Efficient two–scale simulations of engineering structures using the Hashin–Shtrikman type finite element method
Efficient two–scale simulations of engineering structures using the Hashin–Shtrikman type finite element method
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DOI：
10.1007/s00466-019-01758-4
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发表时间：
2019-08
影响因子：
4.1
通讯作者：
Fabiola Cavaliere;S. Reese;S. Wulfinghoff
中科院分区：
文献类型：
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作者：
Fabiola Cavaliere;S. Reese;S. Wulfinghoff
利用Hashin-Shtrikman型有限元（HSFE）方法求解微尺度问题，提出了一种有效的非线性微结构FE 2类数值均匀化方法。后者结合了Hashin-Shtrikman型均匀化方法的小计算量和全场FE解的准确性。关键点是一个降阶方法的基础上的Hashin-Shtrikman型变分公式结合数据聚类，这是基于离线有限元模拟的微观结构（快照）。所提出的微观模型具有显着较少的微观自由度相比，经典的FE 2-方法。在微观结构内的应力计算的数量大大减少。切算子，它结合了微观和宏观尺度之间的耦合，推导出解析。不同的数值例子进行了研究，其中一个非线性RVE附加到每个积分点的宏观结构。与全场有限元模拟的比较表明，HSFE方法可以很好地捕获宏观响应和局部场。
An efficient FE2-like numerical homogenization approach for nonlinear microstructures is proposed using the Hashin–Shtrikman type finite element (HSFE) method to solve the microscale problem. The latter combines the small computational effort of Hashin–Shtrikman type homogenization approaches with the accuracy of full-field FE-solutions. The key point is a reduced order method based on a Hashin–Shtrikman type variational formulation combined with data-clustering, which is based on offline FE-simulations of microstructures (snapshots). The presented microscopic model has significantly less microscopic degrees of freedom in comparison to the classic FE2-method. The number of stress computations within the microstructure is highly reduced. The tangent operator, which incorporates the coupling between the microscopic and macroscopic scale, is derived analytically. Different numerical examples are investigated, where a nonlinear RVE is attached to each integration point of a macrostructure. A comparison to full-field FE-simulations shows that the macro-response and local fields are well captured by the HSFE method.