Stationary rarefaction waves in discrete materials with strain-softening behavior

This article details some of the techniques used to derive exact solutions from the discrete equations of motion of strongly and weakly nonlinear discrete systems. The distinction between strongly and weakly nonlinear systems is related to the amplitude of a traveling pulse and the external confining load. Materials with an anomalous strain-softening behavior will be emphasized (i.e., [Formula: see text], [Formula: see text]), though this choice does not preclude applications for strain-hardening systems like those with Hertzian potentials. Discrete materials with tunable acoustic transmission properties and novel impact mitigation capacity have gained interest in recent years due to their practical application across many scientific fields. Wave-guides comprised of discrete materials with a nonlinear interaction potential have been used to investigate the interplay between nonlinearity, dispersion and dissipation.