The objective of the present paper is to develop a finite element formulation for modeling nearly incompressible materials at large strains using polygonal elements. The present finite element formulation is a simplified version of the three-field mixed formulation and, in particular, it reduces the functional of the internal potential energy by expressing the field of the average volume-change in terms of the displacement field, where the latter is discretized using the Wachspress shape functions. The reduced mixed formulation eliminates the volumetric locking in nearly incompressible materials and enhances the computational efficiency as the static condensation is circumvented. A detailed implementation of the finite element formulation is presented in this study. Also, different example problems, including eigenvalue analysis, nonlinear patch test and other benchmark problems are presented for demonstrating the accuracy and the reliability of the developed formulation for polygonal elements.

中文翻译：

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用于模拟几乎不可压缩材料的多边形有限元公式

本论文的目的是开发一种有限元公式，用于使用多边形单元对大应变下几乎不可压缩的材料进行建模。目前的有限元公式是三场混合公式的简化版本，特别是它通过用位移场表示平均体积变化场来减少内部势能的泛函，其中后者使用 Wachspress 形状函数进行离散化。简化的混合公式消除了几乎不可压缩材料中的体积锁定，并在避免静态冷凝时提高了计算效率。本研究介绍了有限元公式的详细实施。此外，不同的示例问题，包括特征值分析，