Abstract The paper explores the ability of an explicit time integration procedure to simulate the dynamics of shear rupture between unbounded elastic blocks on frictional interface, modeled with the finite element method. The behaviour of the interface is governed by Rate and State (RS) friction laws, proposed to describe the rate dependent phenomena observed in experiments on rocks and many other materials in sliding contact. The method for the frictional contact between bodies is integrated in the framework of heterogeneous asynchronous time integrator (HATI). Dual formulation, requiring the introduction of Lagrange multipliers, is adopted by dealing in a weak way with the normal contact conditions as well as the tangential frictional conditions expressed in velocity. Taking advantage of the flexibility of the HATI framework, precise formulations of Perfectly Matched Layers (PML) are also incorporated, enabling us to treat semi-infinite media in frictional contact. Simulations concerning an unbounded elastic block on a rigid flat plane, initially compressed and sheared with remote loadings, are carried out. Advantages of the PML are underlined during the preliminary stages of loading as well as during the nucleation and propagation of the shear rupture along the interface. Numerical oscillations inherent from the high non-linearity of the RS friction law, characterized by significant variations of the friction coefficient with small changes in tangential velocity, are drastically reduced thanks to the HATI method.

中文翻译：

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与速率和状态定律摩擦接触的无界域的显式动态方法

摘要 本文探讨了显式时间积分程序模拟摩擦界面上无界弹性块之间剪切断裂动力学的能力，使用有限元方法建模。界面的行为受速率和状态 (RS) 摩擦定律控制，建议描述在岩石和许多其他滑动接触材料的实验中观察到的速率相关现象。物体间摩擦接触的方法集成在异构异步时间积分器（HATI）框架中。需要引入拉格朗日乘子的双重公式通过以弱方式处理法向接触条件以及以速度表示的切向摩擦条件而采用。利用HATI框架的灵活性，还结合了完美匹配层 (PML) 的精确配方，使我们能够处理摩擦接触中的半无限介质。对刚性平面上的无边界弹性块进行了模拟，该块最初被远程载荷压缩和剪切。PML 的优势在加载的初始阶段以及剪切断裂沿界面的成核和传播过程中得到了强调。由于 HATI 方法，RS 摩擦定律的高度非线性所固有的数值振荡，其特征是摩擦系数随着切向速度的微小变化而显着变化。对刚性平面上的无边界弹性块进行了模拟，该块最初被远程载荷压缩和剪切。PML 的优势在加载的初始阶段以及剪切断裂沿界面的成核和传播过程中得到了强调。由于 HATI 方法，RS 摩擦定律的高度非线性所固有的数值振荡，其特征是摩擦系数随着切向速度的微小变化而显着变化。对刚性平面上的无边界弹性块进行了模拟，该块最初被远程载荷压缩和剪切。PML 的优势在加载的初始阶段以及剪切断裂沿界面的成核和传播过程中得到了强调。由于 HATI 方法，RS 摩擦定律的高度非线性所固有的数值振荡，其特征是摩擦系数随着切向速度的微小变化而显着变化。