A paradigm for higher-order polygonal elements in finite elasticity using a gradient correction scheme

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• 作者：Heng Chi^a ; ^{hchi6@gatech.edu" class="auth_mail" title="E-mail the corresponding author} ; Cameron Talischi^b ; ^{talischi@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Oscar Lopez-Pamies^b ; ^{pamies@illinois.edu" class="auth_mail" title="E-mail the corresponding author} ; Glaucio H. Paulino^a ; ^{paulino@gatech.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Gradient correction ; Finite elasticity ; Quadratic polygonal element ; Mixed variational principle ; Filled elastomers ; Cavitation
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2016
• 出版时间：1 July 2016
• 年：2016
• 卷：306
• 期：Complete
• 页码：216-251
• 全文大小：7415 K

文摘

Recent studies have demonstrated that polygonal elements possess great potential in the study of nonlinear elastic materials under finite deformations. On the one hand, these elements are well suited to model complex microstructures (e.g. particulate microstructures and microstructures involving different length scales) and incorporating periodic boundary conditions. On the other hand, polygonal elements are found to be more tolerant to large localized deformations than the standard finite elements, and to produce more accurate results in bending and shear. With mixed formulations, lower order mixed polygonal elements are also shown to be numerically stable on Voronoi-type meshes without any additional stabilization treatment. However, polygonal elements generally suffer from persistent consistency errors under mesh refinement with the commonly used numerical integration schemes. As a result, non-convergent finite element results typically occur, which severely limit their applications. In this work, a general gradient correction scheme is adopted that restores the polynomial consistency by adding a minimal perturbation to the gradient of the displacement field. With the correction scheme, the recovery of optimal convergence for solutions of displacement-based and mixed formulations with both linear and quadratic displacement interpolants is confirmed by numerical studies of several boundary value problems in finite elasticity. In addition, for mixed polygonal elements, the various choices of the pressure field approximations are discussed, and their performance on stability and accuracy are numerically investigated. We present applications of those elements in physically-based examples including a study of filled elastomers with interphasial effect and a qualitative comparison with cavitation experiments for fiber reinforced elastomers.