Details
| Original language | English |
|---|---|
| Pages (from-to) | 1365-1376 |
| Number of pages | 12 |
| Journal | Computational mechanics |
| Volume | 65 |
| Issue number | 5 |
| Early online date | 7 Feb 2020 |
| Publication status | Published - May 2020 |
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
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, Vol. 65, No. 5, 05.2020, p. 1365-1376.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Mixed peridynamic formulations for compressible and incompressible finite deformations
AU - Bode, Tobias
AU - Weißenfels, Christian
AU - Wriggers, Peter
N1 - Funding Information: Open Access funding provided by Projekt DEAL.
PY - 2020/5
Y1 - 2020/5
N2 - 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.
AB - 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.
KW - Interpolating moving least squares
KW - Meshfree methods
KW - Mixed methods
KW - Nonlinear elasticity
KW - Peridynamic correspondence formulation
KW - Peridynamic Petrov–Galerkin method
UR - http://www.scopus.com/inward/record.url?scp=85079139264&partnerID=8YFLogxK
U2 - 10.1007/s00466-020-01824-2
DO - 10.1007/s00466-020-01824-2
M3 - Article
AN - SCOPUS:85079139264
VL - 65
SP - 1365
EP - 1376
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 5
ER -