Macroscale mesh sensitivity and RVE size dependence are the two major issues that make the conventional homogenization techniques incapable of modeling the softening behavior of quasi-brittle materials. In this paper, a new continuous–discontinuous multiscale modeling approach to failure is presented. Inspired by the classical crack band model of Bazant and Oh (1983), this approach is built upon an extended computational homogenization (CH) scheme for representing the macroscale crack behavior. During the multiscale computation, once a macroscale material point loses its stability with the XFEM, a new crack segment represented is inserted for which cohesive RVE models using the extended CH and with copied initial states are coupled to crack integration points. In the extended CH, the macroscale strain applied to the boundary of the cohesive RVE model is enriched with a macroscale discontinuity related term regularized with the effective length of the microscale localization band. This helps alleviate the RVE size dependency of the homogenized cohesive response. The weakly periodic BCs that are aligned with the localization direction are employed to minimize spurious boundary effects. Several numerical examples are provided to demonstrate the effectiveness of this framework, with a comparison against direct numerical simulations.

中文翻译：

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准脆性材料应变定位的多尺度失效建模框架

宏观网格敏感性和 RVE 尺寸依赖性是使传统均质化技术无法模拟准脆性材料的软化行为的两个主要问题。在本文中，提出了一种新的连续-不连续多尺度故障建模方法。受 Bazant 和 Oh (1983) 的经典裂纹带模型的启发，这种方法建立在用于表示宏观裂纹行为的扩展计算均匀化 (CH) 方案之上。在多尺度计算过程中，一旦宏观材料点在 XFEM 中失去稳定性，就会插入一个新的裂纹段，其中使用扩展 CH 和复制初始状态的内聚 RVE 模型耦合到裂纹积分点。在扩展的 CH 中，应用到内聚 RVE 模型边界的宏观尺度应变富含宏观尺度不连续性相关项，该项用微观尺度定位带的有效长度进行正则化。这有助于减轻均质内聚响应的 RVE 大小依赖性。采用与定位方向对齐的弱周期性 BC 来最小化虚假边界效应。提供了几个数值示例来证明该框架的有效性，并与直接数值模拟进行了比较。采用与定位方向对齐的弱周期性 BC 来最小化虚假边界效应。提供了几个数值示例来证明该框架的有效性，并与直接数值模拟进行了比较。采用与定位方向对齐的弱周期性 BC 来最小化虚假边界效应。提供了几个数值示例来证明该框架的有效性，并与直接数值模拟进行了比较。