Such a connection between these theories has not been extensively explored at the discrete level. At the continuum level, it has been demonstrated that classical (local) elasticity is a special case of peridynamics. The peridynamic theory of solid mechanics is a nonlocal reformulation of the classical continuum mechanics theory. As a result for either cases of spatial discretization, the bond-associated correspondence material model predicts the most accurate results. For the case of irregular and non-uniform spatial discretization, models formulated specifically for this configuration give much better more » results than the conventional formulations which don’t consider the neighborhood difference among material points in the spatial discretization. It’s found that for the case of irregular but semi-uniform spatial discretization, all these models yield good predictions compared to analytical local solutions. In this study, a systematic comparison study on results predicted by eight peridynamic models, including bond-based, ordinary state-based and non-ordinary state-based mechanics and heat conduction models, for three different types of problems, including thermal, mechanical and coupled thermo-mechanical, with irregular spatial discretization are performed. The applicability of peridynamic models to problems with irregular non-uniformly discretized solution domain is critical. Furthermore, the accuracy of this approach is verified against benchmark solutions, and its applicability to engineering problems is demonstrated by considering thermally induced cracking in a nuclear fuel pellet. It also removes the requirement for correction of peridynamic material parameters due to surface effects. This study presents a modification to the original peridynamic theory in which the strain energy associated with an interaction between two material points is split according to the volumetric ratio arising from the more » presence of non-uniform discretization and a variable horizon. However, the use of non-uniform discretization and a variable horizon requires consideration of possible unbalanced interactions between two material points, adjustment of peridynamic material parameters, and arbitrary shapes of interaction domains. Non-uniform discretization of the solution domain in models based on peridynamic theory can improve computational efficiency by allowing for local refinement where needed for accuracy, and helps remove the effect of mesh bias in the simulations.
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