Phase-field modeling of stochastic fracture in heterogeneous quasi-brittle solids
Phase-field modeling of stochastic fracture in heterogeneous quasi-brittle solids
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DOI：
10.1016/j.cma.2023.116332
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发表时间：
2023-11
影响因子：
7.2
通讯作者：
Jian‐Ying Wu;Jinghua Yao;J. Le
中科院分区：
文献类型：
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作者：
Jian‐Ying Wu;Jinghua Yao;J. Le
由于非均匀性的随机性，准脆性材料的损伤和断裂行为表现出相当程度的不确定性。准脆性材料随机断裂的数值模拟已成为工程结构分析和设计中不可缺少的工具。为此，本文结合随机场理论和相场粘聚区模型（PF-CZM），提出了一个计算框架来捕获非均质准脆性固体中的概率断裂。材料强度和断裂能的空间变化由Karhunen-Loève展开产生的互相关二元随机场表示。最近提出的PF-CZM被用来模拟准脆性固体中随机裂纹的形核和扩展。通过对相场长度尺度参数和随机场的相关长度施加特定的条件，实现了蒙特-卡罗模拟的客观性。特别地，在这种情况下，断裂过程区（FPZ）的宽度显著小于随机场的相关长度，使得FPZ内的材料不表现出机械性能的显著空间变化。由于PF-CZM中固有地包含断裂能，因此在这种情况下没有必要明确考虑FPZ宽度。将所得的概率PF-CZM组合应用于不同几何形状混凝土结构断裂的蒙特-卡罗模拟。结果表明，随机模拟结果是不敏感的相场长度尺度参数和有限元网格离散在以前的确定性分析。PF-CZM通过对所涉及的特征长度的特定条件进行增强，为准脆性结构的损伤和断裂随机模拟提供了一个可行的工具。
Owing to the random nature of heterogeneity, damage and fracture behavior of quasi-brittle materials exhibits a considerable degree of uncertainty. Computational modeling of stochastic fracture in quasi-brittle materials has become an indispensable tool for analysis and design of engineering structures. To this end, we present in this paper a computational framework to capture probabilistic fracture in heterogeneous quasi-brittle solids by combining the random field theory and the phase-field cohesive zone model (PF-CZM). The spatial variation of the material strength and fracture energy is represented by a cross-correlated bivariate random field generated by the Karhunen–Loève expansion. The recently proposedPF-CZMis employed to simulate the stochastic crack nucleation and propagation in quasi-brittle solids. The objectivity of the Monte-Carlo simulation is achieved by imposing a specific condition on the phase-field length scale parameter and the correlation length of the random field. In particular, upon this condition the width of the fracture process zone (FPZ) is considerably smaller than the correlation length of the random field such that the material inside the FPZ does not exhibit significant spatial variations of mechanical properties. As the fracture energy is intrinsically incorporated in thePF-CZM, it is unnecessary in this case to explicitly consider the FPZ width. The resulting probabilisticPF-CZMtogether is applied to the Monte-Carlo simulations of fracture in concrete structures of different geometries. It is shown that the stochastic simulation results are insensitive to both the phase-field length scale parameter and the finite element mesh discretization as in the previous deterministic analyses. Enhanced with the specific condition on the involved characteristic lengths, thePF-CZMprovides a viable tool for stochastic simulations of damage and fracture in quasi-brittle structures.