This work introduces a novel phase-field solution for simulating and predicting fractures in elastic solids. In this phase-field fracture model, the crack growth is driven by the material energy–momentum flux, or the configurational force, inspired by a null divergence conservation law and its variational theory, as opposed to employing the commonly-used strain energy degradation-based crack-driving force. By doing so, the crack growth or material configuration change is solely determined by the physics-based Eshelby energy–momentum tensor density or the Rice J-integral flux, which aligns with the energy release criterion of the celebrated Griffith–Eshelby–Rice (GER) theory. The proposed method not only preserves the integrity of the balance of linear momentum principle at the crack tip region but also provides a correct stress asymptotic field in front of the crack tip, while accurately capturing the crack growth.

中文翻译：

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材料能量动量通量驱动的相场断裂力学模型

这项工作介绍了一种用于模拟和预测弹性固体断裂的新型相场解决方案。在这个相场断裂模型中，裂纹扩展是由材料能量动量通量或构型力驱动的，其灵感来自于零发散守恒定律及其变分理论，而不是采用常用的应变能退化-为基础的裂纹驱动力。通过这样做，裂纹扩展或材料构型变化完全由基于物理的 Eshelby 能量动量张量密度或 Rice J 积分通量决定，这与著名的 Griffith-Eshelby-Rice (GER) 的能量释放准则一致） 理论。该方法不仅保留了裂纹尖端区域线性动量平衡原理的完整性，而且在裂纹尖端前面提供了正确的应力渐近场，同时准确捕获裂纹扩展。