A consistent and versatile computational approach for general fluid‐structure‐contact interaction problems

Ager, Christoph; Seitz, Alexander; Wall, Wolfgang A.

doi:10.1002/nme.6556

Cited by 15 publications

(44 citation statements)

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“…This allows to save the total number of degrees of freedom and thus improve efficiency, which is mandatory in view of three-dimensional applications. Regarding the contact in a FSI framework, this could be a limit of the method compared to others, such as the Cut-FEM in [2] and the fully-Eulerian approach in [24], which allow the possibility to use the continuous Finite Element method far from the interfaces and thus reducing the computational cost.…”

Section: Discussionmentioning

confidence: 99%

“…The authors prove a stability result and show some two-dimensional numerical examples obtained with conforming meshes. In [2], the Cut Finite Element Method (Cut-FEM) is employed to discretize the FSI problem and frictionless contact conditions are included via a consistent penalty method. In addition, it is proposed a transition from no-slip to slip coupling condition close to the contact limit, based on the general Navier condition, see e.g.…”

Section: Introductionmentioning

confidence: 99%

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A Polygonal Discontinuous Galerkin Formulation for Contact Mechanics in Fluid-Structure Interaction Problems

Zonca¹,

Antonietti²,

Vergara³

2021

CICP

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In this work, we propose a formulation based on the Polygonal Discontinuous Galerkin (PolyDG) method for contact mechanics that arises in fluid-structure interaction problems. In particular, we introduce a consistent penalization approach to treat the frictionless contact between immersed structures that undergo large displacements. The key feature of the method is that the contact condition can be naturally embedded in the PolyDG formulation, allowing to easily support polygonal/polyhedral meshes. The proposed approach introduced a fixed background mesh for the fluid problem overlapped by the structure grid that is able to move independently of the fluid one. To assess the validity of the proposed approach, we report the results of several numerical experiments obtained in the case of contact between flexible structures immersed in a fluid.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Polygonal Discontinuous Galerkin Formulation for Contact Mechanics in Fluid-Structure Interaction Problems

Zonca¹,

Antonietti²,

Vergara³

2021

CICP

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“…In order to make them accessible for the lubrication domain, they need to be defined with respect to the coordinates of the slave surface. For a point x (1) on the slave surface (in spatial configuration), one can find an associated point x (2) on the master surface by projecting x (1) along its current outward normal vector n…”

Section: Lubrication Partmentioning

confidence: 99%

A Mortar Finite Element Formulation for Large Deformation Lubricated Contact Problems with Smooth Transition Between Mixed, Elasto-Hydrodynamic and Full Hydrodynamic Lubrication

Faraji¹,

Seitz²,

Meier³

et al. 2022

Preprint

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This work proposes a novel model and numerical formulation for lubricated contact problems describing the mutual interaction between two deformable 3D solid bodies and an interposed fluid film. The solid bodies are consistently described based on nonlinear continuum mechanics allowing for finite deformations and arbitrary constitutive laws. The fluid film is modelled as a quasi-2D flow problem on the interface between the solids governed by the (thickness-)averaged Reynolds equation, which relates pressure to velocity and film thickness, with the latter two fields being provided by the averaged surface velocity and gap profile of the interacting solid bodies. The averaged Reynolds equation accounts for surface roughness utilizing spatially homogenized, effective fluid parameters and for cavitation through a positivity constraint imposed on the pressure field. In contrast to existing approaches, the proposed model accounts for the co-existence of frictional contact tractions and hydrodynamic fluid tractions at every local point on the contact surface of the interacting bodies and covers the entire range from boundary lubrication to mixed, elastohydrodynamic, and eventually to full film hydrodynamic lubrication in one unified modelling framework with smooth transition between these different regimes. Critically, the model relies on a recently proposed regularization scheme for the mechanical contact constraint combining the advantages of classical penalty and Lagrange multiplier approaches by expressing the mechanical contact pressure as a function of the effective gap between the solid bodies while at the same time limiting the minimal gap value occurring at the (theoretical) limit of infinitely high contact pressures. From a methodological point of view, this is the key ingredient to regularize the pressure field in the averaged Reynolds equation, i.e., to avoid the pressure field's singularity in the limit of vanishing fluid film thickness, and thus to enable a smooth transition between all relevant lubrication regimes. From a physical point of view, this approach can be considered as a model for the elastic deformation of surface asperities, with a bounded magnitude depending on the interacting solids' surface roughness. The finite element method is applied for spatial discretization of the 3D solid-mechanical problems and the 2D interface effects, consisting of the averaged Reynolds equation governing the fluid film and the non-penetration constraint of the mechanical contact problem, the latter relying on variationally consistent mortar methods for contact traction discretization. A consistent and accurate model behavior is demonstrated and validated by employing several challenging and practically relevant benchmark test cases. The ability of the model to accurately represent the velocity-dependent friction coefficient of the different lubrication regimes (i.e. mixed, elasto-hydrodynamic and full film lubrication) according to the well-known Stribek curve is also demonstrated via test cases. Eventually, a pa...

