Structure preserving time integration schemes for thermomechanical systems

本研究项目的主题是发展耦合系统接触问题的数值模拟方法。特别地，我们针对完全耦合的热力问题和相应的接触公式，考虑了在空间和时间上变分一致的方法来数值处理产生的系统。因此，需要发展用于热力系统空间离散的Morar方法和用于时间离散的结构保持积分器。考虑了基于拉格朗日和NURBS(等几何分析，IGA)的基本有限元方法的离散化。在第二个资助期的建议中，我们重点发展了IGA砂浆接触单元的结构保持时间积分格式。此外，我们的目标是结合复杂和高度非线性的摩擦定律来精确模拟热机械摩擦问题。

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.