Interface damage modeled by spring boundary conditions for in-plane elastic waves

Abstract

In-plane elastic wave propagation in the presence of a damaged interface is investigated. The damage is modeled as a distribution of small cracks and this is transformed into a spring boundary condition. First the scattering by a single interface crack is determined explicitly in the low frequency limit for the case of a plane wave normally incident to the interface. The transmission at an interface with a random distribution of small cracks is then determined and is compared to periodically distributed cracks. The cracked interface is then described by a distributed spring boundary condition. As an illustration the dispersion relation of the first modes in a thick plate with a damaged interface in the middle is given.

Effective spring boundary conditions for a damaged interface between dissimilar media in three-dimensional case

“…Analogous comparisons have been made for dissimilar media with the method proposed by Glushkov and Glushkova (1996), with a very good correspondence (?). Following the scheme used in Golub and Boström (2011), consider a plane P or S wave incident normally to an interface with a random distribution of circular cracks of the same radius a, see Fig. 3.…”

“…It is then possible to neglect the interaction between the cracks if they are not located too close to each other, see more comments later on. The ensemble average of the total scattered field by a random distribution of cracks can be constructed in the same manner as in (Boström and Golub, 2009;Golub and Boström, 2011) in the form of outgoing plane waves propagating in the ±x 3 direction:…”

“…The present paper is an extension of previous work on distributions of strip-like cracks between dissimilar media (Boström and Golub, 2009;Golub, 2010;Golub and Boström, 2011;Kvasha et al, 2011) and the study of Boström and Wickham (1991), where a distribution of circular contacts between two identical half-spaces were considered. The aim of this study is to obtain expressions for the spring boundary conditions in three dimensions describing wave propagation through a damaged interface between dissimilar isotropic media in terms of elastic moduli and damage parameters.…”

“…An imperfection can be simulated as a set or multiple cracks (Achenbach, 1989;Achenbach and Zhang, 1990) or as a deviation from perfect contact (Tattersall, 1973;Baik and Thompson, 1984), and this leads to a modification of the continuous boundary conditions at the interface. Although the approaches are technically different, they lead to similar results related to wave propagation in composites with damaged interfaces (Baik and Thompson, 1984;Achenbach, 1989;Golub and Boström, 2011;Kvasha et al, 2011).…”

“…This substitution should lead to the same wavefields in the far-field zone from the interface. It should be mentioned that normal and transverse spring stiffnesses are equal in the case of in-plane motion (Lekesiz et al, 2011;Golub and Boström, 2011), while they differ in the three-dimensional case (Lekesiz et al, 2013a). Baik and Thompson (1984) used a quasi-static approximation for plane P-waves and obtained the expression for effective normal spring stiffness for identical materials.…”