A new mixed finite element based on different approximations of the minors of deformation tensors

Jorg Schroder; Peter Wriggers; Daniel Balzani

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A new mixed finite element based on different approximations of the minors of deformation tensors

机译：基于变形张量的次要近似的新混合有限元

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Finite element formulations for arbitrary hyperelastic strain energy functions that are characterized by a locking-free behavior for incompressible materials, a good bending performance and accurate solutions for coarse meshes need still attention. Therefore, the main goal of this contribution is to provide an improved mixed finite element for quasi-incompressible finite elasticity. Based on the knowledge that the minors of the deformation gradient play a major role for the transformation of infinitesimal line-, area- and volume elements, as well as in the formulation of polyconvex strain energy functions a mixed finite element with different interpolation orders of the terms related to the minors is developed. Due to the formulation it is possible to condensate the mixed element formulation at element level to a pure displacement form. Examples show the performance and robustness of the element.

机译：用于任意超弹性应变能函数的有限元公式化，其特征在于不可压缩材料的无锁定行为，良好的弯曲性能和针对粗网格的精确解决方案仍然值得关注。因此，这一贡献的主要目的是为准不可压缩的有限弹性提供一种改进的混合有限元。基于这样的认识，即变形梯度的次要因素在无穷小线，面积和体积元素的转换中起着重要作用，并且在多凸应变能的公式化中，具有不同插值阶数的混合有限元制定了与未成年人有关的术语。由于该配方，可以将混合的元素配方在元素水平上冷凝为纯置换形式。实例显示了该元件的性能和耐用性。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2011年第52期|p.3583-3600|共18页
作者
Jorg Schroder; Peter Wriggers; Daniel Balzani;
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作者单位

Institut fuer Mechanik, Fakultaet fuer Ingenieurwissenschaften, Abteilung Bauwissenschaften, Universitaet Duisburg-Essen, Universitaetsstr. 15, 45117 Essen, Germany;

Institut fuer Kontinuumsmechanik, Fakultaet fuer Maschinenbau, Leibniz Universitaet Hannover, Appelstr. 11, 30167 Hannover, Germany;

Institut fuer Mechanik, Fakultaet fuer Ingenieurwissenschaften, Abteilung Bauwissenschaften, Universitaet Duisburg-Essen, Universitaetsstr. 15, 45117 Essen, Germany;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
mixed finite elements; quasi-incompressible elasticity; anisotropy; polyconvexity;

机译：混合有限元准不可压缩弹性各向异性多凸性;

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A new mixed finite element based on different approximations of the minors of deformation tensors

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