Abstract This work provides an analytical method for determining the time-dependent effective constitutive response of linear viscoelastic composites with particulate microstructures by means of a differential-algebraic system (DAS) of equations. By making use of differential equations instead of difference equations and utilizing, as primary variables, the variances of the field fluctuations instead of the properties of fictitious linear comparison composites, the new formulation is found to be more robust and to alleviate some of the issues associated with earlier incremental approaches. Remarkably, the new formulation can be shown to recover the exact results of the correspondence principle for isotropic incompressible composites subjected to proportional loading, as well as for isotropic compressible composites subjected to purely hydrostatic loading. More generally, the proposed formulation is not exact but still delivers reasonably accurate estimates in most cases. Lastly, a generalization of the DAS formulation is provided for nonlinear viscoelastic composites with incompressible phases and also found to be more robust than earlier approaches.

中文翻译：

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一种估计颗粒粘弹性复合材料宏观响应和场统计的微分均匀化方法

摘要 这项工作提供了一种通过微分代数系统 (DAS) 方程确定具有颗粒微结构的线性粘弹性复合材料随时间变化的有效本构响应的分析方法。通过使用微分方程而不是差分方程，并利用场波动的方差作为主要变量，而不是虚拟线性比较复合物的特性，发现新公式更加稳健并减轻了一些相关问题使用早期的增量方法。值得注意的是，新公式可以显示出在比例载荷作用下各向同性不可压缩复合材料的对应原理的准确结果，以及承受纯静水载荷的各向同性可压缩复合材料。更一般地说，提议的公式并不准确，但在大多数情况下仍能提供相当准确的估计。最后，为具有不可压缩相的非线性粘弹性复合材料提供了 DAS 公式的推广，并且还发现它比早期方法更稳健。