Sliding along frictional interfaces separating dissimilar elastic materials
is qualitatively different from sliding along interfaces separating identical
materials due to the existence of an elastodynamic coupling between interfacial
slip and normal stress perturbations in the former case. This bimaterial
coupling has important implications for the dynamics of frictional interfaces,
including their stability and rupture propagation along them. We show that
while this bimaterial coupling is a monotonically increasing function of the
bimaterial contrast, when it is coupled to interfacial shear stress
perturbations through a friction law, various physical quantities exhibit a
non-monotonic dependence on the bimaterial contrast. In particular, we show
that for a regularized Coulomb friction, the maximal growth rate of unstable
interfacial perturbations of homogeneous sliding is a non-monotonic function of
the bimaterial contrast, and provide analytic insight into the origin of this
non-monotonicity. We further show that for velocity-strengthening
rate-and-state friction, the maximal growth rate of unstable interfacial
perturbations of homogeneous sliding is also a non-monotonic function of the
bimaterial contrast. Results from simulations of dynamic rupture along a
bimaterial interface with slip-weakening friction provide evidence that the
theoretically predicted non-monotonicity persists in non-steady, transient
frictional dynamics.Comment: 14 pages, 5 figure
