Post-instability behavior of solids

Abstract

The necessity of model reformulation in elasticity results from the failure of hyperbolicity of the governing equations of motion for classical models. The reformulation is based upon the introduction of additional kinematical microstructures in the form of multivalued displacement and velocity field (or fractal functions) which are generated by the mechanism of the instability. The small scale motions describing this microstructure interact with the original large scale motion and restore the hyperbolicity of new governing equations of motion. The applications of the reformulated models to the problem of vibrational control and impact energy absorption are discussed.