标题： 随机微观结构中残余应力的统计：平均场估计与全场验证 显示英文标题

标题： Statistics of Residual Stress in Random Microstructures: Mean-Field Estimates and Full-Field Validations

摘要： 局部场的波动对于预测不同尺度下随机复合材料的失效以及估计其非弹性行为至关重要。这可以通过局部场的二阶矩进行统计量化，而这些二阶矩可以使用均场均质化（MFH）快速估算。然而，精确的波动场可以通过全场方法进行估算，尽管这需要大量的计算资源，并且难以扩展到复杂的微观结构。在本工作中，MFH被用于估算场量的统计变化，并通过全场方法对线性热弹性均质化问题进行交叉验证。基于Hill-Mandel条件，得到了利用MFH计算线性热弹性问题中局部场二阶矩的解析表达式。这些表达式本质上依赖于线性弹性问题的解，而该解又取决于Hill极化张量的导数。在先前的工作[1]中，该导数项已经通过解析和半解析方法进行了推导。计算了颗粒和单向纤维复合材料中残余应力张量分量和等效应力的统计分布，并将其与全场均质化结果进行了比较。全场模拟表明应力分量呈现非高斯分布，而等效残余应力则呈现出类似Weibull的分布。然而，在均场估计中假设的高斯分布能够捕捉到基本特征。 显示英文摘要

摘要： Fluctuations of local fields are crucial for the prediction of failure in random composites across different scales as well as estimating the inelastic behaviour of it. This can be quantified statistically through second moments of the local fields, which can be quickly estimated using mean field homogenization (MFH). However, the exact fluctuation field can be estimated using full-field methods though it comes at the cost of intensive computational resources and limited scalability to complex microstructures. In this work, MFH is used to estimate the statistical variation of the field quantities and then cross-verified with full-field methods for a linear-thermoelastic homogenization problem. An analytical expression to calculate the second moments of the local fields for a linear thermo-elastic problem using MFH is obtained based on the Hill-Mandel condition. The expressions fundamentally rely on the solution of linear elastic problem which in turn depends on the derivatives of Hill's polarization tensor. Solution of this derivative term has been analytically and semianalytically derived in previous work [1]. The statistical distribution of residual stress tensor components and equivalent stress in particulate and unidirectional fibrous composites, arising purely due to differential thermal expansion, is computed and compared with full-field homogenization. Full-field simulations indicated a non-Gaussian distribution of stress components, whereas Weibull-like distributions for equivalent residual stress. Nevertheless, the assumed Gaussian distribution in mean-field estimates captures the essential features.