We present a consistent approach that allows to solve challenging general nonlinear fluid‐structure‐contact interaction (FSCI) problems. The underlying formulation includes both “no‐slip” fluid‐structure interaction as well as frictionless contact between multiple elastic bodies. The respective interface conditions in normal and tangential orientation and especially the role of the fluid stress within the region of closed contact are discussed for the general problem of FSCI. A continuous transition of tangential constraints from no‐slip to frictionless contact is enabled by using the general Navier condition with varying slip length. Moreover, the fluid stress in the contact zone is obtained by an extension approach as it plays a crucial role for the lift‐off behavior of contacting bodies. With the given continuity of the formulation, continuity of the discrete system of equations for any variation of the coupled system state (which is essential for the convergence of Newton's method) is reached naturally. As topological changes of the fluid domain are an inherent challenge in FSCI configurations, a noninterface fitted cut finite element method (CutFEM) is applied to discretize the fluid domain. All interface conditions, that is the “no‐slip” FSI, the general Navier condition, and frictionless contact are incorporated using Nitsche based methods, thus retaining the consistency of the model. To account for the strong interaction between the fluid and solid discretization, the overall coupled discrete system is solved monolithically. Numerical examples of varying complexity are presented to corroborate the developments. In a first example, the fundamental properties of the presented formulation such as the contacting and lift‐off behavior, the mass conservation, and the influence of the slip length for the general Navier interface condition are analyzed. Beyond that, two more general examples demonstrate challenging aspects such as topological changes of the fluid domain, large contacting areas, and underline the general applicability of the presented method.

中文翻译：

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针对一般流体-结构-接触相互作用问题的一致且通用的计算方法

我们提出了一种一致的方法，可以解决具有挑战性的一般非线性流体-结构-接触相互作用（FSCI）问题。基本的配方既包括“防滑”流体结构相互作用，也包括多个弹性体之间的无摩擦接触。对于FSCI的一般问题，讨论了法向和切向方向上的各个界面条件，尤其是在闭合接触区域内流体应力的作用。通过使用具有不同滑移长度的一般Navier条件，可以实现切向约束从无滑接触到无摩擦接触的连续过渡。此外，接触区域中的流体应力是通过扩展方法获得的，因为它对于接触体的举升行为起着至关重要的作用。在给定的配方连续性的情况下，对于耦合系统状态的任何变化（对于牛顿方法的收敛必不可少的），自然可以达到离散方程组的连续性。由于流体域的拓扑变化是FSCI配置中固有的挑战，因此采用非界面拟合有限元切割方法（CutFEM）离散化流体域。使用基于Nitsche的方法将所有界面条件（即“防滑” FSI，一般的Navier条件和无摩擦接触）结合在一起，从而保持了模型的一致性。为了解决流体离散和固体离散之间的强相互作用，整体耦合的离散系统需要整体求解。提出了各种复杂程度的数值示例，以证实这一进展。在第一个例子中 分析了所提出配方的基本特性，例如接触和剥离行为，质量守恒以及滑移长度对一般Navier界面条件的影响。除此之外，还有两个更通用的示例说明了具有挑战性的方面，例如流体域的拓扑变化，较大的接触面积，并突显了所提出方法的一般适用性。