Two-dimensional implementation of the coarsening method for linear peridynamics

Galadima, Yakubu and Oterkus, Erkan and Oterkus, Selda (2019) Two-dimensional implementation of the coarsening method for linear peridynamics. AIMS Materials Science, 6 (2). pp. 252-275. ISSN 2372-0484 (https://doi.org/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.

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