A note for analysis of thermo-mechanical contact problems

A discussion about the bifurcation and non-uniqueness of solutions in the analysis of thermomechanical contact problems with initial gap is given. Without loss of generality, a mechanical contact problem coupled with steady heat transfer is studied and an example of non-uniqueness of solutions caused by the thermo-mechanical mechanism is presented. The important work is that the non-uniqueness of solutions, which is different from that found in the analysis of the traditional frictional contact problems, is studied in detail. The possible oscillation and non-convergence problems in the iteration process of the numerical computation are discussed, and an enhanced algorithm is put forward to overcome the difficulties.