The bipotential method: A constructive approach to design the complete contact law with friction and improved numerical algorithms

Saxcé, Géry de; Feng, Zhi-Qiang

doi:10.1016/s0895-7177(98)00119-8

Cited by 156 publications

(134 citation statements)

References 9 publications

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“…De Saxcé and Feng [12] have shown that the contact law (13) is equivalent to the following differential inclusion:…”

Section: The Bi-potential Methodsmentioning

confidence: 99%

“…In order to avoid nondifferentiable potentials that occur in nonlinear mechanics, such as in contact problems, it is convenient to use the Augmented Lagrangian Method [9][10][11][12][13]. For the contact bi-potential b c , given by (17), provided thatu n ≥ 0 and r ∈ K μ , we have:…”

Section: The Bi-potential Methodsmentioning

confidence: 99%

“…In consequence, the unilateral contact and the friction are coupled via a contact bi-potential. The application of the augmented Lagrangian method to the contact laws leads to an equation of projection onto Coulomb's cone, strictly equivalent to the original inequality [12]. For additional comments, see also the interesting discussion by Klarbring et al [13,14].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bi-First: A simple and efficient algorithm to identify dissipated energy in impact problems

Feng

Magnain

Cros

et al. 2007

Int. J. Simul. Multidisci. Des. Optim.

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-The bi-potential method has been successfully applied for the modelling of frictional contact problems in static cases. This paper presents the extension of this method for dynamic analysis of impact problems with multiple deformable bodies. Instead of second order algorithms, a first order algorithm is applied for the numerical integration of the time-discretized equation of motion. The solution algorithm, named Bi-First, is simple and efficient. The principle of energy conservation for the given exemples is well preserved using the algorithm without any regularization. The numerical results also show clearly the physical energy dissipation introduced by frictional effects between the solids in contact.

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“…De Saxcé and Feng [12] have shown that the contact law (13) is equivalent to the following differential inclusion:…”

Section: The Bi-potential Methodsmentioning

confidence: 99%

Section: The Bi-potential Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bi-First: A simple and efficient algorithm to identify dissipated energy in impact problems

Feng

Magnain

Cros

et al. 2007

Int. J. Simul. Multidisci. Des. Optim.

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“…Another possibility, coming from De Saxcé bipotential theory (see [13,30]) is to replace the two separate projections (10) and (11) for the contact and friction conditions by the following single one:…”

Section: Using De Saxcé's Projectionmentioning

confidence: 99%

“…The uniqueness for both r > 0 and F ≥ 0 small enough can be obtained as follows: (20) is unique provided that a(·, ·) is coercive, the inf-sup condition (13) is satisfied and for r > 0 and F ≥ 0 small enough.…”

Section: Integral Approximation Of the Contact Conditionmentioning

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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Three‐dimensional finite element computations for frictional contact problems with non‐associated sliding rule

Feng

Saxcé²,

Mróz

2004

Numerical Meth Engineering

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International audienceThis paper presents an algorithm for solving anisotropic frictional contact problems where the sliding rule is non-associated. The algorithm is based on a variational formulation of the complex interface model that combine the classical unilateral contact law and an anisotropic friction model with a non-associated slip rule. Both the friction condition and the sliding potential are elliptical and have the same principal axes but with different semi-axes ratio. The frictional contact law and its inverse are derived from a single non-differentiable scalar-valued function, called a bi-potential. The convexity properties of the bi-potential permit to associate stationary principles with initial/boundary value problems. With the present formulation, the time-integration of the frictional contact law takes the form of a projection onto a convex set and only one predictor-corrector step addresses all cases (sticking, sliding, no-contact). A solution algorithm is presented and tested on a simple example that shows the strong influence of the slip rule on the frictional behaviour

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The bipotential method: A constructive approach to design the complete contact law with friction and improved numerical algorithms

Cited by 156 publications

References 9 publications

Bi-First: A simple and efficient algorithm to identify dissipated energy in impact problems

Bi-First: A simple and efficient algorithm to identify dissipated energy in impact problems

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

Three‐dimensional finite element computations for frictional contact problems with non‐associated sliding rule

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