论文标题
非线性弹性的三场混合有限元方法
Three-field mixed finite element methods for nonlinear elasticity
论文作者
论文摘要
在本文中，我们将切向置换正常正常压力连续（TDNN）方法从[26]扩展到非线性弹性。通过Hu-washizu原理，位移载体的分离衍生物被提升为常规应变张量。我们引入了三种不同的方法，其中变形梯度，考奇绿应变张量或两者都用作自变量。在线性子问题中，只能在局部消除所有应力和应变变量，从而导致位移变量中的方程式系统。通过几个数值示例证明了提出方法的良好性能和准确性（可通过www.gitlab.com/mneunteufel/nonlinelear_elasticity获得）。
In this paper, we extend the tangential-displacement normal-normal-stress continuous (TDNNS) method from [26] to nonlinear elasticity. By means of the Hu-Washizu principle, the distibutional derivatives of the displacement vector are lifted to a regular strain tensor. We introduce three different methods, where either the deformation gradient, the Cauchy-Green strain tensor, or both of them are used as independent variables. Within the linear sub-problems, all stress and strain variables can be locally eliminated leading to an equation system in displacement variables, only. The good performance and accuracy of the presented methods are demonstrated by means of several numerical examples (available via www.gitlab.com/mneunteufel/nonlinear_elasticity).
