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Nonlinear analyses with a micromorphic computational homogenization framework for composite materials

机译：用于复合材料的微晶计算均质化框架的非线性分析

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摘要

A small deformation micromorphic computational homogenization framework for matrix-inclusion composites was recently presented in Biswas and Poh (2017), where standard continuum models at the micro-scale are translated consistently onto the macro-scale to recover a micromorphic continuum. In this contribution, the micromorphic framework is extended to the regime of significant geometrical and material nonlinearities. Following the small deformation framework, an additional degree of freedom is introduced to capture the influence of rapid fluctuations within a unit cell. In this contribution, we elaborate on the specific choice of decomposition for the kinematic fields, where certain higher-order modes are deliberately neglected. Several examples are considered to illustrate the influence of different higher-order modes, and how the corresponding size effect emerges naturally in the homogenized micromorphic model. In the regime of geometrical softening, the higher order term provides a regularizing effect to give mesh independent solutions, albeit with a stiffer response. A detailed discussion on this phenomenon is provided. The homogenization framework is implemented using a client-server based parallel processing algorithm to reduce the computational time. The excellent predictive capability and efficiency of the micromorphic approach are demonstrated with a mixed loading problem on a composite plate with non-uniform cross-section. Furthermore, the micromorphic solutions are shown to be independent of the choice of a unit cell. (C) 2019 Elsevier B.V. All rights reserved.
机译：最近介绍了用于基质包合物的小变形微观计算均化框架，并且在BISWAS和POH（2017）中呈现，其中微尺度的标准连续体型始终转换为宏观级以回收微观连续体。在这一贡献中，微立框架延伸到重要的几何和材料非线性的方案。在小变形框架之后，引入了额外的自由度以捕获单元电池内快速波动的影响。在这一贡献中，我们详细阐述了运动场的特定选择，其中特定的高阶模式是故意忽略的。认为有几个例子是说明不同高阶模式的影响，以及如何在均质微观模型中自然出现的相应尺寸效应。在几何软化的制度中，较高的阶项提供了正规化效果，以提供网状独立解决方案，尽管具有更纤巧的反应。提供了关于这种现象的详细讨论。使用基于客户端 - 服务器的并行处理算法来实现均化框架以减少计算时间。微观方法的优异预测能力和效率在具有非均匀横截面的复合板上进行了混合的装载问题。此外，显示微晶溶液与单位细胞的选择无关。 （c）2019 Elsevier B.v.保留所有权利。

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