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A. Curnier - One of the best experts on this subject based on the ideXlab platform.
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Large deformation Frictional Contact mechanics: continuum formulation and augmented Lagrangian treatment
Computer Methods in Applied Mechanics and Engineering, 1999Co-Authors: G. Pietrzak, A. CurnierAbstract:Absract A complete methodology for the formulation and solution of unilateral Contact problem with non-associated, threshold friction between solids undergoing large deformations is presented. The approach includes a continuum Contact mechanics model combined with an augmented Lagrangian method for treating the Contact and friction inequality constraints. The main developments are a precise statement of the incremental Contact minimization problem, the exact computations of the first and second variations of the normal gap and the tangential slip velocity and an extension of the augmented Lagrangian formulation for Frictional Contact problems from the discrete to the continuum framework. The corresponding saddle-point functional first variation (mixed virtual work) and second variation (exact linearization) are given. The development are illustrated by numerical simulations of Frictional Contact problems between rigid, elastic and elastoplastic bodies. A new severe benchmark for large slip Frictional Contact elements is also proposed.
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A mixed formulation for Frictional Contact problems prone to Newton like solution methods
Computer Methods in Applied Mechanics and Engineering, 1991Co-Authors: P. Alart, A. CurnierAbstract:Abstract A mixed penalty-duality formulation of the Frictional Contact problem, inspired from an augmented Lagrangian approach is proposed. The continuity of the resulting conewise linear operator is used to establish a uniqueness condition on the coefficient of friction. Modified and generalized Newton methods are examined and sufficient conditions for their convergence conjectured. A cylindrical Frictional Contact problem assesses the stability of the method. Mixed penalty-duality methods are found more accurate and stabler than penalty methods and as economical as them.
P. Wriggers - One of the best experts on this subject based on the ideXlab platform.
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three dimensional mortar based Frictional Contact treatment in isogeometric analysis with nurbs
Computer Methods in Applied Mechanics and Engineering, 2012Co-Authors: I Temizer, P. Wriggers, Thomas J R HughesAbstract:A three-dimensional mortar-based Frictional Contact treatment in isogeometric analysis with NURBS is presented in the finite deformation regime. Within a setting where the NURBS discretization of the Contact surface is inherited directly from the NURBS discretization of the volume, the Contact integrals are evaluated through a mortar approach where the geometrical and Frictional Contact constraints are treated through a projection to control point quantities. The formulation delivers a non-negative pressure distribution and minimally oscillatory local Contact interactions with respect to alternative Lagrange discretizations independent of the discretization order. These enable the achievement of improved smoothness in global Contact forces and moments through higher-order geometrical descriptions. It is concluded that the presented mortar-based approach serves as a common basis for treating isogeometric Contact problems with varying orders of discretization throughout the Contact surface and the volume.
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Application of Frictional Contact in Geotechnical Engineering
International Journal of Geomechanics, 2007Co-Authors: Daichao Sheng, P. Wriggers, Scott W. SloanAbstract:Soil-structure interaction is traditionally simplified to prescribed boundary conditions or modeled by joint elements. Both of these approaches are limited to small and continuous relative displacements at the interface. The use of Contact constraints opens up a fresh range of possibilities for geotechnical analysis, especially for cases involving large interfacial deformation. This paper demonstrates the application of computational Contact mechanics in geotechnical engineering. It first outlines a general description of kinematic constraints for Frictional Contact and the associated numerical algorithms. A number of classical geotechnical problems are then analyzed using finite-element Contact methods. These problems include a strip footing under eccentric and inclined loads and a cone penetration test. It is shown that the finite-element method with Frictional Contact is indeed very useful in geotechnical analysis, and can provide solutions to problems that are otherwise very difficult to analyze.
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Improved numerical algorithms for Frictional Contact in pile penetration analysis
Computers and Geotechnics, 2006Co-Authors: Daichao Sheng, P. Wriggers, Scott W. SloanAbstract:Abstract This paper presents a numerical formulation for Frictional Contact problems associated with pile penetration. The Frictional Contact at the soil–pile interface is formulated using the theory of hardening/softening plasticity, so that advanced models for the interface can be dealt with. A smooth discretisation of the pile surface is proposed using Be zier polynomials. An automatic load stepping scheme is proposed, which features an error control algorithm and automatic subincrementation of the load increments. The numerical algorithms are then used to analyse the installation process of pushed-in axial piles. It is shown that the smooth discretisation of the pile surface is effective in reducing the oscillation in the predicted pile resistances and the automatic load stepping scheme outperforms the classical Newton–Raphson scheme for this type of problem.
