Isogeometric Analysis and thermomechanical Mortar contact problems

•We present a Mortar based approach for thermomechanical contact problems.•An isogeometric approach for the discretisation is considered.•A consistent thermodynamical model is used.•Constitutive laws for the thermomechanical contact interface are applied. Thermomechanical Mortar contact algorithms and their application to NURBS based Isogeometric Analysis are investigated in the context of nonlinear elasticity. Mortar methods are applied to both the mechanical field and the thermal field in order to model frictional contact, the energy transfer between the surfaces as well as the frictional heating. A series of simplifications are considered so that a wide range of established numerical techniques for Mortar methods such as segmentation can be transferred to IGA without modification. The performance of the proposed framework is illustrated with representative numerical examples.