Effect of the Internal Length Scale Parameter in Gradient Damage Mechanics

Gradient enhanced continuum damage mechanics is one of the best methods to remedy the mesh sensitivity and mathematically infeasible results usually obtained in the numerical implementation of continuum damage mechanics theories. It involves the introduction of internal length scales through nonlocal averaging. We evaluate the effects of the internal length scale parameter on structural response in this study. A half model of a single-edge notched specimen is analyzed with large and small length scale parameters using an in-house MATLAB code assuming isotropic damage and plane strain conditions. A scalar damage variable with exponential evolution law is considered. The results demonstrate that with increasing internal length scale parameter, the damage spread increases and its maximum value decreases; hence, its selection should be made considering the experimental responses of a material. A detailed description of finite element formulations and implementation algorithms for solving the nonlinear problem is elucidated.