高对比度介电弹性体复合材料的均匀化
Homogenization of high-contrast dielectric elastomer composites
AI总结：
本文研究高对比度介电弹性体复合材料的均匀化问题，通过分析含刚性颗粒的非均质材料的电-弹性弱耦合系统，推导得到均质化PDE系统，揭示了高对比度系数会引发非局部效应。
摘要：
本文聚焦高对比度介电弹性体复合材料的均匀化问题，这类材料可响应电刺激发生形变。所研究的非均质材料由基体材料嵌入颗粒构成，由静电方程与附加电致伸缩项的弹性方程组成的弱耦合系统描述。研究假设当细尺度参数趋近于零时，颗粒逐渐变为刚性。研究表明，该系统的等效响应对应一种均质介电弹性体，由偏微分方程（PDE）的弱耦合系统描述。均匀化方程的系数受多种因素影响，包括复合材料的几何结构、原始微结构的周期性，以及表征初始非均质材料的系数。尤其值得注意的是，这些系数受细尺度问题系数的高对比度特性显著影响。因此，正如预期，原始材料的高对比度系数会在均匀化响应中产生非局部效应。
英文摘要：
This paper focuses on the homogenization of high-contrast dielectric elastomer composites, materials that deform in response to electrical stimulation. The considered heterogeneous material consisting of an ambient material with inserted particles is described by a weakly coupled system of an electrostatic equation with an elastic equation enriched with electrostriction. It is assumed that particles gradually become rigid as the fine-scale parameter approaches zero. This study demonstrates that the effective response of this system entails a homogeneous dielectric elastomer, described by a weakly coupled system of PDEs. The coefficients of the homogenized equations are dependent on various factors, including the composite's geometry, the original microstructure's periodicity, and the coefficients characterizing the initial heterogeneous material. Particularly, these coefficients are significantly influenced by the high-contrast nature of the fine-scale problem's coefficients. Consequently, as anticipated, the high-contrast coefficients of the original yield non-local effects in the homogenized response.
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