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

Christian Willberg,Falk Heinecke,Jan-Timo Hesse

doi:10.1007/s42102-021-00079-6

Christian Willberg, Falk Heinecke + Show 1 more

Open Access

https://doi.org/10.1007/s42102-021-00079-6

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Abstract

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.

Highlights

Wind energy is one of the main pillars for the production of low-carbon emission electricity
The main advantage of the method is that there are no singularities in the region of damage as in classical continuum mechanics [4]
It can be said that the chall of Peridynamics is to clearly define integration domain size rules for damage problems from a mathematical or material modeling point and not from the best practice point of view

Summary

Introduction

Wind energy is one of the main pillars for the production of low-carbon emission electricity. The main advantage of the method is that there are no singularities in the region of damage as in classical continuum mechanics [4]. This is achieved by an integral description of the conservation of momentum. If the domain size approaches zero, the same problems result as with classical continuum mechanics. It can be said that the chall of Peridynamics is to clearly define integration domain size rules for damage problems from a mathematical or material modeling point and not from the best practice point of view

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