Crack propagation with adaptive grid refinement in 2D peridynamics

The most common technique for the numerical implementation of peridynamic theory is based on a mesh-free approach, in which the whole body is discretized with a uniform grid and a constant horizon. As a consequence of that computational resources may not be used efficiently. The present work proposes adaptive refinement algorithms for 2D peridynamic grids. That is an essential component to generate a concurrent multiscale model within a unified approach. Adaptive grid refinement is here applied to the study of dynamic crack propagation in two dimensional brittle materials. Refinement is activated by using a new trigger concept based on the damage state of the material, coupled with the more traditional energy based trigger, already proposed in the literature. We present as well a method, to generate the nodes in the refined zone, which is suitable for an efficient numerical implementation. Moreover, strategies for the mitigation of spurious reflections and distortions of elastic waves due to the use of a non-uniform grid are presented. Finally several examples of crack propagation in planar problems are presented, they illustrate the potentialities of the proposed algorithms and the good agreement of the numerical results with experimental data.