Correspondence *Mohsen Zayernouri, Department of Computational Mathematics, Science, and Engineering, Michigan State University, 428 S Shaw Ln, East Lansing, MI, 48824. Email: zayern@msu.edu Summary Materials accumulate energy around voids and defects under external loading, causing the formation of micro-cracks. With increasing or repeated loads, those micro-cracks eventually coalesce to form macro-cracks, which in a brittle material can cause catastrophic failure without apparent permanent deformation. At the continuum level, a stochastic phase-field model is employed to simulate failure through introducing damage and fatigue variables. The damage phase-field is introduced as a continuous dynamical variable representing the volumetric portion of fracturedmaterial and fatigue is treated as a continuous internal field variable to model the effects of micro-cracks arising from energy accumulation. We formulate a computationalmathematical framework for quantifying the corresponding model uncertainties and sensitivities in order to unfold and mitigate the salient sources of unpredictability in the model, hence, leading to new possible modeling paradigms. Considering an isothermal isotropic linear elastic material with viscous dissipation under the hypothesis of small deformations, we employed Monte Carlo and Probabilistic Collocation methods to perform the forward uncertainty propagation, in addition to local-toglobal sensitivity analysis. We demonstrate that the model parameters associated with free-energy potentials contribute significantly more to the total model output uncertainties, motivating further investigations for obtaining more predictable model forms, representing the damage diffusion.

中文翻译：

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用于材料损伤随机相场建模的综合灵敏度-不确定性量化框架

通讯 *Mohsen Zayernouri，密歇根州立大学计算数学、科学与工程系，428 S Shaw Ln, East Lansing, MI, 48824。电子邮件：zayern@msu.edu 摘要 材料在外部负载下在空隙和缺陷周围积累能量，导致微裂纹的形成。随着载荷的增加或重复，这些微裂纹最终会合并形成宏观裂纹，这在脆性材料中会导致灾难性的破坏，而不会产生明显的永久变形。在连续体层面，采用随机相场模型通过引入损伤和疲劳变量来模拟失效。损伤相场被引入为代表断裂材料体积部分的连续动态变量，疲劳被视为连续的内部场变量，以模拟能量积累引起的微裂纹的影响。我们制定了一个计算数学框架，用于量化相应的模型不确定性和敏感性，以展开和减轻模型中不可预测性的显着来源，从而产生新的可能的建模范式。考虑在小变形假设下具有粘性耗散的等温各向同性线弹性材料，除了局部到全局灵敏度分析外，我们还采用蒙特卡罗和概率搭配方法进行前向不确定性传播。