Methods and algorithms for contact mechanics.

由于接触力学可以处理各种工业应用，因此在计算力学领域中变得越来越重要。自本世纪初以来，许多研究项目集中在空间和时间上的所有一致公式的变分上。该研究项目的中心目标是开发一种最常见的接触公式，该方法可以处理接触表面的以下特性：接触中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结效应。要开发的公式将是最常见的，并且在很大程度上与所选的离散化无关。特别是，在等几何分析的背景下，考虑了拉格朗日网格以及NURBS和T样条线。此外，还将考虑实际接触区域的潜在断裂效应，使用现代相场方法。各种系统强制使用隐式积分器。因此，为了得到稳定的数值模拟，需要建立保持结构不变的时间积分格式。综上所述，将建立一个完整的、现代的、高效的、几乎可以应用于所有情况的接触模型。由于前一个项目的前期工作，这一目标只能在一个单一的供资期间内实现。

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.