A reduced integration finite element technology based on a thermomechanically consistent stabilisation for 3D problems

In this paper we suggest a new finite element technology for thermomechanically fully coupled problems. It is based on the method of reduced integration with hourglass stabilisation. The proposed formulation allows the evaluation of the additional thermal field at one Gauss point, e.g. in the centre of the element. One crucial aspect is the Taylor expansion of all constitutively dependent variables, as e.g. the heat flux, the internal and the external rates of dissipation, with respect to the centre of the element. In this way a so-called thermal hourglass stabilisation, analogously to the classical mechanical hourglass stabilisation, is derived. The thermal stabilisation parameters are defined well and the computational efficiency which comes along with the consistent formulation is very high. The new element formulation is applied on thermomechanically coupled problems of finite elastoplasticity. It can be also easily used in the context of other multi-field problems.