Abstract The extension of the 3D cell-centered Finite Volume EUCCLHYD scheme to the hyperelasticity system is proposed here. This study is based on the left Cauchy-Green tensor B which enables to work in a fully updated Lagrangian formalism. The second order extension of this scheme is proposed using a MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) procedure combined with a GRP (Generalized Riemann Problem) approach. In particular, the limitation of the tensor fields is done in a component-wise manner. Moreover, the complete GRP procedure is proposed in the case of Neo-Hookean compressible solids. The scheme is validated on several test cases introducing small as well as large deformations. In particular, good results are found on the non trivial problems of oscillating and twisting beams.

中文翻译：

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用于超弹性系统数值建模的以 3D 单元为中心的拉格朗日二阶方案

摘要 这里提出了以 3D 单元为中心的有限体积 EUCCLHYD 方案对超弹性系统的扩展。本研究基于左柯西-格林张量 B，它能够在完全更新的拉格朗日形式主义中工作。该方案的二阶扩展是使用 MUSCL（守恒定律的单调上游中心方案）程序与 GRP（广义黎曼问题）方法相结合提出的。特别是，张量场的限制是以组件方式完成的。此外，在 Neo-Hookean 可压缩固体的情况下提出了完整的 GRP 程序。该方案在引入小变形和大变形的几个测试用例上得到验证。特别是，在振荡梁和扭转梁的非平凡问题上发现了良好的结果。