An alternative method for the integration of continuum damage evolution laws

Abstract

In this study the elasto-plastic constitutive equations are reformulated using the assumption of constant strain rate direction within a load increment. This assumption allows the constitutive evolution laws to be rewritten as ordinary differential equations (ODEs). The set of ODEs is reduced using the Krieg and Krieg description of the deviatoric stress space. Although this approach does generally not allow an exact integration to be performed, it results in a significantly reduced set of ODEs, allowing an efficient integration scheme to be obtained. The possibility of forming an algorithmic stiffness tensor associated with the proposed integration scheme is investigated. It is shown that, in order to calculate the algorithmic tangent, an extra set of ODEs needs to be solved. This set of additional ODEs is solved simultaneously with the evolution equations allowing an efficient numerical implementation to be obtained. To investigate the properties of the solution method, with respect to both accuracy and convergence when using the Newton–Raphson method, an elasto-plastic damage model based on von Mises isotropic hardening plasticity is taken as a model problem.