Modeling and Simulation of cracks and fractures with peridynamics in brittle materials

Abstract

Today, ceramic materials are an essential component of batteries for electric cars. One key feature of this kind of battery is the safety of the ceramic core. Here, the precise approximation of the evolution of damage after the impact and the wave propagation is important to analyze the safety of the battery. The initiation of cracks is especially essential, because the core is normally not damaged. <br /> This thesis studies bond-based peridynamics (PD), a non-local generalization of continuum mechanics, with a focus on discontinuous displacements as they arise in fracture mechanics. With respect to the modeling, the initiation and growth of cracks, two bond-based peridynamic material models for linear isotropic elastic materials are considered. One important feature here is to relate the PD energy to the classical theory energy. <br /> The PD is a model, discretized here with the EMU nodal discretization. The neighbor search in node clouds is an essential part of the computational costs. Therefore, an efficient sorting-based library for the neighbor search in generic node clouds is presented. To achieve the full utilization of modern super computers, a combination of processors and acceleration cards is essential. The asynchronous integration of CUDA into the High Performance ParallelX framework is presented. For the comparison with experimental data, two post processing techniques for the extraction of fragments and stress waves are shown.<br /> Finally, three numerical results for the initiation and evolution of cracks are considered. First, the evolution of damage and wave propagation according to the Edge-On impact experiment. Second, the critical traction prescribed value for the critical traction for Mode I crack opening by Linear Fracture Mechanics (LEFM) is compared with the ones obtained in the simulation for a wide range of materials. Third, the Poisson ratio and the Young modulus obtained by a tensile test for PMMA are compared with the computed values.