A generalized multiscale finite element method is introduced to address the computationally taxing problem of elastic fracture across scales. Crack propagation is accounted for at the microscale utilizing phase field theory. Both the displacement‐based equilibrium equations and phase field state equations at the microscale are mapped on a coarser scale. The latter is defined by a set of multinode coarse elements, where solution of the governing equations is performed. Mapping is achieved by employing a set of numerically derived multiscale shape functions. A set of representative benchmark tests is used to verify the proposed procedure and assess its performance in terms of accuracy and efficiency compared with the standard phase field finite element implementation.

中文翻译：

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脆性断裂的广义相场多尺度有限元方法

为了解决跨尺度弹性断裂的计算繁重问题，引入了一种通用的多尺度有限元方法。利用相场理论在微观尺度上解释了裂纹扩展。微观尺度上基于位移的平衡方程和相场状态方程都以较粗略的比例绘制。后者由一组多节点粗糙元素定义，在其中执行控制方程式的求解。通过采用一组数字派生的多尺度形状函数来实现映射。与标准相场有限元实现相比，一组代表性的基准测试用于验证所建议的过程并评估其性能的准确性和效率。