LAUSR

Abstract This paper presents a constitutive equation for anisotropic inelastic deformation rate applied to sheet metal forming based on recently developed invariants for nonlinear orthotropic elastic–inelastic material response. These invariants are based on Eulerian evolution equations for microstructural vectors that characterize directions of anisotropy and elastic deformations which cause stress. These microstructural vectors are used here to model directions of orthotropy for sheet metal forming. This Part I of a two-part paper modifies an anisotropic yield function for sheet metal analysis based on stress components determined by elastic deformations of microstructural vectors. Specific expressions are proposed for the direction of inelastic distortional deformation rate, which automatically satisfies the rate of material dissipation inequality, and for the direction of inelastic spin. The material parameters are calibrated for the aluminum alloy AA6022-T43, steel MP980 sheets and cold rolled low carbon steel sheets. The results of stress anisotropy and R-value distributions are shown to be in good agreement with the experimental data. Part II describes the implementation of this model into a finite element program and presents a comparison of Eulerian and Lagrangian formulations.