Numerical analysis of anisotropic plasticity and damage based on the inelastic predictor-elastic corrector method
Zhichao Wei, Sanjeev Koirala, Steffen Gerke, Michael Brünig
Abstract
This paper addresses the numerical implementation algorithm for an advanced anisotropic plasticity and damage continuum model. The framework of the proposed theory is based on the introduction of effective undamaged configurations, where no damage occurs, and the damaged configurations that account for elastic–plastic deformation and damage. The anisotropic plastic behavior is characterized by the Hoffman yield condition. The onset of damage is defined by a combination of the first and second deviatoric stress invariants related to the growth and coalescence of micro-defects (micro-voids and micro-shear-cracks). A stress-state-dependent damage strain rate tensor is introduced to capture the damage evolution caused by tension- and shear-induced mechanisms. The constitutive rate equations are numerically integrated using an explicit inelastic (plastic or plastic-damage) predictor-elastic corrector method. The consistent tangent modulus is derived and used to ensure quadratic convergence in the global finite element method. Moreover, numerical calculations for various biaxial loading conditions, including shear- and tension-induced damage mechanisms, demonstrate the accuracy and efficiency of the numerical algorithm. Numerical results are compared with experimental data at both the global load–displacement curve and the local strain fields, measured using the digital image correlation (DIC) technique. Scanning electron microscopy (SEM) is employed to compare the numerically predicted damage mechanism by examining fracture surfaces. • Anisotropic damage model coupled with anisotropic plasticity behavior. • Explicit integration using an inelastic predictor-elastic corrector scheme. • Consistent tangent moduli ensure fast and stable quadratic convergence. • The algorithm provides stable and accurate results with few integration steps. • Biaxial tests with different specimen orientations show varied damage behavior.