Determination of horizon size in state-based peridynamics

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Wang, Bingquan and Oterkus, Selda and Oterkus, Erkan (2023) Determination of horizon size in state-based peridynamics. Continuum Mechanics and Thermodynamics, 35 (3). pp. 705-728. ISSN 0935-1175 (https://doi.org/10.1007/s00161-020-00896-y)

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Abstract

Peridynamics is based on integro-differential equations and has a length scale parameter called horizon which gives peridynamics a non-local character. Currently, there are three main peridynamic formulations available in the literature including bond-based peridynamics, ordinary state-based peridynamics and non-ordinary state-based peridynamics. In this study, the optimum horizon size is determined for ordinary state-based peridynamics and non-ordinary state-based peridynamics formulations by using uniform and non-uniform discretisation under dynamic and static conditions. It is shown that the horizon sizes selected as optimum sizes for uniform discretisation can also be used for non-uniform discretisation without introducing significant error to the system. Moreover, a smaller horizon size can be selected for non-ordinary state-based formulation which can yield significant computational advantage. It is also shown that same horizon size can be used for both static and dynamic problems.

ORCID iDs

Wang, Bingquan, Oterkus, Selda ORCID logoORCID: https://orcid.org/0000-0003-0474-0279 and Oterkus, Erkan ORCID logoORCID: https://orcid.org/0000-0002-4614-7214;
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