Polygonal finite elements for finite elasticity
Polygonal finite elements for finite elasticity
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DOI：
10.1002/nme.4802
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发表时间：
2015-01-27
影响因子：
2.9
通讯作者：
Paulino, Glaucio H.
中科院分区：
文献类型：
--
作者：
Chi, Heng;Talischi, Cameron;Paulino, Glaucio H.
非线性弹性材料具有很大的工程意义，但用标准有限元建模具有挑战性。之所以出现挑战，是因为非线性弹性材料具有非凸存储能量函数的特征，因为它们能够承受大的可逆变形，不可压缩或几乎不可压缩，并且通常具有复杂的微观结构。在这项工作中，我们提出并探索了一种使用多边形离散化来模拟二维有限弹性问题的替代方法。我们提出了基于低阶位移的有限元近似和混合多边形有限元近似，后者由分段恒压场和单元级的线性完整位移场组成。通过数值研究，表明混合多边形有限元是稳定且收敛的。出于演示目的，我们部署了所提出的多边形离散化来研究填充有随机和周期性分布的刚性颗粒的橡胶的非线性弹性响应，以及包含空洞缺陷的弹性体中空化不稳定性的发展。这些基于物理的示例说明了多边形有限元在研究和建模有限变形下具有复杂微结构的非线性弹性材料方面的潜力。版权所有 (c) 2014 约翰·威利父子有限公司
Nonlinear elastic materials are of great engineering interest, but challenging to model with standard finite elements. The challenges arise because nonlinear elastic materials are characterized by non-convex stored-energy functions as a result of their ability to undergo large reversible deformations, are incompressible or nearly incompressible, and often times possess complex microstructures. In this work, we propose and explore an alternative approach to model finite elasticity problems in two dimensions by using polygonal discretizations. We present both lower order displacement-based and mixed polygonal finite element approximations, the latter of which consist of a piecewise constant pressure field and a linearly-complete displacement field at the element level. Through numerical studies, the mixed polygonal finite elements are shown to be stable and convergent. For demonstration purposes, we deploy the proposed polygonal discretization to study the nonlinear elastic response of rubber filled with random and periodic distributions of rigid particles, as well as the development of cavitation instabilities in elastomers containing vacuous defects. These physically-based examples illustrate the potential of polygonal finite elements in studying and modeling nonlinear elastic materials with complex microstructures under finite deformations. Copyright (c) 2014 John Wiley & Sons, Ltd.