Computational Method for a Gradient-Enhanced Damage Theory

Abstract

In the last years different continuum damage theories have been proposed to describe the behavior of elastic materials. Among these theories, some introduce higher order gradients of the damage variable in the constitutive model, in order to avoid the loss of well-posedness in the postlocalization range. Although such theories allow a mathematically correct modelling of the strain localization phenomena, they are usually considered complex to handle from the numerical point of view. The present work is concerned with the numerical implementation of a gradient-enhanced damage theory for elastic materials. A simple numerical technique, based on the finite element method, is proposed to approximate the solution of the resulting nonlinear mathematical problem. The coupling between damage and strain variables is circumvented by means of a splitting technique, which permit to transform the nonlinear coupled problem in a sequence of simpler linear problems. In order to evaluate the physical coherence of the model and to access the main features of the numerical method some problems and different numerical techniques are analyzed.