Abstract We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of discrete data points, leading to a model-free data-driven method of solution. The solution at a given load step is identified as the point within the data set that best satisfies either the Kuhn–Tucker conditions stemming from the variational fracture problem or global minimization of a suitable energy functional, leading to data-driven counterparts of both the local and the global minimization approaches of variational fracture mechanics. Both formulations are tested on different test configurations with and without noise and for Griffith and R-curve type fracture behavior.

中文翻译：

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数据驱动的断裂力学

摘要 我们提出了一种新的数据驱动的变分脆性断裂力学范式。去除了与断裂相关的材料建模假设，并将源自变分原理的控制方程与一组离散数据点相结合，从而形成无模型的数据驱动解决方案。给定载荷步的解被确定为数据集中最能满足源自变分断裂问题的 Kuhn-Tucker 条件或合适的能量函数的全局最小化的点，从而导致两个局部的数据驱动对应物以及变分断裂力学的全局最小化方法。两种配方都在不同的测试配置上进行了测试，有无噪声以及格里菲斯和 R 曲线型断裂行为。