Methods and algorithms for contact mechanics.

接触力学在计算力学领域中占有越来越重要的地位，因为它可以处理各种工业应用。自本世纪初以来，许多研究项目都集中在空间和时间上的变异和一致公式上。提出的研究项目的中心目标是开发一致接触公式的最常用方法，该方法可以处理接触面的以下特性：接触的两个表面都经历有限变形，库仑定律的各向异性效应和法向的粘着效应。要开发的公式将是最常见的，并且在很大程度上独立于所选择的离散化。特别地，拉格朗日网格以及NURBS和t样条在等几何分析的背景下被考虑。此外，还将使用现代相场方法考虑实际接触区域的潜在断裂效应。许多系统强制使用隐式积分器。因此，为了数值稳定的模拟，需要开发保持结构的时间积分方案。总结，一个完整的，现代的和有效的接触模型将被开发，可以应用于几乎所有的情况。由于前期项目的前期工作，该目标只能在一个资助期内完成。

Contact mechanics has become increasingly important in the field of computational mechanics since it can deal with a variety of industrial applications. Since the beginning of this century, many research projects focus on variationall consistent formulations in space and time. The central goal of the proposed research project is to develop a most common approach for consistent contact formulations, which can deal with the following properties of the contact surface: Both surfaces in contact undergo finite deformations, anisotropic effects of Coulomb's law and adhesive effects in normal directions.The formulation to be developed will be most common and largely independent of the chosen discretisation. In particular, Lagrangian meshes as well as NURBS and T-Splines within the context of isogeometric analysis are considered. Furthermore, potential fracture effects at the actual contact area will be considered as well, using modern phase-field methods. Various systems force the usage of implicit integrators. Therefore, structure preserving time integration schemes are to be developed for the sake of a numerically stable simulation.Summarised, a complete, modern and efficient contact model will be developed which can be applied to nearly all situations. The goal can be accomplished within only a single funding period due to preliminary work within the prior project.