Nonlinear elastic brittle damage: numerical solution by means of operator split methods

To avoid the loss of well-posedness in the post-localization range, some continuum damage theories for elastic materials introduce higher order gradients of the damage variable into the constitutive model. Although such theories allow for mathematically correct modelling of the strain localization phenomena, they are usually considered to be very complex to handle from the numerical point of view. The present work deals 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 to the resulting nonlinear mathematical problems. The coupling between damage and strain variables is circumvented by means of a splitting technique.