334 research outputs found

    Space-time adaptive finite elements for nonlocal parabolic variational inequalities

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    This article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction, both in the domain and on the boundary. For a large class of parabolic variational inequalities associated to the fractional Laplacian we obtain a priori and a posteriori error estimates and study the resulting space-time adaptive mesh-refinement procedures. Particular emphasis is placed on mixed formulations, which include the contact forces as a Lagrange multiplier. Corresponding results are presented for elliptic problems. Our numerical experiments for 22-dimensional model problems confirm the theoretical results: They indicate the efficiency of the a posteriori error estimates and illustrate the convergence properties of space-time adaptive, as well as uniform and graded discretizations.Comment: 47 pages, 20 figure

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

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    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 pp and p−2p-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

    A Bipotential Method Coupling Contact, Friction and Adhesion

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    International audience– The paper is related to the analysis and the modeling of structural interface behaviors when unilateral contact, friction and adhesion interact. Among the contact models in literature, the model developed by Raous, Cangémi, Cocou and Monerie (RCCM model) is retained. It consists to include strict unilateral contact to avoid interpenetration, initial adhesion progressively decreases when the load increases, and Coulomb's friction which is progressively activated when adhesion decreases. Because of its implicit character, the Coulomb friction law with adhesion is non-associated, and the notion of superpotential with normality rule cannot be used anymore. In the present work, to overcome this non-associated character, a specific potential adapted to coupling unilateral contact, friction and adhesion is build and named bipotential. A numerical model is proposed and improved to solve the boundaries values problem. The algorithm is implemented in the finite element code SYMEF which has been developed at the University of Bechar (Algeria). A comparative study is made between the bipotential model and the previously developed RCCM model. The numerical results show that, this approach is robust and efficient in terms of numerical stability, precision convergence and CPU time compared to the RCCM model

    Generalized Newton methods for the 2D-Signorini contact problem with friction in function space

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    International audienceThe 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented Lagrangians allows to apply an infinite-dimensional semi-smooth Newton method for the solution of the problem with given friction. The resulting algorithm is locally superlinearly convergent and can be interpreted as active set strategy. Combining the method with an augmented Lagrangian method leads to convergence of the iterates to the solution of the original problem. Comprehensive numerical tests discuss, among others, the dependence of the algorithm's performance on material and regularization parameters and on the mesh. The remarkable efficiency of the method carries over to the Signorini problem with Coulomb friction by means of fixed point ideas

    Numerical modeling of three dimensional divided structures by the Non Smooth Contact dynamics method: Application to masonry structures

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    International audienceThis paper outlines a computational method for modelling 3D divided structures by means of interface models, characterized by unilateral properties. The theoretical framework belongs to the field of non-smooth mechanics which aims at solving problems where severe time and space discontinuities are encountered. Multi-valued and stiff interfaces laws, e.g., Signorini's condition and Coulomb's friction, are solved using tools and formalisms provided by convex analysis. This general framework is adapted to micro-modelling approach of masonry structures, specifying interfaces models to mortar joints behaviour. The various stages in the development and implementation of an algorithm are delineated. Reaching a quasistatic equilibrium of floating structure is discussed and some numerical applications are presented on didactic tests

    Adaptive numerical simulation of contact problems : Resolving local effects at the contact boundary in space and time

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    This thesis is concerned with the space discretization of static and the space and time discretization of dynamic contact problems. In particular, we derive a new efficient and reliable residual-type a posteriori error estimator for static contact problems and a new space-time connecting discretization scheme for dynamic contact problems in linear elasticity. The methods enable the efficient resolution of local effects at the contact boundary in space and time. Firstly, we prove efficiency and reliability of the new residual-type a posteriori error estimator for the case of simplicial meshes. Several numerical examples in the two- and three-dimensional case show the performance of the residual-type a posteriori error estimator for simplicial and even for non-simplicial meshes. Secondly, for the discretization in time, we present a new method which allows to implicitly compute the local impact times of each node without decreasing the time step size. As it turns out this method gives rise to a generalization of the Newmark scheme which takes into account the local impact times without additional computational effort
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