Finite deformation coupled thermomechanical problems and generalized standard materials

Technological forming processes of thermo-elastoviscoplastic solids are numerically simulated via nite elements based on an appropriate theoretical framework. Departing from the local balance laws of linear momentum and internal energy, the constitutive behaviour is introduced via the concept of `generalized standard materials (gsm)ʹ,1{3 where a thermodynamic potential and a dissipation potential are the only two scalar quantities needed. They are expressed in invariants of symmetric mixed-variant tensors, respectively. Then the dissipation term evolves from the thermodynamic potential in a very natural way as well as the evolution equations for the internal variables emanate from the dissipation potential. An Eulerian setting is used. The numerical solution (of the non-linear coupled thermomechanical problem) is carried out via `displacement and assumed enhanced displacement-gradientʹ-based nite ring-elements4 in an `isentropicʹ mechanical phase and via `temperatureʹ-based nite ring-elements in an isogeometrical thermal phase and a global Newton{Raphson iterative method in both phases, respectively. The coupled consistent tangent moduli are carefully derived. Numerical results of the thermally triggered necking of a circular bar and of the impact of a copper rod on a rigid wall are given.