Dynamic frictional slip along an interface between plastically compressible solids

Dynamic frictional slip along an interface between plastically compressible solids is analyzed. The plane strain, small deformation initial/boundary value problem formulation and the numerical method are identical to those in Shi et al. (Int J Fract 162:51, 2010) except that here the material constitutive relation allows for plastic compressibility. The interface is characterized by a rate and state dependent friction law. The specimens have an initial compressive stress and are subject to shear loading by edge impact near the interface. Two loading conditions are analyzed, one giving rise to a crack-like mode of slip propagation and the other to a pulse-like mode of slip propagation. In both cases, the initial compressive stress is taken to vary with plastic compressibility such that the associated initial effective stress is the same for all values of plastic compressibility. The volume change for the crack-like slip mode is mainly plastic while the elastic volume change plays a larger role for the pulse-like mode. For the crack-like slip mode, the proportion of plastic dissipation in the material increases with the increasing plastic compressibility, but the effect of plastic compressibility on the energy partitioning for the pulse-like slip mode is much smaller. The predicted propagation speeds approach a speed about the dilational wave speed for both the crack-like and pulse-like slip modes and this speed is not sensitive to the value of the plastic compressibility parameter. Plastic dissipation is found to be mainly associated with the deformation induced by the loading wave rather than with the deformation arising from slip propagation. The amplitude of the slip rate in the slip pulses is found to be largely governed by the value of the initial compressive stress regardless of the value of plastic compressibility.