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A strong-form meshfree method for stress analysis of hyperelastic materials

机译：一种用于超弹性材料应力分析的强形式无网格方法

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摘要

A strong-form based meshfree method for stress analysis of hyperelastic materials under large deformations is presented in this research. The non-linear elastic response of hyperelastic materials is modeled by the compressible Mooney-Rivlin strain energy function. Simple implementation and truly meshfree nature are some of the advantages of strong-form meshfree methods. In the presented meshfree formulation, second derivatives of the strain energy function with respect to the components of the deformation gradient tensor appear. These second derivatives are obtained analytically. Various plane stress and plane strain problems with different boundary conditions are considered. The effects of the value of the shape parameter, the number of the nodes in the support domain, and the total number of nodes on the performance of the method are investigated. Various techniques for applying boundary conditions such as the direct collocation method and the use of fictitious nodes are examined, and an alternative method is presented to apply boundary conditions in the proposed meshfree method.
机译：本研究提出了一种基于强形式的无网格方法，用于大变形下超弹性材料的应力分析。通过可压缩的Mooney-Rivlin应变能函数对超弹性材料的非线性弹性响应进行建模。简单实施和真正的无网格性质是强形式无网格方法的优点。在提出的无网格公式中，出现了相对于变形梯度张量分量的应变能函数的二阶导数。这些二阶导数通过分析获得。考虑了具有不同边界条件的各种平面应力和平面应变问题。研究了形状参数的值，支持域中节点的数量以及节点总数对方法性能的影响。研究了各种应用边界条件的技术，例如直接配置方法和虚拟节点的使用，并提出了一种替代方法来在提出的无网格方法中应用边界条件。

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