONSTITUTIVE LAW FOR SHEET-METAL FORMING

Based on Hill's quadratic orthotropic yield function, a yield function in the stress resultant space is approximated in quadratic form for s heets with planar isotropy and normal anisotropy. An equivalent stress resultant is defined and the equivalent work-conjugate generalized pl astic strain rate is then derived. A power-law hardening rule between the equivalent stress resultant and generalized plastic strain is obta ined under proportional straining conditions. A hemispherical punch st retching 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 re sults also indicate that the computational time of the simulations bas ed on the stress resultant constitutive law is much shorter than that based on the through-the-thickness integration method.