Comparison of reduced order homogenization techniques: pRBMOR, NUTFA and MxTFA
Comparison of reduced order homogenization techniques: pRBMOR, NUTFA and MxTFA
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DOI：
10.1007/s11012-017-0814-y
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发表时间：
2018-04-01
期刊：
影响因子：
2.7
通讯作者：
Sacco, E.
中科院分区：
文献类型：
--
作者：
Covezzi, F.;de Miranda, S.;Sacco, E.
复合材料在工程应用中的引入导致需要能够预测机械响应并考虑材料不均匀性的工具，以便安全地设计复杂结构。这些预测需要足够准确，但计算成本低，特别是在处理非线性材料时：对于这些材料，内部变量的数量和计算时间都可能变得非常高。本文详细比较了三种模型降阶均匀化方法：基于势函数的降基模型降阶（pRBMOR）、非均匀变换场分析和混合变换场分析（MxTFA）。所有方法都是在非均匀TFA的框架内开发的，该框架最初由Michel和Suquet介绍。两个说明的方法，pRBMOR和MxTFA，偏离TFA的米歇尔和Suquet，因为它们是基于混合变分制剂。比较将调查的差异和相似性的技术方面的减少的自由度及其演变规律，存储要求和准确性的有效本构行为。三维周期复合材料在复杂的法向和剪切载荷路径下的数值试验将显示该技术的性能。
The introduction of composites in engineering applications led to a need for tools that can predict the mechanical response with account for the heterogeneities in the materials in order to safely design complex structures. These predictions are required to be sufficiently accurate yet computationally inexpensive, especially when dealing with nonlinear materials: for these the amount of internal variables and the computing times can both become prohibitively high. Here, three model order reduction homogenization methods are compared in detail: the potential-based Reduced Basis Model Order Reduction (pRBMOR), the NonUniform Transformation Field Analysis and the Mixed Transformation Field Analysis (MxTFA). All methods are developed in the framework of the Nonuniform TFA, initially introduced by Michel and Suquet. Two of the illustrated methods, the pRBMOR and the MxTFA, deviate from the TFA of Michel and Suquet in that they are based on mixed variational formulations. The comparison will investigate differences and similarities of the techniques in terms of the reduced degrees of freedom and their evolution law, the storage requirements and the accuracy of the effective constitutive behavior. Numerical tests on three-dimensional periodic composites under complex normal and shear loading paths will show the performances of the techniques.