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TFA and HS based homogenization techniques for nonlinear composites
International Journal of Solids and Structures ( IF 3.6 ) Pub Date : 2021-04-16 , DOI: 10.1016/j.ijsolstr.2021.111050
Alfredo Castrogiovanni , Sonia Marfia , Ferdinando Auricchio , Elio Sacco

The paper presents two reduced order homogenization techniques for studying the response of nonlinear composite materials. The first approach is based on Transformation Field Analysis, which considers the presence of eigenstrains to account for inelastic strains, while the second approach is derived from Hashin–Shtrikman variational principle, which introduces eigenstresses, namely polarization stresses, on a homogeneous elastic reference material to account for the heterogeneity and the inelastic response. In particular, the case of elasto-plastic periodic composites is investigated. A Unit Cell is identified and divided in subsets. In each subset, the eigenstrains or eigenstresses are assumed uniform. A very effective technique is derived for the Hashin–Shtrikman approach updating the elastic reference material properties during the inelastic strain evolution. Numerical procedures are implemented to derive the nonlinear response of composites with plastic constituents. Several numerical applications are carried out to assess the effectiveness of the two presented reduced order models. A deep investigation on the differences and similarities of the two approaches is presented, proving their equivalence under particular circumstances. Simple and complex loading histories are considered, comparing the results with a finite element solution, considered as the reference solution.



中文翻译:

基于TFA和HS的非线性复合材料均质化技术

本文提出了两种用于研究非线性复合材料响应的降阶均质技术。第一种方法基于“转换场分析”,它考虑了本征应变的存在以解决非弹性应变,而第二种方法则源自Hashin–Shtrikman变分原理,该原理引入了均质弹性基准材料上的本征应力,即极化应力。解释了异质性和非弹性响应。特别是,研究了弹塑性周期性复合材料的情况。识别单位晶胞并将其划分为子集。在每个子集中,假设本征应变或本征应力是均匀的。Hashin–Shtrikman方法获得了一种非常有效的技术,可在非弹性应变演化过程中更新弹性参考材料的特性。实施了数值程序以导出具有塑料成分的复合材料的非线性响应。进行了几个数值应用程序来评估两个提出的降阶模型的有效性。对这两种方法的异同进行了深入研究,证明了它们在特定情况下的等效性。考虑简单和复杂的加载历史,将结果与有限元解决方案(被视为参考解决方案)进行比较。进行了几个数值应用程序来评估两个提出的降阶模型的有效性。对这两种方法的异同进行了深入研究,证明了它们在特定情况下的等效性。考虑简单和复杂的加载历史,将结果与有限元解决方案(被视为参考解决方案)进行比较。进行了几个数值应用程序来评估两个提出的降阶模型的有效性。对这两种方法的异同进行了深入研究,证明了它们在特定情况下的等效性。考虑简单和复杂的加载历史,将结果与有限元解决方案(被视为参考解决方案)进行比较。

更新日期:2021-05-04
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