Hyperplastic homogenized law for reinforced elastomer at finite strain with edge effects
Hyperplastic homogenized law for reinforced elastomer at finite strain with edge effects
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DOI：
10.1007/bf01176742
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发表时间：
1998-01-01
期刊：
影响因子：
2.7
通讯作者：
Pruchnicki, E
中科院分区：
文献类型：
--
作者：
Pruchnicki, E
本文研究了周期超弹性复合材料在有限应变下的静力微观结构效应。在距离边界足够远的区域，采用经典的双尺度渐近均匀化过程，并假设弹性体的近不可压缩。本文给出了周期性分层复合材料的应用。这种均匀化演化规律是在规定的宏观变形梯度上确定的。采用迭代Newton-Raphson格式求解该问题。在假定弹性体和钢分别服从Mooney-Rivlin和StVenant-Kirchhoff定律的情况下，分析了弹性体/钢复合材料的性能。然后，我们研究了用Taylor-Young展开近似局部第一Piola-Kirchhoff张量得到的这一均匀化定律简化公式的有效性。在新hookean组分的情况下，我们表明连续统均匀化模型可以解析确定。由于经典渐近在边界的邻域中不成立，我们通过引入边界层展开来修正该区域内的微力学量。这样，分别只处理一个边界和两个边界的影响。
This paper investigates the static microstructural effects of periodic hyperelastic composites at finite strain. In the region far enough from the boundaries, the classic two-scale asymptotic homogenization process is used with the assumption of near incompressibility of the elastomer. An application of this approach is given using periodically stratified composites. This homogenized evolution law is determined on a prescribed macroscopic deformation gradient. An iterative Newton-Raphson's scheme is used in solving this problem. The behavior of an elastomer/steel composite is analysed when elastomer and steel are respectively assumed to obey the Mooney-Rivlin and StVenant-Kirchhoff laws. We then study the validity of simplified formulations of this homogenized law obtained by approximating the local first Piola-Kirchhoff tensor with a Taylor-Young's expansion. In the case of neo-Hookean constituents, we show that the continuum homogenized model can be determined analytically. Since the classic asymptotic is not valid in the neighbourhood of the boundaries, we modify the micromechanical quantities in such a region by introducing a boundary layer expansion. In this way, the effects of respectively only one boundary and two boundaries are treated.