An introduction to the nonlocal macro-meso-scale consistent damage model

Cracks may appear in the structural components, leading to damage or even collapse of structures subjected to service or extreme loads. Therefore, crack simulation is important in the design and safety evaluation of engineering structures. For this purpose, a novel nonlocal macro-meso-scale consistent damage (NMMD) model for crack simulation and nonlinear analysis was proposed recently. In this model, the meso-scale damage is determined based on the deformation of point pairs, and the macroscale topologic damage, as a metric of degree of discontinuity in the sense of geometry, is the weighted average of mesoscopic damage in material point pairs within the influence domain. The topologic damage is then incorporated into the framework of continuum damage mechanics through the energetic degradation function, which bridges the damage in the sense of energy and the damage in the sense of geometry. This model can be solved numerically by, e.g., the finite element method. The potential intrinsic connection of the NMMD model with peridynamics and the phase field theory will be discussed. Then, a simple approach to determine the energetic degradation function physically for tension-dominated problems and a method for decomposing the topologic damage driving force will be presented. Several numerical examples are shown to verify the model.