The present work is devoted to prove that unstable crack propagation events do not comply with quasi-static hypotheses and thus should be modelled by dynamic approaches. Comprehensive supporting evidence is provided on the basis of three different analyses conducted on multi-ligament unstable fracture conditions, including a simplified Spring-Mass model, detailed quasi-static and dynamic Phase Field fracture models, and bespoke experiments with 3D printed specimens. The obtained results unequivocally show that neglecting the inertial effects can lead to unsafe predictions in the presence of energetic barriers for the development of fracture. Likewise, quasi-static Phase Field fracture models are proven to yield crack patterns that disagree with the experimental evidence because they overlook the progressive diffusion of the mechanical information within the continuum. Moreover, the inability of quasi-static approaches to follow unstable crack propagation is shown to weaken the crucial irreversibility condition of fracture. Overall, these experimentally backed insights should be gravely reckoned with, for they are not exclusive to Phase Field fracture models but common to (almost) any variational approach to fracture, Cohesive Zone Models or Continuum Damage Mechanics.

中文翻译：

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关于不稳定裂纹扩展的准静态变分断裂模型的（缺乏）代表性

目前的工作致力于证明不稳定裂纹扩展事件不符合准静态假设，因此应通过动态方法进行建模。基于对多韧带不稳定断裂条件进行的三种不同分析，包括简化的弹簧质量模型、详细的准静态和动态相场断裂模型以及 3D 打印样本的定制实验，提供了全面的支持证据。获得的结果明确表明，在存在断裂发展的能量障碍的情况下，忽略惯性效应可能会导致不安全的预测。同样，准静态相场断裂模型被证明会产生与实验证据不一致的裂纹模式，因为它们忽略了连续体中机械信息的逐渐扩散。此外，准静态方法无法跟踪不稳定裂纹扩展，这削弱了断裂的关键不可逆条件。总体而言，这些实验支持的见解应该受到认真对待，因为它们并非相场断裂模型所独有，而是（几乎）任何断裂变分方法、内聚区模型或连续损伤力学所共有的。