In this article, the 3D viscoelastic computational grains (CGs) with spherical inclusions, with and without interphases/coatings are developed to study the viscoelastic behavior of polymer-based heterogeneous materials. Papkovich–Neuber solutions and spherical harmonics are adopted to develop the independent displacement fields inside the grains, and Wachspress coordinate is used to interpolate compatible displacement fields at inter-element surfaces. The elemental stiffness matrices are developed with multi-field boundary variational principles in the Laplace domain, after which Zakian technique is adopted to invert both the homogenized and localized responses back to the time domain with good accuracy and efficiency. With different kinds of models to describe the property of the viscoelastic polymers, the generated homogenized moduli and localized stress distributions are validated against the experimental data, simulations by commercial FE software, and predictions by composite spherical assemblage models. Parametric studies are also carried out to investigate the influence of material and geometric parameters on the behavior of viscoelastic composites. Finally, the viscoelastic CG is also used to study the effect of the negative Young's modulus of particles on the stability and loss tangent of viscoelastic composites.

中文翻译：

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具有或不具有界面/涂层的球形夹杂物的 3D 粘弹性计算晶粒，用于异质材料的微观力学建模

在本文中，开发了带有和不带有界面/涂层的球形夹杂物的 3D 粘弹性计算晶粒 (CG)，以研究基于聚合物的异质材料的粘弹性行为。Papkovich-Neuber 解和球谐函数用于开发晶粒内部的独立位移场，Wachspress 坐标用于插值单元间表面的兼容位移场。单元刚度矩阵是在拉普拉斯域中使用多场边界变分原理开发的，之后采用 Zakian 技术将均匀化和局部化的响应以良好的精度和效率反演回时域。用不同的模型来描述粘弹性聚合物的特性，生成的均质模量和局部应力分布根据实验数据、商业有限元软件的模拟以及复合球形组合模型的预测进行验证。还进行了参数研究，以研究材料和几何参数对粘弹性复合材料行为的影响。最后，粘弹性 CG 还用于研究颗粒的负杨氏模量对粘弹性复合材料的稳定性和损耗角正切的影响。