Robust implementation of contact under friction and large sliding with the eXtended finite element method

Siavelis, Maximilien; Massin, Patrick; Guiton, Martin; Mazet, Sylvain; Moës, Nicolas

doi:10.3166/ejcm.19.189-203

Cited by 12 publications

(6 citation statements)

References 14 publications

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“…Mixed Lagrange multiplier and mortar methods are studied by Liu and Borja (2010) and Giner et al (2010), respectively. Finite deformations are considered, for example, by Nistor et al (2009), Siavelis et al (2010, Taheri Mousavi and Taheri Mousavi (2011) and Biotteau and Ponthot (2012). In this study we adopt a Lagrange multiplier approach, similar to the one of Geniaut et al (2007), for modeling sliding contact problems assuming a linear elastic material behavior and infinitesimal strains.…”

Section: Introductionmentioning

confidence: 99%

Level set topology optimization of problems with sliding contact interfaces

Lawry

Maute

2015

Struct Multidisc Optim

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This paper introduces a topology optimization method for the design of two-component structures and two-phase material systems considering sliding contact and separation along interfaces. The geometry of the contact interface is described by an explicit level set method which allows for both shape and topological changes in the optimization process. The mechanical model assumes infinitesimal strains, a linear elastic material behavior, and a quasi-static response. The contact conditions are enforced by a stabilized Lagrange multiplier method and an active set strategy. The mechanical model is discretized by the extended finite element method which retains the crispness of the level set geometry description and allows for the convenient integration of the weak form of the contact conditions at the phase boundaries. The formulation of the optimization problem is regularized by introducing a perimeter penalty into the objective function. The optimization problem is solved by a nonlinear programming scheme computing the design sensitivities by the adjoint method. The main characteristics of the proposed method are studied by numerical examples in two dimensions. Consideration of contact leads to the formation of barb-type features that increase the interface stiffness. The numerical results further demonstrate the significant difference in the optimized geometries when assuming perfect bonding versus considering contact.

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Section: Introductionmentioning

confidence: 99%

Level set topology optimization of problems with sliding contact interfaces

Lawry

Maute

2015

Struct Multidisc Optim

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“…In that case, this is generally the non-positivity on each node of the multiplier which is considered. A third possibility, used more or less implicitly is some references (for instance in [30,39]) is to use directly a non constrained integral weak formulation of the contact condition. From the resolution with a Newton algorithm point of view, the two first alternatives are very close.…”

Section: Finite Element Approximationmentioning

confidence: 99%

Generalized Newton’s methods for the approximation and resolution of frictional contact problems in elasticity

Renard

2013

Computer Methods in Applied Mechanics and Engineering

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In this paper, some new generalized Newton's methods for the resolution of elastostatic frictional contact problem approximated by finite elements are presented and compared to existing ones. A numerical experimentation is performed to compare the different methods, especially with respect to the sensitivity to the method parameter. Two different strategies to approximate the contact and friction condition are considered: a nodal and an integral one. Existence and uniqueness results of the solution to the discretized problem are also discussed.

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“…However, it can easily be extended to recent improvements (treatment of blending elements for improved convergence rate, new discontinuous enrichments, etc.) 14, 15, 17, 18, 29, 33.…”

Section: X‐fem Discretization and Non‐linear Solver Dedicated To Cmentioning

confidence: 99%

“…Even local convergence can be ensured locally, both on the normal and tangential problems, it is well known that two‐field or three‐field formulation with Lagrange multipliers can involve spurious oscillations on the dual fields. Indeed, some numerical experiments (depending on the type of finite elements in the bulk, interface discretization, mortar operators, non‐linear behavior along the crack faces, such as friction) and also previous contributions 14, 16–18, 28, 29, 41 clearly illustrate the need to avoid these oscillations.…”

Section: X‐fem Discretization and Non‐linear Solver Dedicated To Cmentioning

confidence: 99%

“…Recently, many attempts have been proposed in the literature to study and improve the stability properties of enriched finite element methods and more particularly the extended finite element method with frictional interfaces. Mortar methods and reduced Lagrange methods 7, 14–19have been used to solve over‐constrained contact problems by reducing the discrete interpolation space, i.e. the number of integration points, on the interface.…”

Section: Introductionmentioning

confidence: 99%

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Stabilized global-local X-FEM for 3D non-planar frictional crack using relevant meshes

Gravouil

Pierres

Baietto

2011

Int. J. Numer. Meth. Engng.

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SUMMARYA stabilized global-local quasi-static contact algorithm for 3D non-planar frictional crack is presented in the X-FEM/level set framework. A three-field weak formulation is considered and allows an independent discretization of the bulk and the crack interface. Then, a fine discretization of the interface can be defined according to the possible complex contact state along the crack faces independently from the mesh in the bulk. Furthermore, an efficient stabilized non-linear LATIN solver dedicated to contact and friction is proposed. It allows solving in a unified framework frictionless and frictional contact at the crack interface with a symmetric formulation, no iterations on the local stage (unilateral contact law with/without friction), no calculation of any global tangent operator, and improved convergence rate. 2D and 3D patch tests are presented to illustrate the relevance of the proposed model and an actual 3D frictional crack problem under cyclic fretting loading is modeled.

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Robust implementation of contact under friction and large sliding with the eXtended finite element method

Cited by 12 publications

References 14 publications

Level set topology optimization of problems with sliding contact interfaces

Level set topology optimization of problems with sliding contact interfaces

Generalized Newton’s methods for the approximation and resolution of frictional contact problems in elasticity

Stabilized global-local X-FEM for 3D non-planar frictional crack using relevant meshes

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