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.

我们研究平面内弹性波与不完整界面的相互作用，该界面由空隙或裂缝的周期性阵列组成。一个有效的模型是基于两尺度均化和匹配渐近技术的高阶渐近分析得出的。在二维弹性中，我们获得了在平面位移和法向应力上设置的跳跃条件。跳跃还涉及静态提供的有效参数，基本问题与经典两尺度均质化中的单元问题等效。模型的推导是在瞬态过程中进行的，其稳定性由有效界面能的正性来保证。弹簧模型被设想为特殊情况。表明无质量弹簧在小孔隙厚度和共线裂纹的极限内恢复了模型。相比之下，在正常情况下使用质量弹簧模型是合理的，否则是不合理的。我们提供了对模型的定量验证，并通过与简谐形式中的直接数值计算进行比较的方式与弹簧模型进行了比较。