Calibrating Bond-Based Peridynamic Parameters Using a Novel Least Squares Approach
Abstract
Here, we present a novel procedure to calibrate bond micromoduli in a discrete bond-based peridynamics setting. Conventionally, an analytical expression has been used based on strain energy equivalence. In the present work, the micromoduli for individual bonds in a neighborhood are calibrated by equating the effective peridynamic stiffness to the reference material stiffness and posed as a set of linear system of equations. The solution to this is found by a least squares approach which aims to reduce the error in the components of the stiffness matrix. Finally, results for an isotropic case in a local neighborhood of particles are shown to demonstrate the feasibility of this approach.
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1489956
- Report Number(s):
- LA-UR-18-23644
Journal ID: ISSN 2522-896X
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Peridynamics and Nonlocal Modeling
- Additional Journal Information:
- Journal Volume: 1; Journal Issue: 1; Journal ID: ISSN 2522-896X
- Publisher:
- Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Peridynamics; Surface effects; Micromoduli
Citation Formats
Prakash, Naveen. Calibrating Bond-Based Peridynamic Parameters Using a Novel Least Squares Approach. United States: N. p., 2018.
Web. doi:10.1007/s42102-018-0002-z.
Prakash, Naveen. Calibrating Bond-Based Peridynamic Parameters Using a Novel Least Squares Approach. United States. https://doi.org/10.1007/s42102-018-0002-z
Prakash, Naveen. Thu .
"Calibrating Bond-Based Peridynamic Parameters Using a Novel Least Squares Approach". United States. https://doi.org/10.1007/s42102-018-0002-z. https://www.osti.gov/servlets/purl/1489956.
@article{osti_1489956,
title = {Calibrating Bond-Based Peridynamic Parameters Using a Novel Least Squares Approach},
author = {Prakash, Naveen},
abstractNote = {Here, we present a novel procedure to calibrate bond micromoduli in a discrete bond-based peridynamics setting. Conventionally, an analytical expression has been used based on strain energy equivalence. In the present work, the micromoduli for individual bonds in a neighborhood are calibrated by equating the effective peridynamic stiffness to the reference material stiffness and posed as a set of linear system of equations. The solution to this is found by a least squares approach which aims to reduce the error in the components of the stiffness matrix. Finally, results for an isotropic case in a local neighborhood of particles are shown to demonstrate the feasibility of this approach.},
doi = {10.1007/s42102-018-0002-z},
journal = {Journal of Peridynamics and Nonlocal Modeling},
number = 1,
volume = 1,
place = {United States},
year = {Thu Oct 25 00:00:00 EDT 2018},
month = {Thu Oct 25 00:00:00 EDT 2018}
}
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Figure 1: Kinematics of peridynamic material particles, material particle $x$ and $x′$ correspond to an interacting pair of particles within the horizon region of $x$, having a volume dVx′.
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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.