Formulation of implicit stress integration and consistent tangent modulus for an anisotropic hardening constitutive model

Abstract

An anisotropic hardening constitutive model based on the generalized isotropic hardening (GIH) rule was implemented into the nonlinear finite element method. The GIH rule describes discrete formation of homology centers and simultaneous hardening of both inner and outer yield surfaces. Consequently, yielding in the field of reverse loading can be accurately modeled by this rule. In order to preserve the accuracy of nonlinear finite element analysis, an implicit stress integration technique employing the generalized trapezoidal rule was applied to the GIH constitutive equation. Furthermore, the consistent tangent modulus was formulated and coded into a nonlinear FEA program, which has the advantage of the quadratic rate of convergence in Newton's iteration. Accuracy and convergence were successfully verified through examples, and thus the anisotropic hardening constitutive model could assess the plastic straining mobilized in overconsolidated state and versatile loading sequences. (C) 2001 Elsevier Science B.V. All rights reserved.