Initiation of damage with implicit gradient-enhanced damage models

Through a mixed local and nonlocal formulation, a continuous transition from a local to a nonlocal behavior is obtained. Initially driven by the local action, the damage driving quantity at a material point in non-damaged materials is later influenced by the nonlocal effect only if the occurrence of damage is effectively found in the surroundings. Qualitative resemblance is hence expected in the prediction of damage initiation by the non-regularized and regularized damage models. Numerical simulations with simple tests and comparisons with existing nonlocal damage models show the qualitative improvement of the mixed formulation in the prediction of damage initiation for 1D and 2D damaged structures.