A quasi-flow corner theory of elastic—plastic finite deformation

Abstract

A quasi-flow comer theory of elastic—plastic finite deformation of ductile materials has been proposed. By introducing a decreasing function of quasi-elastic modulus with respect to strain into the classical flow theory and normality law and by modifying the common decomposition of elastic-plastic strain rate, the present quasi-flow comer theory achieves smooth and continuous transitions from the normality law (the Prandtl-Reuss equation) to the non-normality law with strain, and from plastic loading to elastic unloading. On isotropic condition, the J2 flow and deformation theories can be included as special cases of the quasi-flow corner theory. The proposed theory is then applied to simulate the instability and deformation localization under plane strain tension and uniaxial tension of anisotropic sheet metals. Some of the numerical results have been compared with experimental ones.