Abstract
This study focuses on the stability of the quasi-static evolution of strain-rate-dependent solids and structures. This approach can deal with the stability of the non-linear problem, and not only with the linearised one. The linearisation method of nonautonomous evolution equations provides a sufficient stability condition. This condition given by the strict positiveness of the second derivative of the total free energy is compared to Hill's non-bifurcation criterion. Finally, some illustrative examples of visco-elasticity and visco-plasticity are presented.
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