On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models

作者: Pablo Seleson , Qiang Du , Michael L. Parks

DOI: 10.1016/J.CMA.2016.07.039

关键词:

摘要: The peridynamic theory of solid mechanics is a nonlocal reformulation the classical continuum theory. At level, it has been demonstrated that (local) elasticity special case peridynamics. Such connection between these theories not extensively explored at discrete level. This paper investigates consistency nearest-neighbor discretizations linear elastic models and finite difference Navier–Cauchy equation elasticity. While in peridynamics have numerically observed to present grid-dependent crack paths or spurious microcracks, this focuses on different, analytical aspect such discretizations. We demonstrate that, even absence cracks, may be problematic unless proper selection weights used. Specifically, we using standard meshfree approach peridynamics, do reduce, general, corresponding models. study nodal-based quadratures for discretization models, derive quadrature result discretized lead are, however, model-/discretization-dependent. motivate choice those through quadratic approximation ofmore » displacement fields. stability schemes Fourier mode analysis. Finally, an based normalization constitutive constants level explored. results desired one-dimensional but does work higher dimensions. presented suggest though should avoided simulations involving are viable, example verification validation purposes, problems characterized by smooth deformations. Furthermore, better rules can obtained functional form solutions.« less

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