Damage modeling employing strain gradient continuum theory

A damage model for quasi-brittle materials embedded into the two dimensional C1 continuity triangular finite element formulation based on the strain gradient continuum theory is considered. The isotropic damage law is applied to the higher-order stress-strain constitutive model, which enables the analysis of both homogeneous and heterogeneous materials. Such softening formulation also ensures a decrease of the intensity of the material nonlocality associated with the damage growth, which is necessary for the correct description of the narrow localized deformation. In order to obtain the required constitutive matrices, the second-order homogenization procedure is applied to the various representative volume elements in the frame of a multiscale approach. The derived finite element formulation is implemented into the finite element program ABAQUS by means of user subroutines. The superior regularization capabilities, as well as the accuracy and efficiency of the proposed higher-order gradient damage model are demonstrated by the standard benchmark examples.