Abstract This work is concerned with multiscale analysis of nano-reinforced heterogeneous materials. Such materials exhibit surface effects that are typically taken into account through interface models in mean-field homogenization theories. However, both experiments and numerical simulations demonstrate the existence of a perturbed area at the boundary between the inclusion and the matrix phase. This area is modeled as an interphase whose elastic properties randomly fluctuate from point to point and must be characterized from a probabilistic standpoint. In this study, we therefore address (i) the stochastic modeling of the interphase and (ii) the study of the relationship between the random interphase model and a deterministic interface model. The aim of this work is twofold. First of all, we are interested in constructing a probabilistic model for the matrix-valued random field, modeling the elastic properties of the interphase. Then, this model is used to perform a parametric study for the apparent tensor associated with the microstructure. Simulations are specifically used to characterize the influence of both the random interphase and interface models on the material’s overall properties. When the interface model is consistent from a physical point of view, the associated elastic surface properties are computed by solving an optimization problem involving the effective properties of the random medium.

中文翻译：

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纳米增强材料表面效应的概率建模

摘要 这项工作涉及纳米增强异质材料的多尺度分析。这种材料表现出的表面效应通常通过平均场均匀化理论中的界面模型加以考虑。然而，实验和数值模拟都表明在夹杂物和基体相之间的边界处存在扰动区域。该区域被建模为一个界面，其弹性特性随机地从点到点波动，必须从概率的角度进行表征。因此，在本研究中，我们解决 (i) 界面的随机建模和 (ii) 随机界面模型与确定性界面模型之间关系的研究。这项工作的目的是双重的。首先，我们有兴趣为矩阵值随机场构建概率模型，对界面的弹性特性进行建模。然后，该模型用于对与微观结构相关的表观张量进行参数研究。模拟专门用于表征随机界面和界面模型对材料整体属性的影响。当界面模型从物理角度一致时，通过求解涉及随机介质有效属性的优化问题来计算相关的弹性表面属性。模拟专门用于表征随机界面和界面模型对材料整体属性的影响。当界面模型从物理角度一致时，通过求解涉及随机介质有效属性的优化问题来计算相关的弹性表面属性。模拟专门用于表征随机界面和界面模型对材料整体属性的影响。当界面模型从物理角度一致时，通过求解涉及随机介质有效属性的优化问题来计算相关的弹性表面属性。