Details
| Original language | English |
|---|---|
| Article number | 113605 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 374 |
| Early online date | 9 Dec 2020 |
| Publication status | Published - 1 Feb 2021 |
Abstract
The Peridynamic Petrov–Galerkin (PPG) method is a meshfree particle method based on the weak form of the peridynamic momentum equation. It can be applied to arbitrary constitutive laws from the classical continuum mechanics theory. With non-linear approximation functions the rank deficiency present in many nodally integrated discretization schemes is prevented. The consistency of trial functions is not sufficient for the convergence with irregular particle distributions. In this paper the consistency of the test space is examined and possible correction techniques are presented. The resulting variationally consistent PPG method is able to pass the patch test and to restore the optimal convergence rates. A correction of the test functions that preserves the linear trial function consistency allows the use of displacement–pressure–dilation formulations and exhibits stability and robustness for 3-D in the regime of non-linear elasticity. Besides, the direct nodal coupling with Finite Elements and the application of symmetry boundary conditions are enabled.
Keywords
- Finite element coupling, Integration correction, Meshfree methods, Peridynamics, Symmetry boundary conditions, Variationally consistent
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 374, 113605, 01.02.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A consistent peridynamic formulation for arbitrary particle distributions
AU - Bode, T.
AU - Weißenfels, C.
AU - Wriggers, P.
PY - 2021/2/1
Y1 - 2021/2/1
N2 - The Peridynamic Petrov–Galerkin (PPG) method is a meshfree particle method based on the weak form of the peridynamic momentum equation. It can be applied to arbitrary constitutive laws from the classical continuum mechanics theory. With non-linear approximation functions the rank deficiency present in many nodally integrated discretization schemes is prevented. The consistency of trial functions is not sufficient for the convergence with irregular particle distributions. In this paper the consistency of the test space is examined and possible correction techniques are presented. The resulting variationally consistent PPG method is able to pass the patch test and to restore the optimal convergence rates. A correction of the test functions that preserves the linear trial function consistency allows the use of displacement–pressure–dilation formulations and exhibits stability and robustness for 3-D in the regime of non-linear elasticity. Besides, the direct nodal coupling with Finite Elements and the application of symmetry boundary conditions are enabled.
AB - The Peridynamic Petrov–Galerkin (PPG) method is a meshfree particle method based on the weak form of the peridynamic momentum equation. It can be applied to arbitrary constitutive laws from the classical continuum mechanics theory. With non-linear approximation functions the rank deficiency present in many nodally integrated discretization schemes is prevented. The consistency of trial functions is not sufficient for the convergence with irregular particle distributions. In this paper the consistency of the test space is examined and possible correction techniques are presented. The resulting variationally consistent PPG method is able to pass the patch test and to restore the optimal convergence rates. A correction of the test functions that preserves the linear trial function consistency allows the use of displacement–pressure–dilation formulations and exhibits stability and robustness for 3-D in the regime of non-linear elasticity. Besides, the direct nodal coupling with Finite Elements and the application of symmetry boundary conditions are enabled.
KW - Finite element coupling
KW - Integration correction
KW - Meshfree methods
KW - Peridynamics
KW - Symmetry boundary conditions
KW - Variationally consistent
UR - http://www.scopus.com/inward/record.url?scp=85097355443&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2020.113605
DO - 10.1016/j.cma.2020.113605
M3 - Article
AN - SCOPUS:85097355443
VL - 374
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 113605
ER -