Important physical observations in rupture dynamics such as static fault friction, short-slip, self-healing, and the supershear phenomenon in cracks are studied. A continuum model of rupture dynamics is developed using the field dislocation mechanics (FDM) theory. The energy density function in our model encodes accepted and simple physical facts related to rocks and granular materials under compression. We work within a 2-dimensional ansatz of FDM where the rupture front is allowed to move only in a horizontal fault layer sandwiched between elastic blocks. Damage via the degradation of elastic modulus is allowed to occur only in the fault layer, characterized by the amount of plastic slip. The theory dictates the evolution equation of the plastic shear strain to be a Hamilton–Jacobi (H-J) equation, resulting in the representation of a propagating rupture front. A Central-Upwind scheme is used to solve the H-J equation. The rupture propagation is fully coupled to elastodynamics in the whole domain, and our simulations recover static friction laws as emergent features of our continuum model, without putting in by hand any such discontinuous criteria in the formulation. Estimates of material parameters of cohesion and friction angle are deduced. Short-slip and slip-weakening (crack-like) behaviors are also reproduced as a function of the degree of damage behind the rupture front. The long-time behavior of a moving rupture front is probed, and it is deduced that equilibrium profiles under no shear stress are not traveling wave profiles under non-zero shear load in our model. However, it is shown that a traveling wave structure is likely attained in the limit of long times. Finally, a crack-like damage front is driven by an initial impact loading, and it is observed in our numerical simulations that an upper bound to the crack speed is the dilatational wave speed of the material unless the material is put under pre-stressed conditions, in which case supersonic motion can be obtained. Without pre-stress, intersonic (supershear) motion is recovered under appropriate conditions.

中文翻译：

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地球物理破裂连续体模型中的新兴断层摩擦和超剪切


研究了断裂动力学中的重要物理观测，如静断层摩擦、短滑、自愈和裂缝中的超剪切现象。使用场位错力学 （FDM） 理论开发了断裂动力学的连续体模型。我们模型中的能量密度函数编码了与压缩下的岩石和颗粒材料相关的公认和简单的物理事实。我们在 FDM 的二维拟设中工作，其中破裂前沿只允许在夹在弹性块之间的水平断层中移动。弹性模量退化造成的损坏只允许在断层中发生，其特征是塑性滑移量。该理论将塑性剪切应变的演化方程定义为 Hamilton-Jacobi （H-J） 方程，从而表示传播的破裂前沿。Central-Upwind 方案用于求解 H-J 方程。破裂传播与整个域中的弹性动力学完全耦合，我们的仿真将静摩擦定律恢复为连续体模型的新兴特征，而无需在公式中手动输入任何此类不连续标准。推导出内聚力和摩擦角的材料参数的估计值。短滑和滑移减弱（裂纹状）行为也作为破裂前缘后面损伤程度的函数再现。探究了移动破裂前沿的长期行为，并推断出在我们的模型中，无剪切应力下的平衡剖面不是非零剪切载荷下的行进波剖面。然而，结果表明，在长时间的限制下可能会获得行波结构。 最后，裂纹状损伤前沿由初始冲击载荷驱动，在我们的数值模拟中观察到，裂纹速度的上限是材料的膨胀波速度，除非材料处于预应力条件下，在这种情况下可以获得超音速运动。在没有预应力的情况下，在适当的条件下恢复音速（超剪切）运动。