Solution of a semi-coercive contact problem in a non-linear thermo-elastic rheology

In the paper a contact problem in non-linear thermo-elastic rheology is studied. A problem of unilateral contact between bodies in non-linear thermo-elasticity firstly leads to a generalization of non-linear stress–strain relation. The stress–strain relation is derived from a positive definite strain energy density function. The weak solution is defined on the basis of a variational inequality. Then the secant modules method is used. We prove the convergence of the secant modules method to the exact solution. The problem analysed corresponds with model problems of mechanics, geomechanics, biomechanics and technology.