The nonlinear evolution of near-neutral and near-body wave modes in a pre-stressed incompressible elastic half-space. Part II: lower branch near-neutral modes

摘要

We consider the evolution of the lower branch near-neutral modes. It is shown that as p=-2 is approached from above, where p is the pressure scaled by the shear modulus, two regions of p values need to be considered separately: an intermediate region where p=-2+ O and over which the near-neutral modes evolve on an O time scale, and a final region where p=-2+ 0 and over which the near-neutral modes evolve on a shorter o time scale, where is a small parameter characterizing the order of the wave amplitude. Numerical results for the intermediate region show the formation of shocks as the non-neutral region is approached but not as the final region is approached.