Adaptive Grid Refinement and Scaling Techniques Applied to Peridynamics

Peridynamics, a recently proposed non-local continuum theory, is particularly suitable to describe fracture phenomena in a wide range of materials. One of most common techniques for its numerical implementation is based on a mesh-free approach, in which the whole body is discretized with a uniform grid and a constant horizon, the latter related to the length-scale of the material and/or of the phenomenon analysed. As a consequence of that, computational resources may not be used efficiently. The present work proposes adaptive refinement/scaling algorithms for 2D and 3D peridynamic grids, to reduce the computational cost of peridynamic based software. Adaptive refinement/scaling is here applied to the study of dynamic crack propagation in 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. The use of a varying horizon and grid spacing over the grid may introduce some anomalies on the numerical peridynamic solution, such anomalies are investigated in detail through static and dynamic analyses. Moreover, while the scientific community is working to assess the full potential of peridynamics, few researchers have observed indirectly that the evolution of crack paths can follow, in an unphysical way, the axes of symmetry of the grid. The main parameter affecting such a numerical phenomenon seems to be the value of the m ratio, namely the ratio between the horizon and the grid spacing. The dependence of the crack path on the grid orientation would be a serious drawback for peridynamic based software since it would undermine what is believed to be one of its most important advantages over other computational methods, i.e. its capability to simulate (multiple) crack nucleation, propagation, branching and interaction in solids in a simple way. Finally, in order to show the effectiveness of the proposed approach, several examples of crack propagation in both 2D and 3D problems are presented. Then, the results obtained are compared with those obtained with other numerical methods and with experimental data.