Interface waves in almost incompressible elastic materials

[摘要] We study the problem of two elastic half-planes in contact and the Stoneley interface wave that may exist at the interface between two different elastic materials, emphasis being put on the case when the half-planes are almost incompressible. We show that numerical simulations involving interface waves require an unexpectedly high number of grid points per wavelength as the materials become more incompressible. Let lambda, mu, rho and lambda', mu', rho' be the Lame parameters and densities of the first and second half-plane, respectively. A theoretical study shows that if K is a real constant, lambda' = K lambda, mu' = K mu, rho' = K rho and mu -> 0, then for an accurate solution the required number of grid points per wavelength scales as (mu/lambda)(-1/p), where p is the order of accuracy of the numerical method. This requirement becomes very restrictive close to the incompressible limit mu << lambda, especially for lower order methods i.e., a small p. The theoretical findings are supported by numerical experiments that illustrate the demanding resolution requirement as well as the superiority of higher order methods. The scaling is also seen to hold for a more general choice of Lame parameters. Numerical experiments when one of the half-planes is a vacuum are also presented, where the higher resolution requirement is illustrated in a numerical solution of Lamb's problem. (C) 2015 Elsevier Inc. All rights reserved.

[发布日期] 2015-12-15

[关键词] Elastic waves;Interface waves;Surface waves;High order accuracy;SBP-SAT