Mixed peridynamic formulations for compressible and incompressible finite deformations

authored by: Tobias Bode, Christian Weißenfels, Peter Wriggers
Abstract: The large flexibility of meshfree solution schemes makes them attractive for many kinds of engineering applications, like Additive Manufacturing or cutting processes. While numerous meshfree methods were developed over the years, the accuracy and robustness are still challenging and critical issues. Stabilization techniques of various kinds are typically used to overcome these problems, but often require the tuning of unphysical parameters. The Peridynamic Petrov–Galerkin method is a generalization of the peridynamic theory of correspondence materials and offers a stable and robust alternative. In this work, the stabilization free approach is extended to three dimensional problems of finite elasticity. Locking-free mixed formulations for nearly incompressible and incompressible materials are developed and investigated in convergence studies. In general, an efficient implicit quasi-static framework based on Automatic Differentiation is presented. The numerical examples highlight the convergence properties and robustness of the proposed formulations.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Computational mechanics
Volume: 65
Pages: 1365-1376
No. of pages: 12
ISSN: 0178-7675
Publication date: 05.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-020-01824-2 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{0c24001759cc4ca1a3cf6ba5d7c74c50,
title = "Mixed peridynamic formulations for compressible and incompressible finite deformations",
abstract = "The large flexibility of meshfree solution schemes makes them attractive for many kinds of engineering applications, like Additive Manufacturing or cutting processes. While numerous meshfree methods were developed over the years, the accuracy and robustness are still challenging and critical issues. Stabilization techniques of various kinds are typically used to overcome these problems, but often require the tuning of unphysical parameters. The Peridynamic Petrov–Galerkin method is a generalization of the peridynamic theory of correspondence materials and offers a stable and robust alternative. In this work, the stabilization free approach is extended to three dimensional problems of finite elasticity. Locking-free mixed formulations for nearly incompressible and incompressible materials are developed and investigated in convergence studies. In general, an efficient implicit quasi-static framework based on Automatic Differentiation is presented. The numerical examples highlight the convergence properties and robustness of the proposed formulations.",
keywords = "Interpolating moving least squares, Meshfree methods, Mixed methods, Nonlinear elasticity, Peridynamic correspondence formulation, Peridynamic Petrov–Galerkin method",
author = "Tobias Bode and Christian Wei{\ss}enfels and Peter Wriggers",
note = "Funding Information: Open Access funding provided by Projekt DEAL.",
year = "2020",
month = may,
doi = "10.1007/s00466-020-01824-2",
language = "English",
volume = "65",
pages = "1365--1376",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "5",
}