A mortar finite element approach for point, line, and surface contact

Farah, Philipp; Wall, Wolfgang A.; Popp, Alexander

doi:10.1002/nme.5743

Cited by 16 publications

(6 citation statements)

References 63 publications

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“…Mortar methods for 3D continuum contact mechanics have been extensively studied in the literature [9][10][11][12][13][40][41][42][43][44][45][46]. These methods are characterized by contact constraints enforced in a weak sense and a saddle point formulation of the problem, where contact pressures play the role of Lagrange multipliers.…”

Section: Introductionmentioning

confidence: 99%

A mortar formulation for frictionless line-to-line beam contact

et al. 2021

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This paper describes the quasi-static formulation of frictionless line contact between flexible beams by employing the mortar finite element approach. Contact constraints are enforced in a weak sense along the contact region using Lagrange multipliers. A simple projection appropriate for thin beams with circular cross-sections is proposed for the computation of contact regions. It is combined with the geometrically exact beam formalism on the Lie group $SE(3)$ S E ( 3 ) . Interestingly, this framework leads to a constraint gradient and a tangent stiffness invariant under rigid body transformations. The formulation is tested in some numerical examples.

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Section: Introductionmentioning

confidence: 99%

A mortar formulation for frictionless line-to-line beam contact

et al. 2021

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“…More rigorously, second-order elements are often recommended to be utilized in the tread zone close to the ground to ensure proper contact pressure transmission to the ground, as extensively studied in computational mechanics materials [14], [15]. However, we consider linear elements for simplicity and mesh the structure so that the slave body's elements are smaller than the master body's elements.…”

Section: Mesh Propertiesmentioning

confidence: 99%

Toward detailed modeling of tires with linear elastic rubber compounds using finite element method

Tchuigwa,

Krmela,

Pokorny

2024

IOP Conf. Ser.: Earth Environ. Sci.

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Against a backdrop of increasing depletion of natural and energy resources and worsening global warming, the tire industry, like many other industries, is currently confronted with the pressing need to enhance not only its resilience but also the sustainability and cost-effectiveness of its products through advanced numerical simulations. Numerical simulation is a valuable tool in the tire development process that provides manufacturers with in-depth insights into their products from design to mass production. This paper aims to introduce a detailed finite element-based modeling process for tires that can be used for a wide range of simulations, including steady state, transient rolling, and failure scenarios such as layer delamination, blowout, and part breakage. The selected tire for the implementation in this study is designated 175/75R14 and was modeled in a static loading setup in ABAQUS standard with an implicit scheme considering linear elastic rubber compounds and other assumptions. Unlike the commonly used homogenized approach for reinforced layers, the proposed method takes into account the real physical and mechanical properties of the tire structure. In addition, important information pertaining to the creation of mesh and the interactions between elements is provided. The obtained results align with the assumptions and can serve as a proof of concept for more detailed and advanced tire modeling and enhancement in the future.

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“…The first approach consists of ignoring the side elements that are incident to the aforementioned mesh primitives when defining the discrete Lagrange multiplier as in Krause et al [75], hence introducing discontinuities of the solution at these interfaces. The second approach, which would require a set-up similar to Farah et al [76], consists of defining one-to-many relationships for the intersecting primitives. Here, one master primitive has to be determined and continuity is either enforced using interpolation for intersecting nodes, or with a weak equality condition for intersecting edges.…”

Section: Information Transfermentioning

confidence: 99%

Comparison and Application of non-Conforming Mesh Models for Flow in Fractured Porous Media using dual {L}agrange multipliers

Zulian¹,

Schädle²,

Karagyaur³

et al. 2020

Preprint

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Geological settings with reservoir characteristics include fractures with different material and geometrical properties. Hence, numerical simulations in applied geophysics demands for computational frameworks which efficiently allow to integrate various fracture geometries in a porous medium matrix. This study presents a modeling approach for single-phase flow in fractured porous media and its application to different types of non-conforming mesh models. We propose a combination of the Lagrange multiplier method with variational transfer to allow for complex non-conforming geometries as well as hybrid-and equi-dimensional models and discretizations of flow through fractured porous media. The variational transfer is based on the L 2 -projection and enables an accurate and highly efficient parallel projection of fields between non-conforming meshes (e.g., between fracture and porous matrix domain). We present the different techniques as a unified mathematical framework with a practical perspective. By means of numerical examples we discuss both, performance and applicability of the particular strategies. Comparisons of finite element simulation results to widely adopted 2D benchmark cases show good agreement and the dual Lagrange multiplier spaces show good performance. In an extension to 3D fracture networks, we first provide complementary results to a recently developed benchmark case, before we explore a complex scenario which leverages the different types of fracture meshes. Complex and highly conductive fracture networks are found more suitable in combination with embedded hybrid-dimensional fractures. However, thick and blocking fractures are better approximated by equi-dimensional embedded fractures and the equi-dimensional mortar method, respectively.

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A mortar finite element approach for point, line, and surface contact

Cited by 16 publications

References 63 publications

A mortar formulation for frictionless line-to-line beam contact

A mortar formulation for frictionless line-to-line beam contact

Toward detailed modeling of tires with linear elastic rubber compounds using finite element method

Comparison and Application of non-Conforming Mesh Models for Flow in Fractured Porous Media using dual {L}agrange multipliers

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