Thermal-mechanical Coupling in Shear Deformation of Viscoelastic Material as a Model of Frictional Constitutive Relations

-- We propose a thermal-mechanical model of shear deformation of a viscoelastic material to describe the temperature-dependence of friction law. We consider shear deformation of one-dimensional layer composed of a Maxwell linear viscoelastic material under a constant velocity V and temperature T_w at the boundary. The strain rate due to viscous deformation depends both on temperature and shear stress. The temperature inside the layer changes owing to frictional heating and conductive cooling. Steady-state calculations show that the sign of d†^ss/dV, where †^ss is steady-state stress, changes from positive to negative as V increases, and that the threshold velocity above which the sign of d†^ss/dV is negative increases with increasing T_w. These results are in accordance with the conjecture that the downdip limit of seismogenic zones is marked by the transition in the sign of d†^ss/dV due to temperature rise with depth. We also find that the response of steady state to a step change in V is quite similar to the response of frictional slip with constitutive laws which employ state variables. These findings suggest that by further improving the present model a model of constitutive relations along faults or plate boundaries can be developed which contains temperature-dependence in a physically-sound manner.