Wave Propagation in Rocks and Granular Materials Modelled as 1D Heteromodular Elastic Medium

We consider 1D non-stationary essentially nonlinear dynamic problem for heteromodular elastic medium. Heteromodular medium reacts differently to the tension and compression and therefore presents strongly nonlinear behaviour at infinitisemal deformations. It is subjected to the harmonic force which was "switched on" at zero moment of time. We consider the case when the difference in elastic moduli for tension and compression is small, and construct asymptotical solutions for large times. The analytical results are verified numerically. We construct both near and far-field asymptotics, analyse spectral properties of the problem.