- ph ] 1 4 O ct 2 00 5 NUMERICAL MODELING OF ELASTIC WAVES ACROSS IMPERFECT CONTACTS

A numerical method is described for studying how elastic waves interact with imperfect contacts such as fractures or glue layers existing between elastic solids. These contacts have been classicaly modeled by interfaces, using a simple rheological model consisting of a combination of normal and tangential linear springs and masses. The jump conditions satisfied by the elastic fields along the interfaces are called the " spring-mass conditions ". By tuning the stiffness and mass values, it is possible to model various degrees of contact, from perfect bonding to stress-free surfaces. The conservation laws satisfied outside the interfaces are integrated using classical finite-difference schemes. The key problem arising here is how to discretize the spring-mass conditions, and how to insert them into a finite-difference scheme: this was the aim of the present paper. For this purpose, we adapted an interface method previously developed for use with perfect contacts [J. Comput. Phys. 195 (2004) 90-116]. This numerical method also describes closely the geometry of arbitrarily-shaped interfaces on a uniform Cartesian grid, at negligible extra computational cost. Comparisons with original analytical solutions show the efficiency of this approach. 1. Introduction. Here it is proposed to study the propagation of mechanical waves in an elastic medium divided into several subdomains. The wavelengths are assumed to be much larger than the thickness of the contact zones between subdo-mains, or interphases [18]. Each interphase is replaced by a zero-thickness interface, where elastic fields satisfy jump conditions. In elastodynamics, the contacts between elastic media are usually assumed to be perfect [1]. They can therefore be modeled by perfect jump conditions, such as perfectly bonded, perfectly lubricated, or stress-free conditions. For example, perfectly bonded conditions will mean that both elastic displacements and normal elastic stresses are continuous across the interface at each time step. In practice, contacts are often imperfect because of the presence of microcracks or interstitial media in the interphase. Take, for example, fractures in the earth, which are filled with air or liquid, and where jumps occur in the elastic displacements and elastic stresses. The simplest imperfect conditions are the spring-mass conditions (which are sometimes called " linear slip displacements "): these conditions are realistic in the case of incident waves with very small amplitudes [17]. The spring-mass conditions have been extensively studied, both theoretically and experimentally [18, 20, 21]. This approach has been applied in various disciplines, such as nonde-structive evaluation of materials [2, 22] …