Abstract A novel efficient methodology for probabilistic material reliability analysis considering fine-scale microstructure stochasticity is proposed in this paper. Integrated computational material engineering requires efficient multiscale computational capabilities to enable computational design and validation. Two critical challenges are identified: handling uncertainties from microstructures and material properties; and handling the “curse of dimensionality” for probabilistic solvers. The proposed study addresses these two critical challenges. First, an analytical and hierarchical uncertainty quantification method is proposed for the explicit stochastic microstructure representation at the voxel-level. The hierarchy of uncertainties from both phase maps and uncertainties within each phase is modeled using an explicit Gaussian mixture random field. Analytical approximation for the arbitrary non-Gaussian random field is derived, which can facilitate the computation of gradient information in optimization. Following this, an efficient probabilistic solver using adjoint first-order reliability method combining the importance sampling is derived by formulating the material reliability analysis as a constrained optimization problem. The adjoint method is used to efficiently evaluate the responses and exact gradients with the help of the analytical Gaussian mixture random field. Several numerical examples for material reliability calculation with high-dimensional (voxel-level) random fields are subsequently employed to demonstrate and validate the proposed methodology. The results of the proposed method are quantitatively compared to those obtained via the classical first-order reliability method, direct Monte Carlo simulation, subset simulation, and the sequential importance sampling method. The comparisons indicate that the proposed method possesses high efficiency for high-dimensional material reliability problems.

中文翻译：

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具有显式体素级随机微观结构表示的高效高维材料可靠性分析

摘要 本文提出了一种考虑细尺度微观结构随机性的概率材料可靠性分析的新方法。集成计算材料工程需要高效的多尺度计算能力来实现计算设计和验证。确定了两个关键挑战：处理来自微观结构和材料特性的不确定性；并处理概率求解器的“维数灾难”。拟议的研究解决了这两个关键挑战。首先，针对体素级别的显式随机微观结构表示提出了一种分析和分层不确定性量化方法。来自相位图的不确定性层次和每个相位内的不确定性是使用显式高斯混合随机场建模的。推导了任意非高斯随机场的解析逼近，便于计算优化中的梯度信息。在此之后，通过将材料可靠性分析公式化为约束优化问题，推导出使用结合重要性采样的伴随一阶可靠性方法的有效概率求解器。在分析高斯混合随机场的帮助下，伴随方法用于有效评估响应和精确梯度。随后使用高维（体素级）随机场的材料可靠性计算的几个数值示例来演示和验证所提出的方法。将所提出方法的结果与通过经典一阶可靠性方法、直接蒙特卡罗模拟、子集模拟和顺序重要性采样方法获得的结果进行定量比较。比较表明，所提出的方法对高维材料可靠性问题具有高效率。