Mixed finite element formulation in large deformation frictional contact problem

Baillet, Laurent; Sassi, Taoufik

doi:10.3166/reef.14.287-304

Cited by 17 publications

(17 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We use the mortar approach to drive the communication between different (incompatible) meshes. This mortar concept has been successfully extended to the variational inequalities in [5] for linear finite elements and employed in many computations; we refer for instance to [3,20,26,32,37,38,43]. The convergence rates established in this paper for the quadratic finite elements are similar to those already stated in [4,27,28] when matching grids are employed.…”

Section: Resultssupporting

confidence: 62%

See 1 more Smart Citation

Quadratic finite elements with non-matching grids for the unilateral boundary contact

Auliac¹,

Belhachmi²,

Belgacem³

et al. 2013

ESAIM: M2AN

View full text Add to dashboard Cite

Abstract.We analyze a numerical model for the Signorini unilateral contact, based on the mortar method, in the quadratic finite element context. The mortar frame enables one to use non-matching grids and brings facilities in the mesh generation of different components of a complex system. The convergence rates we state here are similar to those already obtained for the Signorini problem when discretized on conforming meshes. The matching for the unilateral contact driven by mortars preserves then the proper accuracy of the quadratic finite elements. This approach has already been used and proved to be reliable for the unilateral contact problems even for large deformations. We provide however some numerical examples to support the theoretical predictions.Mathematics Subject Classification. 35J85, 65N30, 74M15.

show abstract

Section: Resultssupporting

confidence: 62%

“…A literature exists on the linear mortar finite element method for the Signorini problem. We refer to [3,5,25,26,42] without being exhaustive. Users are recommended not to enforce the unilateral conditions on the discrete solution before running the mortar projection.…”

Section: Introductionmentioning

confidence: 99%

Quadratic finite elements with non-matching grids for the unilateral boundary contact

Auliac¹,

Belhachmi²,

Belgacem³

et al. 2013

ESAIM: M2AN

View full text Add to dashboard Cite

show abstract

“…This method has been demonstrated to be robust [40]. The advantage of using the Lagrange multipliers is that the contact laws introduced above are strictly verified, which is primordial for the modeling of contact dynamics generated by the CAN.…”

Section: Contacting Interface Modeling and Contact Lawsmentioning

confidence: 99%

2D finite element modeling of the non-collinear mixing method for detection and characterization of closed cracks

Blanloeuil

Méziane

Bacon

2015

NDT & E International

View full text Add to dashboard Cite

Cite this article as: P. Blanloeuil, A. Meziane, C. Bacon, 2D Finite Element modeling of the non-collinear mixing method for detection and characterization of closed cracks, NDT&E International, http://dx.doi.org/10.1016/j. ndteint. 2015.08.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractThe non-collinear mixing technique is applied for detection and characterization of closed cracks.The method is based on the nonlinear interaction of two shear waves generated with an oblique incidence, which leads to the scattering of a longitudinal wave. A Finite Element model is used to demonstrate its application to a closed crack. Contact acoustic nonlinearity is modeled using unilateral contact law with Coulomb's friction. The method is shown to be effective and promising when applied to a closed crack. Scattering of the longitudinal wave also enables us to image the crack, giving its position and size.

show abstract

“…In the literature, many attempts have been developed to deal with such problems using the finite element method. In most cases, the difficulty caused by the nondifferentiability of contact and friction laws is resolved with either a method of regularization, such as penalization or augmented Lagrangian [21,34], or a mixed method [20,3].Moreover, the spatial discretization of the problem produces difficulties at level of the calculation of mechanical contact. Evaluating the quantities involved in the equations of mechanical contact is difficult when the two boundaries are discretized.…”

mentioning

confidence: 99%

An unbiased Nitsche’s formulation of large deformation frictional contact and self-contact

Mlika

Renard

Chouly

2017

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

In this paper we propose an extension of Nitsche's method for frictional contact in large elastic deformations. In fact we develop an unbiased strategy in which no asymmetry is considered between contact surfaces, conversely to the master-slave strategy. This enables to take into account within the same formalism contact of two elastic bodies as well as self-contact. We provide a numerical study of the performance and robustness of the method.Keywords: large deformation contact, frictional contact and self-contact, Nitsche's method, unbiased formulation. IntroductionFrictional contact problems involve difficulties from both theoretical and numerical viewpoints, especially in large deformations, where complex geometrical and mechanical quantities depend on an a priori unknown mapping between contact surfaces. Contact problems are inherently non-linear, even non-smooth, and involve variational inequalities and constrained minimization. In the literature, many attempts have been developed to deal with such problems using the finite element method. In most cases, the difficulty caused by the nondifferentiability of contact and friction laws is resolved with either a method of regularization, such as penalization or augmented Lagrangian [21,34], or a mixed method [20,3].Moreover, the spatial discretization of the problem produces difficulties at level of the calculation of mechanical contact. Evaluating the quantities involved in the equations of mechanical contact is difficult when the two boundaries are discretized. The most commonly used method is the node-to-surface (NTS) approach under a master-slave configuration [24,30]. The use of the NTS method involves a loss of accuracy in the calculation of displacements and stresses in the contact area. This results from the amplification of spatial discretization errors caused by the node-wise contact constraint enforcement. A way to overcome this problem is the use of the mortar method which has been successfully applied to solve contact problems with finite deformations [15,31,28]. In this method, the enforcement of contact constraints is applied in a weak sense throughout the contact interface. The calculation of contact can also be done by other ways such as contact domain methods [27,17] and intermediate mortar surface method [25]. A theoretical and algorithmic background for the contact between two deformable bodies undergoing large deformations is detailed in, e.g., [23,37].In this paper we introduce a Nitsche's method for the large deformation contact problem. Nitsche's method was originally proposed in [26] to take into account a Dirichlet condition weakly. It was adapted to bilateral contact in [18,38] and to unilateral contact in [8,9]. This method aims at treating the interface conditions in a weak sense, thanks to a consistent penalty term. So it differs from standard penalization techniques which are nonconsistent. Conversely to mixed method and augmented Lagrangian method, the proposed approach is primal; this allows us to eliminate an outer augme...

show abstract

Mixed finite element formulation in large deformation frictional contact problem

Abstract: ABSTRACT. This paper presents a mixed variational framework and numerical examples to

Cited by 17 publications

References 19 publications

Quadratic finite elements with non-matching grids for the unilateral boundary contact

Quadratic finite elements with non-matching grids for the unilateral boundary contact

2D finite element modeling of the non-collinear mixing method for detection and characterization of closed cracks

An unbiased Nitsche’s formulation of large deformation frictional contact and self-contact

Contact Info

Product

Resources

About