How to incorporate the spring-mass conditions in finite-difference schemes

Abstract. The spring-mass conditions are an efficient way to model imperfect contacts between elastic media. These conditions link together the limit values of the elastic stress and of the elastic displacement on both sides of interfaces. To insert these spring-mass conditions in classical finite-difference schemes, we use an interface method, the Explicit Simplified Interface Method (ESIM). This insertion is automatic for a wide class of schemes. The interfaces do not need to coincide with the uniform cartesian grid. The local truncation error analysis and numerical experiments show that the ESIM maintains, with interfaces, properties of the schemes in homogeneous medium