Abstract We study the interplay between the material composition and deformation in dielectric elastomer (DE) composites with periodically and randomly distributed particles embedded in a soft matrix. We focus on the deformation-induced tunability of the effective permittivity in DE composites. We examine the effects of microstructural periodicity and its transition towards random distribution. In particular, we analyze the DE composites with periodic microstructures of (a) circular and (b) elliptical inclusions, (c) pair of inclusions, and (d) randomly distributed inclusions with different numbers of the particles in the unit cell. The finitely deformed DE composites with ideal dielectric elastomer constituents are analyzed numerically. In addition, for the periodic DE composites with circular inclusions, we derive an explicit relation between the effective permittivity and stretch. The effective permittivity of DE composites with periodic microstructures changes with deformation, whereas in DE composites with randomly distributed inclusions, the permittivity is barely affected by deformation. For the latter case, the effective permittivity attains a certain value as the number of particles in the periodic cell increases. To provide the insights on the composite behavior, a two-particle periodic system is examined. The permittivity is found to be sensitive to the orientation of the pairs with respect to the applied electric field, and the distance between the particles. The geometrical effects amplify significantly as the inter-particle distance becomes less than their two diameters. Finally, we illustrate the permittivity tunability in DE periodic porous composites structures experiencing elastic instabilities.

中文翻译：

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有限应变下介电弹性体复合材料的可调介电常数：周​​期性、随机性和不稳定性。

摘要 我们研究了介电弹性体 (DE) 复合材料中的材料成分与变形之间的相互作用，该复合材料具有嵌入软基质中的周期性和随机分布的颗粒。我们专注于 DE 复合材料中有效介电常数的变形诱导可调性。我们研究了微观结构周期性的影响及其向随机分布的转变。特别地，我们分析了具有周期性微观结构的 DE 复合材料：（a）圆形和（b）椭圆形夹杂物，（c）一对夹杂物，（d）在晶胞中具有不同数量颗粒的随机分布的夹杂物。对具有理想介电弹性体成分的有限变形 DE 复合材料进行了数值分析。此外，对于具有圆形夹杂物的周期性 DE 复合材料，我们推导出有效介电常数和拉伸之间的明确关系。具有周期性微观结构的 DE 复合材料的有效介电常数随变形而变化，而在具有随机分布的夹杂物的 DE 复合材料中，介电常数几乎不受变形的影响。对于后一种情况，有效介电常数随着周期单元中粒子数量的增加而达到某个值。为了提供对复合行为的见解，检查了一个两粒子周期系统。发现介电常数对相对于所施加电场的对的方向以及粒子之间的距离很敏感。随着粒子间距离变得小于它们的两个直径，几何效应显着放大。最后，