SummaryIn this paper, we lay out a variational framework for correspondence‐based peridynamic (PD) formulations of solid mechanics. Using the framework, we address the numerical instabilities of the original version of correspondence‐based PD by developing a natural stabilization technique that avoids costly bond‐associated approaches and retains the structure of a method with nodal integration. Accuracy, robustness, and efficiency of the proposed naturally stabilized correspondence‐based PD are demonstrated on several computational test cases ranging from linear elastostatics to large deformation elasto‐plasticity. The computational methodology developed is particularly effective for handling materials undergoing nearly‐incompressible deformations.

中文翻译：

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基于对应的近场动力学的稳定公式以及使用节点积分的方法的计算结构

摘要在本文中，我们为基于对应的固体力学近场动力学（PD）公式制定了一个变分框架。使用该框架，我们通过开发一种自然稳定技术来解决基于对应的 PD 原始版本的数值不稳定性问题，该技术避免了昂贵的键相关方法并保留了节点积分方法的结构。所提出的基于自然稳定对应的 PD 的准确性、鲁棒性和效率在从线性弹静力学到大变形弹塑性的几个计算测试用例中得到了证明。所开发的计算方法对于处理几乎不可压缩变形的材料特别有效。