Nonlocal FEM Simulations of Ductile Damage with Regularized Crack Path Predictions

Constitutive equations of finite strain elasto-plasticity are coupled to continuum damage mechanics to simulate the initiation and propagation of cracks in ductile materials. The diffuse deterioration of material's strength is modelled using porosity as a damage parameter. We show that the local damage model yields simulation results, pathologically dependent on the FEM mesh upon mesh refinement: (i) the structural behaviour becomes unrealistically brittle; (ii) the FEM mesh determines the crack path. To solve these problems, an integral-based approach to nonlocal damage is implemented. It enables physically sound results by introducing the linear size of the microstructure into the model's formulation. To prevent the effect of unrealistic diffusion of damage, the averaging operator is applied not to the porosity, but to its dual parameter, material's continuity. Solutions of test problems for crack propagation in a compact tension specimen are presented. The convergence of FEM solutions is demonstrated for different slopes of the mesh with fine and coarse discretizations.