Cracks in soft materials exhibit diverse dynamic patterns, involving straight, oscillation, branching, and supershear fracture. Here, we successfully reproduce these crack morphologies in a two-dimensional pre-strained fracture scenario and establish crack stability phase diagrams for three distinct nonlinear materials using a fracture phase field model. The contrasting phase diagrams highlight the crucial role of nonlinearity in regulating crack dynamics. In strain-softening materials, crack branching prevails, limiting the cracks to sub-Rayleigh states. Yet strain-stiffening stabilizes crack propagation, allowing for the presence of supershear fracture. The intriguing crack oscillations are verified to be a universal instability closely tied to the local wave speed, as manifested by its onset speed scaling linearly with the characteristic shear wave speed. The wavelength of such instability is shown to be a bilinear function of the nonlinear scale and crack driving force, with a minimum length scale associated with the dissipative zone. Moreover, our findings suggest that the increase in local wave speed near the crack tip can account for the transition of cracks from sub-Rayleigh to supershear regimes in homogeneous materials.

中文翻译：

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非线性调整软材料中的裂纹动力学

软材料中的裂纹表现出不同的动力学模式，包括直线、振荡、分支和超剪切断裂。在这里，我们成功地在二维预应变断裂场景中再现了这些裂纹形态，并使用断裂相场模型为三种不同的非线性材料建立了裂纹稳定性相图。对比鲜明的相图突出了非线性在调节裂纹动力学中的关键作用。在应变软化材料中，裂纹分支占主导地位，将裂纹限制在亚瑞利状态。然而，应变加固稳定了裂纹扩展，允许存在超剪切断裂。有趣的裂纹振荡被证明是一种与局部波速密切相关的普遍不稳定性，其起始速度与特征横波速度呈线性比例。这种不稳定性的波长被证明是非线性尺度和裂纹驱动力的双线性函数，其最小长度尺度与耗散区相关。此外，我们的研究结果表明，裂纹尖端附近局部波速的增加可以解释均质材料中裂纹从亚瑞利状态向超剪切状态的转变。