Explicit dynamic approach for unbounded domains in frictional contact with Rate and State laws

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.