Effective dynamics for low-amplitude transient elastic waves in a 1D periodic array of non-linear interfaces

This article focuses on the time-domain propagation of elastic waves through a 1D periodic medium that contains non-linear imperfect interfaces, i.e. interfaces exhibiting discontinuity in displacement and stress governed by constitutive relation. The array considered is generated a, possibly heterogeneous, cell repeated periodically bonded are associated with transmission conditions “spring–mass” type. More precisely, characterized linear dynamics but elasticity law. latter not specified at first only key theoretical assumptions required. In this context, we investigate transient both low-amplitude long-wavelength, aim deriving homogenized models describe their effective motion. To do so, two-scale asymptotic homogenization method deployed, up to first-order. begin, an model obtained for leading zeroth-order contribution microstructured wavefield. It amounts wave equation stress–strain relation inherited from behavior microscale. next first-order corrector term then shown be expressed terms function solution equation. Without further hypothesis, source depend non-linearly field, as does function. Combining these zeroth- leads approximation macroscopic wavefield its small-scale fluctuations within array. Finally, particularizing prototypical interface law cases homogeneous bilaminated one, illustrated set numerical examples compared full-field simulations. Both influence dominant wavelength amplitude investigated numerically, well characteristic features related phenomena.