Nonlinear analysis and elastic-plastic behavior of anisotropic structures

Abstract

An elastic-plastic analysis of anisotropic work-hardening materials based on a quadratic approximation of the Tsai-Wu criterion is presented. General expressions for the anisotropic parameters in the yield condition are derived for initial and subsequent yielding. Particularly, the plastic constitutive relations are expressed by means of both the flow theory as well as the deformation theory extended to anisotropic plasticity. The numerical algorithms are based upon the notion of a return mapping procedure and a consistent tangent operator valid for anisotropic elastic-plastic materials including work-hardening effects is developed. The solution equations are evaluated by consistent linearization of a nonlinear variational principle and a Newton-Raphson scheme is adopted for the iterative solution of the nonlinear problems. Numerical examples exhibit the reliable performance of the proposed algorithm in some practical calculations. The effects of anisotropy and the differences between flow and deformation theories in the obtained solutions are discussed and compared with available numerical results.