Abstract
We study the interaction of in-plane elastic waves with imperfect interfaces composed of a periodic array of voids or cracks. An effective model is derived from high-order asymptotic analysis based on two-scale homogenization and matched asymptotic technique. In two-dimensional elasticity, we obtain jump conditions set on the in-plane displacements and normal stresses; the jumps involve in addition effective parameters provided by static, elementary problems being the equivalents of the cell problems in classical two-scale homogenization. The derivation of the model is conducted in the transient regime and its stability is guarantied by the positiveness of the effective interfacial energy. Spring models are envisioned as particular cases. It is shown that massless-spring models are recovered in the limit of small void thicknesses and collinear cracks. By contrast, the use of mass-spring model is justified at normal incidence, otherwise unjustified. We provide quantitative validations of our model and comparison with spring models by means of comparison with direct numerical calculations in the harmonic regime.
Highlights
Surfaces of separations between two elastic solids can impact significantly the propagation of waves
We extend the results of Marigo and co-workers [20,21] developed in a static context; the idea is to combine two-scale homogenization theory to treat the periodicity of the inhomogeneities and matched asymptotic technique to deal with the thin layer
We have derived effective jump conditions for an imperfect interface composed of an array of defects, e.g. voids or cracks
Summary
Surfaces of separations between two elastic solids can impact significantly the propagation of waves. In a series of papers, Rokhlin and co-workers have developed accurate transmission conditions and inspected the validity of spring models [5,6,7] This has revealed the limited range of validity of the massless-spring model; in particular, neglecting the inertial terms appears to be unjustified [8,9,10]. The case of thin layer interfaces containing cracks, micropores, voids or faults has received attention in particular for applications in seismology and in engineering for non-destructive testing Their academic study started in the 1980s with the works of Achenbach and his co-workers who investigated the scattering properties in many situations including spaced collinear cracks [11,12], inclined cracks [13], spherical cavities [14] as well as randomly distributed cracks [15]; a review is presented in [16].
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