Simulation results for damage with evolving microstructure and growing strain gradient moduli

In this paper, a strain gradient regularization of continuum damage mechanics is dealt with starting from a variational inequality. Full stress and strain analyses are reported for numerical tests performed with an in-house code based on the element free Galerkin method in two exemplary cases. Simulations show that the non-locality conferred to the model by the strain gradient regularization effectively solves the problem of mesh dependence exhibited by standard damage continuum models and allows to reach convergence up to deformation regimes for which equivalent negative stiffness is observed. Moreover, we will illustrate the case in which new microstructures, and therefore higher values of second gradient moduli, develop due to damage. For illustration a simple monotonic evolution rule is assumed for the growth of the second gradient moduli. Thus, for this simple rule, the simulations show development of a larger diffuse damage zone whose size can be controlled.