The large flexibility of meshfree solution schemes makes them attractive for many kinds of engineering applications, like Additive Manufacturing or cutting processes. While numerous meshfree methods were developed over the years, the accuracy and robustness are still challenging and critical issues. Stabilization techniques of various kinds are typically used to overcome these problems, but often require the tuning of unphysical parameters. The Peridynamic Petrov–Galerkin method is a generalization of the peridynamic theory of correspondence materials and offers a stable and robust alternative. In this work, the stabilization free approach is extended to three dimensional problems of finite elasticity. Locking-free mixed formulations for nearly incompressible and incompressible materials are developed and investigated in convergence studies. In general, an efficient implicit quasi-static framework based on Automatic Differentiation is presented. The numerical examples highlight the convergence properties and robustness of the proposed formulations.

中文翻译：

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可压缩和不可压缩有限变形的混合近场动力学公式

无网格解决方案方案的巨大灵活性使其对多种工程应用具有吸引力，例如增材制造或切割工艺。虽然多年来开发了许多无网格方法，但准确性和鲁棒性仍然是具有挑战性和关键性的问题。各种稳定技术通常用于克服这些问题，但通常需要调整非物理参数。近场动力学 Petrov-Galerkin 方法是对应材料近场动力学理论的推广，并提供了一种稳定而稳健的替代方法。在这项工作中，无稳定性方法被扩展到有限弹性的三维问题。在收敛研究中开发和研究了几乎不可压缩和不可压缩材料的无锁定混合公式。总的来说，提出了一种基于自动微分的高效隐式准静态框架。数值例子突出了所提出的公式的收敛特性和鲁棒性。