Thermo-elastic dynamic instability (TEDI) in frictional sliding of two elastic half-spaces

In some simplified 1D models, we recently studied the coupling of TEI (thermoelastic instability) and DI (dynamic instability), finding that thermal effects can render unstable the otherwise neutrally stable natural elastodynamic modes of the system, giving rise to a new family of instability which we called TEDI.Here, we study the general case of two sliding elastic half-planes, finding again a relatively weak coupling between thermal and dynamic effects, and the general family of instability TEDI class is found to modify both the otherwise separated TEI and DI classes. The growth factor, the phase velocity and the migrating speeds of the perturbations are wavelength-dependent, and it is difficult to give a complete picture given the high number of materials’ parameters, and the dependence on speed, friction coefficient, and the underlying uniform pressure. However, a set of results are given for “large” and “small” mismatch of shear wave speeds in the materials, and as a function of (i) friction coefficient; (ii) sliding speed V0V0; (iii) wavenumber parameter γγ. In the case of small mismatch, generalized Rayleigh waves exists already under frictionless conditions, the critical ff for instability is zero. DI dominates over TEI typically for large wavenumbers, where the growth factors increase without limit and hence become eventually meaningless, requiring regularizations for example with rate–state dependent friction laws. TEI growth factors vice versa have a maximum at a certain wavenumber and therefore are always well posed. Larger coupling effects are noticed for two materials with large mismatch, but significantly only for sliding speeds comparable with the wave speed. In general, TEI growth factors increase with speed, whereas DI growth factors increase with speed for similar materials and decrease when the mismatch between materials is large.