Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity
Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity
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DOI：
10.1016/j.ijnonlinmec.2012.09.001
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发表时间：
2013-03-01
影响因子：
3.2
通讯作者：
Goriely, Alain
中科院分区：
文献类型：
--
作者：
Mihai, L. Angela;Goriely, Alain
提出了非线性弹性中不同剪切变形的有限元模拟。我们特别关注超弹性材料中的坡印廷效应，通过展示特定模型表现的这些效应来补充最近的理论发现。由于有限元方法可以准确计算均匀变形，因此对于简单剪切变形和纯剪应力，可以准确地表示坡印廷效应，而对于变形不均匀的广义剪切和简单扭转，可以有效地逼近解，并保证获得坡印廷效应大小的计算界限。数值结果进一步表明，对于给定的弹性材料，在不同的剪切机制下会出现相同的符号效应，显示了坡印廷效应在各种剪切载荷下的通用性。为了导出表现出正坡印廷效应或负坡印廷效应的数值模型，假设了所谓的广义经验不等式，它比涉及材料参数的通常经验不等式限制较少。 (C) 2012 Elsevier Ltd. 保留所有权利。
Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. (C) 2012 Elsevier Ltd. All rights reserved.