Peridynamic Simulation of a Mixed-Mode Fracture Experiment in PMMA Utilizing an Adaptive-Time Stepping for an Explicit Solver

• Published in: Journal of peridynamics and nonlocal modeling (Online) Vol. 5; no. 2; pp. 205 - 228
• Main Authors: Willberg, Christian, Hesse, Jan-Timo, Heinecke, Falk
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2023
• Subjects: Characterization and Evaluation of Materials; Computational Science and Engineering; Engineering; Original Articles; Solid Mechanics; Peridynamics; Sensitivity analysis; Morris method; Crack propagation
• ISSN: 2522-896X; 2522-8978
• DOI: 10.1007/s42102-021-00079-6

In this paper, a benchmark analysis of a peridynamic correspondence energy-based damage model is presented. The benchmark is an experimental setup of a Polymethyl methacrylate (PMMA) plate with a hole. The plate has a minotch and is subject to a compressive load. With increasing loads, a crack initiates at the tip of the notch and continuously grows. The benchmark is modeled utilizing the peridynamic correspondence formulation as a two-dimensional problem. To reduce numerical issues due to bond failure, an adaptive time-stepping method for a Verlet time integration schema is proposed. The method limits the maximum number of broken bonds per material point by adapting the time-step size. This allows the correspondence formulation to be significantly more stable. The benchmark involves a sensitivity analysis based on the Morris method, which is performed in this context. As a result, uncertainties and the impact of geometrical, numerical and material parameters are evaluated and discussed.