Fragmentation and debris evolution modeled by a point-wise coupled reproducing kernel/finite element formulation

A point-wise evolutionarily coupled reproducing kernel (RK)/finite element (FE) formulation was developed to model fragmentation processes induced by blast and impact loadings. In this coupled approach, each integration point defines a coupling zone so that very localized deformations and damage can be treated. A triggering criterion, such as a damage index for concrete or a critical effective plastic strain for steel, is employed to initiate the fragmentation process, which is realized by changing the morphology of the zone where fragmentation is indicated from a FE model to a meshfree model. The evolutionary coupling, whereby the FE zones can morph into meshfree zones, provides a convenient and more accurate domain from which to track the debris mass and velocity distributions, which is of great interest in many applications. To facilitate the fragmentation modeling, a flexible-to-flexible meshfree contact algorithm was implemented so that high velocity (up to 3000 m/s) impact penetration problems can be effectively analyzed by the coupled Lagrangian RK/FE formulation. Numerical results are shown for structures subjected to quasi-static, blast, and high velocity impact loadings using this coupled formulation and employing widely accepted constitutive models for concrete and steel. The examples show that the coupled formulation can be used to model material fragmentation and the evolution of debris using damage indicators provided by any validated material constitutive model.