Spurious mesh sensitivity is a major challenge in continuum finite element (FE) simulations of damage and fracture of quasibrittle structures. It has been shown that the existing localization limiters, which largely focus on energy regularization, are insufficient for addressing the issue of mesh sensitivity in stochastic analysis. In this study, we investigate the mathematical algorithm for mapping the continuous random fields of material properties onto the FE meshes. This is a fundamental problem in stochastic FE analysis, which has profound implications for the mesh sensitivity in the prediction of the statistics of failure behavior. We adopt a continuum damage constitutive model, and develop a mechanistic mapping method. The projection of the random fields of material properties onto the FE mesh is governed by the prevailing damage pattern of the element. The damage pattern of each finite element is determined based on the spatial distribution of the damage of its surrounding elements. Meanwhile, the prevailing damage pattern also dictates the energy regularization of the constitutive response of the finite element. The combination of energy regularization and mechanistic mapping method ensures that, for each time increment, the random tangential stiffness tensor of each finite element is calculated in accordance with the ongoing damage pattern. A direct consequence of the model is that, depending on the damage pattern, the statistics of the tangential stiffness tensor could vary with the mesh size. The model is applied to stochastic FE analysis of both notched and unnotched flexural specimens under different loading configurations, which exhibit different failure behaviors. The numerical analysis also considers different correlation lengths of the random fields of material properties. The simulation shows that, with the energy regularization scheme, the commonly used local mapping and local averaging methods could yield considerable mesh dependence of the statistics of the peak load capacity. The result also reveals the effect of correlation length on the spurious mesh dependence. By relating the mapping algorithm to the underlying damage pattern, the present model is able to mitigate the mesh sensitivity for different specimen geometries, loading configurations, and correlation lengths.

中文翻译：

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准脆性断裂随机有限元模拟的随机场力学映射

虚假网格敏感性是准脆性结构损伤和断裂的连续有限元 (FE) 模拟中的一个主要挑战。事实证明，现有的局部限制器主要集中在能量正则化上，不足以解决随机分析中的网格敏感性问题。在本研究中，我们研究了将材料属性的连续随机场映射到有限元网格上的数学算法。这是随机有限元分析中的一个基本问题，对于失效行为统计预测中的网格敏感性具有深远的影响。我们采用连续损伤本构模型，并开发了机械映射方法。材料属性随机场在有限元网格上的投影由单元的主要损坏模式控制。每个有限元的损伤模式是根据其周围单元损伤的空间分布来确定的。同时，普遍的损伤模式也决定了有限元本构响应的能量正则化。能量正则化和机械映射方法的结合确保了对于每个时间增量，每个有限元的随机切向刚度张量都根据正在进行的损伤模式计算。该模型的直接结果是，根据损坏模式，切向刚度张量的统计数据可能会随着网格尺寸的变化而变化。该模型适用于不同载荷配置下有缺口和无缺口弯曲样本的随机有限元分析，这些样本表现出不同的破坏行为。数值分析还考虑了材料属性随机场的不同相关长度。仿真表明，通过能量正则化方案，常用的局部映射和局部平均方法可以产生相当大的峰值负载容量统计的网格依赖性。结果还揭示了相关长度对虚假网格依赖性的影响。通过将映射算法与潜在的损伤模式相关联，本模型能够减轻不同样本几何形状、载荷配置和相关长度的网格敏感性。