Two-dimensional implementation of the coarsening method for linear peridynamics

Yakubu Galadima; Erkan Oterkus; Selda Oterkus; Yakubu Galadima; Erkan Oterkus; Selda Oterkus

doi:10.3934/matersci.2019.2.252

AIMS Materials Science

2019, Volume 6, Issue 2: 252-275. doi: 10.3934/matersci.2019.2.252

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Research article Special Issues

Two-dimensional implementation of the coarsening method for linear peridynamics

Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, 100 Montrose Street, Glasgow G4 0LZ, UK

Received: 12 January 2019 Accepted: 19 March 2019 Published: 03 April 2019

Peridynamic theory was introduced to overcome the limitations of classical continuum mechanics (CCM) in handling discontinuous material response. However, for certain problems, it is computationally expensive with respect to CCM based approaches. To reduce the computational time, a coarsening method was developed and its capabilities were demonstrated for one-dimensional structures by substituting a detailed model with a surrogate model with fewer degrees of freedom. The objective of this study is to extend the application of coarsening method for linear peridynamics for two-dimensional analysis. Moreover, the existing one-dimensional coarsening method was further explored by considering various different micromodulus functions. The numerical results demonstrated that coarsening approach has a potential to reduce the computational time with high accuracy for both one-dimensional and two-dimensional problems.
- peridynamics,
- coarsening,
- non-local,
- numerical,
- composite
Citation: Yakubu Galadima, Erkan Oterkus, Selda Oterkus. Two-dimensional implementation of the coarsening method for linear peridynamics[J]. AIMS Materials Science, 2019, 6(2): 252-275. doi: 10.3934/matersci.2019.2.252

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Abstract

Peridynamic theory was introduced to overcome the limitations of classical continuum mechanics (CCM) in handling discontinuous material response. However, for certain problems, it is computationally expensive with respect to CCM based approaches. To reduce the computational time, a coarsening method was developed and its capabilities were demonstrated for one-dimensional structures by substituting a detailed model with a surrogate model with fewer degrees of freedom. The objective of this study is to extend the application of coarsening method for linear peridynamics for two-dimensional analysis. Moreover, the existing one-dimensional coarsening method was further explored by considering various different micromodulus functions. The numerical results demonstrated that coarsening approach has a potential to reduce the computational time with high accuracy for both one-dimensional and two-dimensional problems.

References

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