Diabatic instability of a solid deformed at high strain rates

Summary The model of a thermo-inelastic solid undergoing a very fast deformation is considered beyond the usual linear approximation. It is shown, via a stability analysis of small fluctuations, that a universal stability diagram in control parameter space exists exhibiting a complex topology but only hard-mode (acousticlike) instabilities, due to the hyperbolic nature of the governing equations. It turns out that an adiabatic homogeneous expansion against cohesion forces is no longer possible if a critical strain rate is exceeded, leading to spatial symmetry breaking towards fracture. The validity of this last result is thought to hold qualitatively irrespectively of the nature of the dissipation laws. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.