Effective balance equations for electrostrictive composites
Effective balance equations for electrostrictive composites
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DOI：
10.1007/s00033-020-01365-x
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发表时间：
2020-09-22
影响因子：
2
通讯作者：
Penta, Raimondo
中科院分区：
文献类型：
--
作者：
Di Stefano, Salvatore;Miller, Laura;Penta, Raimondo
本文研究了线弹性电致伸缩复合材料的有效平衡方程，在该平衡方程中，在所谓的小应变和中等电场范围内，由于施加一个给定的电场，可以观察到机械应变。该公式是在主动弹性复合材料的框架内发展起来的。后者被定义为复合材料，由应力张量的加法分解为纯线弹性贡献和另一个分量，当进一步专门用于电致伸缩复合材料时，假定该分量是给定的且在外加电场中为二次分量。通过用theasymptotic(periodic)homogenisationtechnique.描述整个材料的有效力学行为，得到了新的数学模型我们假设，在微观尺度和宏观尺度之间存在明显的分离，微观尺度解决了不同亚相(即夹杂物和/或纤维和/或层)之间的距离，而宏观尺度与手头整个系统的平均尺寸有关。这样，我们通过假设每个物理场和材料属性都取决于宏观尺度和微观尺度，对空间变化进行形式分解。有效的控制方程编码了微结构的作用，对整体应力张量的有效贡献通过求解周期单元上的适当的线弹性单元问题来计算。我们还给出了电致伸缩张量的解析公式，当外加电场在微观上是均匀的，或者由纯微观和宏观变化的分量之间的适当乘法分解给出时。所获得的结果与该领域以前的工作进行了一致的比较，并为改进目前用于工程(可能是生物启发)目的的智能活性材料铺平了道路。
This work concerns the study of the effective balance equations governing linear elasticelectrostrictive composites, where mechanical strains can be observed due to the application of a given electric field in the so-calledsmall strain and moderate electric field regime. The formulation is developed in the framework of theactive elastic composites. The latter are defined as composite materials constitutively described by an additive decomposition of the stress tensor into a purely linear elastic contribution and another component, which is assumed to be given and quadratic in the applied electric field when further specialised to electrostrictive composites. We derive the new mathematical model by describing the effective mechanical behaviour of the whole material by means of theasymptotic(periodic)homogenisationtechnique. We assume that there exists a sharp separation between themicro-scale, where the distance among different sub-phases (i.e. inclusions and/or fibres and/or strata) is resolved, and themacro-scale, which is related to the average size of the whole system at hand. This way, we formally decompose spatial variations by assuming that every physical field and material property are depending on both the macro-scale and the micro-scale. The effective governing equations encode the role of the micro-structure, and the effective contributions to the global stress tensor are to be computed by solving appropriate linear-elastic-type cell problems on the periodic cell. We also provide analytic formulae for the electrostrictive tensor when the applied electric field is either microscopically uniform or given by a suitable multiplicative decomposition between purely microscopically and macroscopically varying components. The obtained results are consistently compared with previous works in the field, and can pave the way towards improvement of smart active materials currently utilised for engineering (possibly bio-inspired) purposes.