An unconstrained integral approximation of large sliding frictional contact between deformable solids

Poulios, Konstantinos; Renard, Yves

doi:10.1016/j.compstruc.2015.02.027

Cited by 27 publications

(39 citation statements)

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“…2(b), is to define y as the closest intersection of the contact surface with the line passing through point x and having direction vector n x . The latter strategy, which can be referred to as ray-tracing, was studied in [29]. Gap functions corresponding to ray-tracing and projection with respect to a point x(X) are respectively defined by:…”

Section: The Mapping and The Gap Functionmentioning

confidence: 99%

“…(2)) with respect to the displacement u in a virtual direction δu (see [29,23,22]) for detailed expressions.…”

Section: The Mapping and The Gap Functionmentioning

confidence: 99%

“…In the presence of friction, normal and tangential stresses at the contact interface are coupled through the sliding velocity vector v. As in [29], we use the frame indifferent definition of velocity described in [12]. Adapted to the current notation v(X) reads:…”

Section: Formulation Of Contact and Friction Conditionsmentioning

confidence: 99%

“…The formulations presented for instance in [15,22] employ the classic projection approach, while [31,36] present formulations that rely on the ray-tracing strategy. According to [29] the ray-tracing is more stable since the expression of the directional derivative of the mapping is quite simpler and expected to be smoother. Moreover, there are generally less special cases to treat when dealing with ray-tracing rather than projection since the probability to come across a non regular point, like a corner of the geometry or simply an element boundary, is negligible for the ray-tracing strategy while it is very frequent for the projection.…”

mentioning

confidence: 99%

“…This classical mapping will in the following be simply referred to as the projection strategy. In [29] this strategy is compared with another one named ray-tracing, where a point of the first surface is mapped to the closest intersection with the other surface along the first surface normal. Unlike projection the definition of the gap and related quantities are governed by the first surface normal n x .…”

mentioning

confidence: 99%

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

Mlika

Renard

Chouly

2017

Computer Methods in Applied Mechanics and Engineering

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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...

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Section: The Mapping and The Gap Functionmentioning

confidence: 99%

“…(2)) with respect to the displacement u in a virtual direction δu (see [29,23,22]) for detailed expressions.…”

Section: The Mapping and The Gap Functionmentioning

confidence: 99%

Section: Formulation Of Contact and Friction Conditionsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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

Mlika

Renard

Chouly

2017

Computer Methods in Applied Mechanics and Engineering

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Lagrangian and Nitsche Methods for Frictional Contact

CHOULY,

HILD,

RENARD

2024

Numerical Methods for Strong Nonlinearities in Mechanics

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An interface finite element based on a frictional contact formulation with an associative plasticity model for the tangential interaction

Michaloudis

Konyukhov

Gebbeken

2017

Numerical Meth Engineering

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Summary In this contribution, a three‐dimensional frictional contact formulation in the form of an interface solid finite element is discussed. The interface element incorporates normal as well as tangential contact conditions and aims at the modeling of phenomena occurring in engineering problems on the interface between different materials. The focus of this work lies on the description of the tangential interaction of bodies on their contact interface. Instead of the widely used Coulomb friction law, a simple elastoplastic material law is applied in order to model the interaction mechanism on the tangent plane. Appropriate local coordinate systems are introduced on the surface and point of contact, and all contact operations are performed in these coordinate systems by adopting a fully covariant description. In this way, we derive a symmetric element stiffness matrix not only for the case of sticking but also for sliding. Exploiting the advantages of the covariant description, we show that the fact that the derived stiffness matrix discretely consists of constitutive and geometrical parts enables us to introduce rather straightforwardly new appropriate interface laws describing the tangential interaction of the contacting bodies. The presented numerical results show very good correlation of the developed approach with ‘pull‐out’ experiments. Copyright © 2016 John Wiley & Sons, Ltd.

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An unconstrained integral approximation of large sliding frictional contact between deformable solids

Cited by 27 publications

References 31 publications

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

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

Lagrangian and Nitsche Methods for Frictional Contact

An interface finite element based on a frictional contact formulation with an associative plasticity model for the tangential interaction

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