An Integral-Generalized Finite Difference Method for Interface Problems in Solid Mechanics

Abstract

Interface problems exist widely in various engineering problems and their high-precision simulation is of great importance. A new computational approach for dealing with interface problems is proposed based on the recently developed integral-generalized finite difference (IGFD) scheme. In this method, the research domain is divided into several subdomains by interfaces, and discretization schemes are established independently in each subdomain. A new cross-subdomain integration scheme is introduced to connect these subdomains. Several two-dimensional elasticity models containing material interfaces are studied to test the effectiveness of the proposed method. The results show that the recently proposed approach without the help of discontinuous functions or auxiliary equations that are commonly used in other numerical methods (e.g., extended finite element method and boundary element method) enables obtaining high accuracy and efficiency in interface problems. The proposed method has great potential in the application of material interface problems in solid mechanics and, furthermore, weak discontinuity problems in various fields.