Comparison of geometrically nonlinear LSFEM formulations based on different hyperelastic models
Comparison of geometrically nonlinear LSFEM formulations based on different hyperelastic models
复制标题
基于不同超弹性模型的几何非线性LSFEM公式的比较
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
B. Müller
中科院分区：
文献类型：
--
作者：
K. Steeger;A. Schwarz;J. Schröder;G. Starke;B. Müller
这一贡献涉及用最小二乘混合有限元法（LSFEM）求解几何非线性弹性问题。自由度（位移和应力）将使用合适的空间进行近似，即W1，p与p > 4和H（div，Ω）。为了定义材料的应力响应，将提出不同的超弹性自由能函数。动量平衡的残差形式和本构方程构成了一阶微分方程组。选择合适的加权算子并应用L2 -范数得到最小二乘泛函_ （P,u）。未知量的插值是用标准的多项式插值来完成的，用矢量值的Raviart - Thomas函数来逼近应力。提出的公式将考虑单轴空间拉伸试验进行比较。（©2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim）
This contribution deals with the solution of geometrically nonlinear elastic problems solved by the least‐squares mixed finite element method (LSFEM). The degrees of freedom (displacements and stresses) will be approximated using suitable spaces, namely W1,p with p > 4 and H(div,Ω). In order to define the stress response of the material, different hyperelastic free energy functions will be presented. The residual forms ℛI of the balance of momentum and the constitutive equation build a system of differential equations of first order. Choosing suitable weighting operators and applying L2‐norms lead to a least‐squares functional ℱ(P,u). The interpolation of the unknowns is accomplished using a standard polynomial interpolation for the displacements and vector‐valued Raviart‐Thomas functions for the approximation of the stresses. The formulations presented will be compared considering a uni‐axial spatial tension test. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)