A two-field state-based Peridynamic theory for thermal contact problems

Peridynamics is a non-local based method and an extension of classical continuum theory that has been proved to have the ability to solve problems involving discontinuities. This work extends the state-based Peridynamic formulation to describe heat transfer process in the adjacent regions via using the domain decomposition technique. The state-based Peridynamic heat conduction model is proposed to couple with a generalized thermal diffusion model in a two-field form, in which both the temperature and the thermal flux are treated as the primary variables. Coupled with thermal interface conditions, the proposed two-field state-based Peridynamic heat conduction naturally leads to a classical differential algebraic equation, which permits the numerical simulations of thermal contacts between various diffusion models. A unified time integration, termed as generalized single step single solve (GS4), is extended to solve the resulting differential algebraic equations. Numerical results of the simulations are reported and compared with those obtained by Finite Element Method which show that the method is promising for these applications in terms of accurately capturing the physics and preserving the interface conditions.