An error estimate for the Signorini problem with Coulomb friction approximated by finite elements

International audienceThe present paper is concerned with the unilateral contact model and the Coulomb friction law in linear elastostatics. We consider a mixed formulation in which the unknowns are the displacement field and the normal and tangential constraints on the contact area. The chosen finite element method involves continuous elements of degree one and continuous piecewise affine multipliers on the contact zone. A convenient discrete contact and friction condition is introduced in order to perform a convergence study. We finally obtain a first a priori error estimate under the assumptions ensuring the uniqueness of the solution to the continuous problem

A uniqueness criterion for the Signorini problem with Coulomb friction

International audienceThe purpose of this paper is to study the solutions to the Signorini problem with Coulomb friction (the so-called Coulomb problem). Some optimal a priori estimates are given, and a uniqueness criterion is exhibited. Recently, nonuniqueness examples have been presented in the continuous framework. It is proved, here, that if a solution satisfies a certain hypothesis on the tangential displacement and if the friction coefficient is small enough, it is the unique solution to the problem. In particular, this result can be useful for the search of multisolutions to the Coulomb problem because it eliminates a lot of uniqueness situations

Residual-based a posteriori error estimation for contact problems approximated by Nitsche's method

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Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem

In this work we analyze a non-clamped dynamic viscoelastic contact problem involving thermal effect. The friction law is described by a nonmonotone relation between the tangential stress and the tangential velocity. This leads to a system of hyperbolic inclusion for displacement and parabolic equation for temperature. We provide a fully discrete approximation of studied problem and find optimal error estimates without any smallness assumption on the data. The theoretical result is illustrated numerically.Comment: 19 pages, unfinishe

A priori error for unilateral contact problems with Lagrange multiplier and IsoGeometric Analysis

In this paper, we consider unilateral contact problem without friction between a rigid body and deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem using an active-set strategy and for a primal space of NURBS of degree $p$ and $p-2$ for a dual space of B-Spline. A inf-sup stability is proved to ensure a good property of the method. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two- and three-dimensional and in small and large deformation demonstrate the accuracy of the proposed method