Representing model uncertainties in brittle fracture simulations
Representing model uncertainties in brittle fracture simulations
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DOI：
10.1016/j.cma.2023.116575
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发表时间：
2024-01
影响因子：
7.2
通讯作者：
Hao Zhang;J. Dolbow;Johann Guilleminot
中科院分区：
文献类型：
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作者：
Hao Zhang;J. Dolbow;Johann Guilleminot
本文主要研究脆性断裂相场模型中模型形式不确定性的表示。例如，这种不确定性可能来自于退化函数的选择，迄今为止还没有对其进行考虑。随机建模框架利用了与非线性动力系统分析相关的最新发展，并依赖于随机降阶模型的构建。在后者中，基于pod的降阶基是随机化的，使用黎曼投影和缩回算子，以及一个信息论公式，可以在一组模型建议定义的凸包中进行适当的集中。由此得到的模型在数学上几乎是可以接受的，它包含一个低维超参数，通过一个二次规划问题的公式可以方便地标定它。在一维和二维应用中进一步评估了建模方法的相关性。结果表明，模型不确定性可以有效地捕获并传播到感兴趣的宏观量。针对前向仿真对样本定位高度敏感的情况，提出了一种基于局部随机化的扩展方法。这项工作构成了方法学的发展，允许相场预测被赋予信心的统计措施，考虑到建模选择引起的可变性。
This work focuses on the representation of model-form uncertainties in phase-field models of brittle fracture. Such uncertainties can arise from the choice of the degradation function for instance, and their consideration has been unaddressed to date. The stochastic modeling framework leverages recent developments related to the analysis of nonlinear dynamical systems and relies on the construction of a stochastic reduced-order model. In the latter, a POD-based reduced-order basis is randomized using Riemannian projection and retraction operators, as well as an information-theoretic formulation enabling proper concentration in the convex hull defined by a set of model proposals. The model thus obtained is mathematically admissible in the almost sure sense and involves a low-dimensional hyperparameter, the calibration of which is facilitated through the formulation of a quadratic programming problem. The relevance of the modeling approach is further assessed on one- and two-dimensional applications. It is shown that model uncertainties can be efficiently captured and propagated to macroscopic quantities of interest. An extension based on localized randomization is also proposed to handle the case where the forward simulation is highly sensitive to sample localization. This work constitutes a methodological development allowing phase-field predictions to be endowed with statistical measures of confidence, accounting for the variability induced by modeling choices.