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“…4 As opposed to the moving-mesh approach considered by Hiromi-Spühler and Hoffman, the manuscript by Ager et al is concerned with an immersed (CutFEM) FSCI formulation, in which a continuous transition from the standard no-slip condition to frictionless contact is enabled by means of a generalized Navier boundary condition with variable slip coefficient. 5 A second important class of FSI problems with auxiliary interactions, pertains to FSI of free-boundary flows, that is, FSI problems in which the fluid subsystem itself exhibits a free surface or an interfaceThis is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.…”

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confidence: 99%

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confidence: 99%

Vanguard developments in computational methods for fluid‐structure interaction

Brummelen

Farhat

2021

Numerical Meth Engineering

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The analytical approach, which lies at the basis of the exact and natural sciences, rests on the notion that complex systems can be reduced to simple components. This divide-and-conquer approach has shaped contemporary science and technology, and has formed the foundation for virtually all scientific breakthroughs in the 19th and 20th century. It is also the origin of the separation of mechanics into fluid and solid mechanics, so much so that these branches of mechanics are commonly considered as distinct scientific disciplines. Notably, the disconnection between fluid and solid mechanics is evidenced by the tremendous advancements in computational methods and commercial simulation codes for fluid-and solid-mechanical systems separately, as compared to the relative underdevelopment of commercial codes for fluid-structure-interaction analyses.With the advancement of analysis capabilities for fluid-and structure-mechanics systems separately, emerged the realization that many problems in science and engineering cannot be appropriately categorized as either a fluid or structure problem, but are fundamentally determined by the interaction of a fluid and a solid. Examples are flutter and buffet instabilities in aerospace and civil engineering, the functioning of heart valves in biomechanics, sloshing and vibrations in flexible fluid containers and fluid conduits, deployment of inflatable structures such as airbeams and airbags, and deformation of soft substrates due to capillary forces, for example, in microfluidic applications and biomechanics. The development of computational methods for fluid-structure-interaction problems commenced in the early 1980s and many important foundations were laid in the 1990s. Despite the significant progress that has been made since then in computational models and methods for Fluid-Structure Interaction (FSI), many open challenges still remain, and computational FSI continues to be an active area of investigation and development.This special issue presents an overview of vanguard developments in computational methods for fluid-structure interaction. The 12 manuscripts in this special issue cover a variety of contemporary topics in computational FSI.The development of efficient and robust partitioned solution methods continues to be an important branch of research in computational FSI. Such partitioned solution methods allow to retain the modularity of the fluid and structure subsystems, thus enabling the reuse of the complete gamut of advanced commercial and open-source simulation software for fluid-dynamics and solid-dynamics problems separately. In this special issue, Cao et al. present a spatially-varying Robin coupling condition to mitigate the added-mass effect of incompressible flows in FSI in partitioned solution procedures. 1 In a similar vein, Dettmer et al. present a new combined two-field relaxation strategy to enhance the stability of the standard Dirichlet-Neumann FSI coupling strategy in the presence of strong added-mass effects. 2 The work by Rüth et al. is concerned wit...

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A consistent and versatile computational approach for general fluid‐structure‐contact interaction problems

Cited by 15 publications

References 55 publications

A Polygonal Discontinuous Galerkin Formulation for Contact Mechanics in Fluid-Structure Interaction Problems

A Polygonal Discontinuous Galerkin Formulation for Contact Mechanics in Fluid-Structure Interaction Problems

A Mortar Finite Element Formulation for Large Deformation Lubricated Contact Problems with Smooth Transition Between Mixed, Elasto-Hydrodynamic and Full Hydrodynamic Lubrication

Vanguard developments in computational methods for fluid‐structure interaction

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