Structure preserving time integration schemes for thermomechanical systems

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Topic of this research project is the development of numerical methods for the simulation of contact problem for coupled systems. In particular, we aim at fully coupled thermomechanical problems and the corresponding contact formulations.Variationally consistent methods in space and time are considered for the numerical treatment of the arising system. Therefore, Mortar methods for the spatial discretisation of the thermomechanical system and structure preserving integrators for the temporal discretisation are to be developed. Lagrangian as well as NURBS (Isogeometric analysis, IGA) based discretisation of the underlying finite element methods are considered.In this proposal for the second funding period we focus on the development of structure preserving time integration schemes for IGA Mortar contact elements. Furthermore, we aim at the incorporation of complex and highly non-linear friction laws for a precise simulation of thermomechanical friction problems.