Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space

The paper aims at derivation of the asymptotic model for surface wave propagating in a pre-stressed incompressible elastic half-space, subject to prescribed surface loading. The approach relies on the slow-time perturbation procedure, extending the previously known hyperbolic-elliptic formulations for surface waves in compressible linearly elastic solids. Within the derived model, the decay away from the surface is governed by a pseudo-static elliptic equation, whereas wave propagation is described by a hyperbolic equation on the surface. The effect of pre-stress, namely, the principal Cauchy stress σ2, is investigated. Finally, an illustrative example of the Lamb problem is considered, demonstrating the efficiency of the approach.