AI 中文总结
研究动态断裂中相场正则化作用，分析脆性、刚度+密度退化及扩展到弹性动力学的内聚断裂相场正则化三种公式，通过一维杆研究波-裂纹相互作用，为新内聚模型推导定律，还研究二维缺口板动态行为。
AI 中文摘要
断裂的相场模型广泛用于模拟裂纹成核和扩展，然而相场正则化在动态状态下的作用尚未完全理解，且严重依赖于损伤变量与位移场的耦合方式。本文分析了三种替代公式：具有刚度退化的脆性模型、具有刚度+密度退化的变体模型，以及我们最近提出的扩展到弹性动力学的内聚断裂相场正则化。通过研究一维杆中拉伸和压缩弹性波与相场裂纹的相互作用，确定了哪些模型和条件下相场正则化保留了尖锐裂纹预期的波-裂纹相互作用特征，并从理论上解释了哪些变量控制该行为。对于扩展到动力学的新内聚模型，进一步推导了分析动态内聚开口定律。最后，研究了二维缺口板在两种加载强度下包括分支的动态行为。
英文摘要
Phase-field models of fracture are widely used for simulating crack nucleation and propagation, yet the role of the phase-field regularization in the dynamic regime is not fully understood and depends critically on how the damage variable is coupled to the displacement field. In this paper, we analyze three alternative formulations: the brittle model with stiffness degradation, its variant with stiffness+density degradation, and our recently proposed phase-field regularization of cohesive fracture, which we extend to elastodynamics. By studying the interaction of a tensile and a compressive elastic wave with a phase-field crack in a one-dimensional bar, we determine for which models and under which conditions the phase-field regularization preserves the features of the wave-crack interaction expected for a sharp crack, and we theoretically explain which variables control the behavior. For the new cohesive model extended to dynamics, we further derive an analytical dynamic cohesive opening law. Finally, we study the dynamic behavior including branching of a two-dimensional notched plate at two loading intensities.
