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【6h】 Computational stability analysis of periodic electroactive polymer composites across scales

机译周期性电活性聚合物复合材料跨尺度的计算稳定性分析

【摘要】This paper is devoted to the multiscale stability analysis of periodic electroactive polymer composites at finite deformations. A particular focus is on the investigation of macroscopic loss of strong ellipticity and microscopic bifurcation-type instabilities. Macroscopic homogenized quantities are determined by use of computational homogenization over selected representative volume elements (RVE). The quasi-incompressible nature of the electroactive polymers is taken into account by considering a four-field variational formulation at micro-level. This formulation includes continuous interpolations of displacement fields and electric vector potentials as well as discontinuous interpolations of pressure and dilatation terms, yielding a saddle-point principle for coupled problems. Static condensation of the terms related to the element-wise constant pressure and dilatation results in a positive definite global microscopic stiffness matrix until a microscopic instability occurs. The microstructure is embedded into a macroscopic driving procedure that imposes periodic mechanical and electrical boundary conditions on the surface of the RVEs. It is known that at certain finite deformations the initial periodicity of microstructures might be altered due to microscopic bifurcation-type instabilities. To incorporate microscopic instabilities and to determine the critical periodicity of microstructures, Bloch-Floquet wave analysis in the context of a finite element discretization is implemented. The macroscopic instabilities, which are related to the long-wavelength microscopic instabilities, are determined by checking the loss of strong ellipticity at macro-scale. The proposed setting is used to study the multiscale stability analysis of electroactive polymer composites with embedded fibers. The influence of fiber volume fraction and aspect ratio of fiber cross sections on instabilities are investigated in detail. Critical periodicities and bifurcation modes are demonstrated for selected boundary value problems. (C) 2018 Elsevier B.V. All rights reserved.

【摘要机译】本文致力于周期性电活性聚合物复合材料在有限变形下的多尺度稳定性分析。特别关注的是宏观椭圆形强椭圆损失和微观分叉型不稳定性的研究。宏观均质化量是通过对选定的代表性体积元素(RVE)进行计算均质化来确定的。电活性聚合物的准不可压缩性质是通过在微观水平上考虑四场变化公式来考虑的。该公式包括位移场和矢量电势的连续插值,以及压力和膨胀项的不连续插值,从而得出耦合问题的鞍点原理。与单元式恒定压力和膨胀有关的术语的静态缩合会导致正确定的全局微观刚度矩阵,直到出现微观不稳定性为止。微观结构被嵌入到宏观驱动程序中,该程序在RVE的表面施加周期性的机械和电气边界条件。已知在某些有限变形下,微观结构的初始周期性可能由于微观分叉型不稳定性而改变。为了纳入微观不稳定性并确定微观结构的临界周期性,在有限元离散化的背景下进行了Bloch-Floquet波分析。与长波长微观不稳定性有关的宏观不稳定性是通过检查宏观尺度上强椭圆率的损失来确定的。拟议的设置用于研究嵌入纤维的电活性聚合物复合材料的多尺度稳定性分析。详细研究了纤维体积分数和纤维横截面的长径比对不稳定性的影响。对于选定的边值问题,证明了临界周期和分叉模式。 (C)2018 Elsevier B.V.保留所有权利。

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机译 均质化;机电;多尺度稳定性; Rank-one凸度;屈曲;电活性高分子复合材料;
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