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首页> 外文期刊>International Journal of Solids and Structures >The helicoidal modeling in computational finite elasticity. Part III: Finite element approximation for non-polar media
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The helicoidal modeling in computational finite elasticity. Part III: Finite element approximation for non-polar media

机译：计算有限弹性中的螺旋建模。第三部分：非极性介质的有限元近似

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The helicoidal modeling of the continuum, as proposed in Part 1, is applied to finite elasticity analyses of simple materials unable of couple-stressing. First, the non-polar medium is introduced via a constitutive postulate and results in a sort of constrained medium, having the axial vector of the Biot stress tensor as a primary unknown field and the statement of polar decomposition of the deformation gradient as a governing equation. Next, the variational formulation is accommodated to the non-polar case, and the ensuing principle is approximated by the finite element method. The nonlinear finite elements have the nodal oriento-positions as degrees-of-freedom and are based on the multiplicative interpolation developed in Part H. The interpolation and an analysis methodology based on the multiplicative updating of the kinematical unknowns, ensure frame-invariant and path-independent solutions. Several examples, with either linear or nearly incompressible Neo-Hookean elastic materials, attest the performance of the proposed modeling in high deformation problems with large three-dimensional rototranslations. (c) 2005 Elsevier Ltd. All rights reserved.
机译：如第1部分所述，连续体的螺旋模型适用于无法耦合应力的简单材料的有限弹性分析。首先，通过本构假设引入非极性介质，并产生一种受约束的介质，其中以毕奥特应力张量的轴向向量为主要未知场，并且以变形梯度的极性分解陈述为控制方程。接下来，将变分公式适应非极性情况，并通过有限元方法近似其原理。非线性有限元具有自由度的节点定向位置，并且基于在H部分中开发的乘法插值。基于运动未知数的乘法更新的插值和分析方法可确保帧不变性和路径独立解决方案。线性或几乎不可压缩的新霍克弹性材料的几个例子证明了所提出的模型在具有大尺寸三维旋转平移的高变形问题中的性能。 （c）2005 Elsevier Ltd.保留所有权利。

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