Details
| Original language | English |
|---|---|
| Title of host publication | Lecture Notes in Applied and Computational Mechanics |
| Place of Publication | Cham |
| Publisher | Springer Nature |
| Pages | 81-104 |
| Number of pages | 24 |
| ISBN (electronic) | 9783030381561 |
| ISBN (print) | 9783030381554 |
| Publication status | Published - 4 Mar 2020 |
Publication series
| Name | Lecture Notes in Applied and Computational Mechanics |
|---|---|
| Volume | 93 |
| ISSN (Print) | 1613-7736 |
| ISSN (electronic) | 1860-0816 |
Abstract
Within the theory of Peridynamics standard continuum mechanical material models can be applied using the so-called correspondence formulation. However, the correspondence formulation is susceptible to instabilities in the resulting displacement field, which makes the method inapplicable for simulations at large strains. Hence, the application of a suitable numerical approach to eliminate this drawback is required. Besides a general introduction into Peridynamics, different possibilities to prevent the appearing of the arising instabilities are presented in this chapter. One such approach comes without the necessity of additional stabilisation parameters and is based on the subdivision of the non-local interaction region of interest. Further, it is denoted as the enhanced peridynamic correspondence formulation. In the numerical examples it is demonstrated that for this formulation the instabilities in the displacement field disappear for three-dimensional examples at large strains. In addition, previously unknown limitations of the enhanced peridynamic correspondence formulation are shown within the numerical examples. These are slight, non-physical, deviations in the deformation field and in case of torsion dominated problems a non-physical representation of the stress field.
ASJC Scopus subject areas
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
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Lecture Notes in Applied and Computational Mechanics. Cham: Springer Nature, 2020. p. 81-104 (Lecture Notes in Applied and Computational Mechanics; Vol. 93).
Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review
}
TY - CHAP
T1 - Application of Enhanced Peridynamic Correspondence Formulation for Three-Dimensional Simulations at Large Strains
AU - Hartmann, Philipp
AU - Weißenfels, Christian
AU - Wriggers, Peter
N1 - Funding information: The author kindly acknowledges the DFG and ViVaCE (IRTG 1627) for financial support.
PY - 2020/3/4
Y1 - 2020/3/4
N2 - Within the theory of Peridynamics standard continuum mechanical material models can be applied using the so-called correspondence formulation. However, the correspondence formulation is susceptible to instabilities in the resulting displacement field, which makes the method inapplicable for simulations at large strains. Hence, the application of a suitable numerical approach to eliminate this drawback is required. Besides a general introduction into Peridynamics, different possibilities to prevent the appearing of the arising instabilities are presented in this chapter. One such approach comes without the necessity of additional stabilisation parameters and is based on the subdivision of the non-local interaction region of interest. Further, it is denoted as the enhanced peridynamic correspondence formulation. In the numerical examples it is demonstrated that for this formulation the instabilities in the displacement field disappear for three-dimensional examples at large strains. In addition, previously unknown limitations of the enhanced peridynamic correspondence formulation are shown within the numerical examples. These are slight, non-physical, deviations in the deformation field and in case of torsion dominated problems a non-physical representation of the stress field.
AB - Within the theory of Peridynamics standard continuum mechanical material models can be applied using the so-called correspondence formulation. However, the correspondence formulation is susceptible to instabilities in the resulting displacement field, which makes the method inapplicable for simulations at large strains. Hence, the application of a suitable numerical approach to eliminate this drawback is required. Besides a general introduction into Peridynamics, different possibilities to prevent the appearing of the arising instabilities are presented in this chapter. One such approach comes without the necessity of additional stabilisation parameters and is based on the subdivision of the non-local interaction region of interest. Further, it is denoted as the enhanced peridynamic correspondence formulation. In the numerical examples it is demonstrated that for this formulation the instabilities in the displacement field disappear for three-dimensional examples at large strains. In addition, previously unknown limitations of the enhanced peridynamic correspondence formulation are shown within the numerical examples. These are slight, non-physical, deviations in the deformation field and in case of torsion dominated problems a non-physical representation of the stress field.
UR - http://www.scopus.com/inward/record.url?scp=85081565867&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-38156-1_5
DO - 10.1007/978-3-030-38156-1_5
M3 - Contribution to book/anthology
AN - SCOPUS:85081565867
SN - 9783030381554
T3 - Lecture Notes in Applied and Computational Mechanics
SP - 81
EP - 104
BT - Lecture Notes in Applied and Computational Mechanics
PB - Springer Nature
CY - Cham
ER -