Abstract With the increasing popularity of nanocomposites appears the necessity of the development of efficient modelization procedures. In particular, numerical strategies have to be developed to reproduce and predict the size effect observed on such materials. Usually, the size effect is taken into account by introducing a surface elasticity at the interface between the nano-inclusions and the matrix. Whereas a lot of works have been developed from the analytical point of view, few contributions are related to numerical description and implementation of such surface elasticity in Finite Element codes. In this work, we present a comparative study between two different numerical approaches of the literature namely XFEM [1] and interface element [2]. For a fair comparison, these two approaches have been implemented in the same framework, considering the same element topology. After validation of the implemented strategies, we investigate, in particular, the influence of the homogenization hypothesis in terms of boundary conditions on the computed effective mechanical properties. The comparison in the present work gives an evaluation of the two studied approaches and it is expected to be a good basis to elaborate an optimal numerical computation method.

中文翻译：

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纳米复合材料中的尺寸效应：XFEM/水平集方法和界面元素方法

摘要 随着纳米复合材料的日益普及，出现了开发高效建模程序的必要性。特别是，必须开发数值策略来重现和预测在此类材料上观察到的尺寸效应。通常，通过在纳米夹杂物和基体之间的界面处引入表面弹性来考虑尺寸效应。尽管已经从分析的角度开展了大量工作，但很少有贡献与有限元代码中这种表面弹性的数值描述和实现有关。在这项工作中，我们对文献的两种不同数值方法进行了比较研究，即 XFEM [1] 和界面元素 [2]。为了公平比较，这两种方法已在同一框架中实现，考虑相同的元素拓扑。在验证所实施的策略后，我们特别研究了均质化假设在边界条件方面对计算出的有效机械性能的影响。目前工作中的比较对两种研究方法进行了评估，有望为阐述最佳数值计算方法奠定良好的基础。