Vol. 14, No. 2, 2019

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A mode-dependent energy-based damage model for peridynamics and its implementation

Christian Willberg, Lasse Wiedemann and Martin Rädel

Vol. 14 (2019), No. 2, 193–217
Abstract

The mathematical modeling of failure mechanisms in solid materials and structures is a long standing problem. In recent years, peridynamics has been used as a theoretical basis for numerical studies of fracture initiation, evolution and propagation. In order to investigate damage phenomena numerically, suitable material and damage models have to be implemented in an efficient numerical framework. This framework should be highly parallelizable in order to cope with the computational effort due to the high spatial and, depending on the problem, temporal resolution required for high accuracy. The open-source peridynamic framework Peridigm offers a computational platform upon which new developments of the peridynamic theory can be implemented. Today, isotropic material models and a very simple damage model are implemented in Peridigm.

This paper proposes three energy-based damage criteria. The implementation approach as well as the extension of Peridigm with these physically motivated models is described. The original criterion of Foster et al. is adapted for ordinary state based material. The other two criteria utilize the decomposition of peridynamic states in isotropic and deviatoric parts to account for the failure-mode dependency.

The original criterion is verified by the numerical simulation of two mechanical problems. At first, a virtual double cantilever beam (DCB) experiment is performed to determine the energy release rate. This value is the fundamental material property required for the proposed criteria. Additionally, the DCB problem is then used to investigate the convergence of the numerical scheme implemented in Peridigm. In a second step, a model of a plate with a cylindrical hole under tensile loading is compared with an extended finite element method solution. Results of both numerical solutions are in good agreement. Finally, a fiber reinforced micro structure model is used to analyze the effect of the different criteria to the damage initiation and crack propagation under a more complex loading condition.

Keywords
peridynamics, damage model, open source
Milestones
Received: 21 December 2017
Revised: 25 October 2018
Accepted: 2 November 2018
Published: 29 May 2019
Authors
Christian Willberg
German Aerospace Center
Institute of Composite Structures and Adaptive Systems
38108 Brunswick
Germany
Lasse Wiedemann
German Aerospace Center
Institute of Composite Structures and Adaptive Systems
38108 Brunswick
Germany
Martin Rädel
German Aerospace Center
Institute of Composite Structures and Adaptive Systems
38108 Brunswick
Germany