4. Resistance Spot Welding

In the current chapter we debate a joining process called resistance spot welding which finds many applications ranging from the automobile industry to robotics. In the first part of the chapter we present the construction of a non-local mathematical model illustrating the phase transition occurs during this joining process. Since the derived model consists of a degenerate non-local parabolic equation its analytical study is rather hard due to many arising technicalities and so we appeal to a numerical approach. We then consider a time discretization scheme for solving the resulting non-local moving boundary problem. The scheme consists of solving at each time step a linear elliptic partial differential equation and then making a correction which takes into account the nonlinearity. The stability and error estimates of the developed scheme are also investigated. Finally, some numerical experiments are presented which verify the efficiency of the developed numerical algorithm, as well as demonstrate the emergent interfaces due to the degeneracy of the problem.