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Improved numerical algorithms for Frictional Contact in pile penetration analysis
Computers and Geotechnics, 2006Co-Authors: Daichao Sheng, P. Wriggers, Scott W. SloanAbstract:This paper presents a numerical formulation for Frictional Contact problems associated with pile penetration. The Frictional Contact at the soil–pile interface is formulated using the theory of hardening/softening plasticity, so that advanced models for the interface can be dealt with. A smooth discretisation of the pile surface is proposed using BéZIER polynomials. An automatic load stepping scheme is proposed,which features an error control algorithm and automatic subincrementation of the load increments. The numerical algorithms are then used to analyse the installation process of pushed-in axial piles. It is shown that the smooth discretisation of the pile surface is effective in reducing the oscillation in the predicted pile resistances and the automatic load stepping scheme outperforms the classical Newton–Raphson scheme for this type of problem
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Frictional Contact between 3d beams
Computational Mechanics, 2002Co-Authors: Przemyslaw Litewka, P. WriggersAbstract:The paper deals with Frictional Contact between 3D beams with rectangular cross-sections. In the analysis large displacements and small strains are allowed. Hence the cross-section behaves like a rigid body undergoing displacement and rotations. Contact between the beams is assumed to be point-wise between their edges. For the friction the simple non-associated Coulomb law is adopted. The analogy to rigid plasticity is used where stick and slip conditions are considered and backward Euler scheme is applied whenever the yield condition is violated. Contact constraints for normal and tangential part are introduced using the active set strategy and the penalty method. A consistent linearisation of both Contact contributions is derived and expressed in suitable matrix form, easy to use in FEM approximations. Several numerical examples including the comparison to the full 3D-solid analysis depict the efficiency of the presented approach.
Anthony Gravouil - One of the best experts on this subject based on the ideXlab platform.
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A multiscale LATIN/FAS algorithm with time-space model reduction for Frictional Contact problems
International Journal for Numerical Methods in Engineering, 2014Co-Authors: Anthony Giacoma, David Dureisseix, Anthony Gravouil, Michel RochetteAbstract:A multiscale strategy using model reduction for Frictional Contact computation is presented. This new approach aims to improve computation time of finite element simulations involving Frictional Contact between linear and elastic bodies. This strategy is based on a combination between the LATIN (LArge Time INcrement) method and the FAS multigrid solver. The LATIN method is an iterative solver operating on the whole time-space domain. Applying an a posteriori analysis on solutions of different Frictional Contact problems shows a great potential as far as reducibility for Frictional Contact problems is concerned. Time-space vectors forming the so-called reduced basis depict particular scales of the problem. It becomes easy to make analogies with multigrid method to take full advantage of multiscale information.
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A multiscale large time increment/FAS algorithm with time-space model reduction for Frictional Contact problems
International Journal for Numerical Methods in Engineering, 2013Co-Authors: Anthony Giacoma, David Dureisseix, Anthony Gravouil, Michel RochetteAbstract:A multiscale strategy using model reduction for Frictional Contact computation is presented. This new approach aims to improve computation time of finite element simulations involving Frictional Contact between linear and elastic bodies. This strategy is based on a combination between the LATIN (LArge Time INcrement) method and the FAS multigrid solver. The LATIN method is an iterative solver operating on the whole time-space domain. Applying an a posteriori analysis on solutions of different Frictional Contact problems shows a great potential as far as reducibility for Frictional Contact problems is concerned. Time-space vectors forming the so-called reduced basis depict particular scales of the problem. It becomes easy to make analogies with multigrid method to take full advantage of multiscale information.
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A new fatigue Frictional Contact crack propagation model with the coupled X-FEM/LATIN method
Computer Methods in Applied Mechanics and Engineering, 2007Co-Authors: Rachelle Ribeaucourt, Marie-christine Baietto, Anthony GravouilAbstract:A fatigue crack model addressing Frictional Contact along crack faces and multi-axial non-proportional sollicitations is proposed. In this respect, an X-FEM numerical model coupled with unilateral Contact with friction is presented within the linear elastic fracture mechanics framework (LEFM). Hysteresis effects are addressed through an incremental formulation. Furthermore, a modified LATIN iterative solver and a local convergence indicator adapted for the Frictional Contact problem are proposed. It ensures the local convergence of the normal and tangential problems independently. A generalized expression for the J-integral under Frictional Contact conditions is derived. In the same way, a path-independent domain interaction integral is implemented in order to extract the mode I and mode II stress intensity factors. The crack propagation direction is predicted according to Hourlier’s criterion adapted to multi-axial non-proportional sollicitations. Crack growth predictions are presented for three fatigue crack lengths under rolling Contact loading. Stress intensity factors (SIF) are computed and the crack growth direction is determined. These numerical results agree quantitatively with previous results obtained according to a reference model.
Michel Rochette - One of the best experts on this subject based on the ideXlab platform.
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A multiscale LATIN/FAS algorithm with time-space model reduction for Frictional Contact problems
International Journal for Numerical Methods in Engineering, 2014Co-Authors: Anthony Giacoma, David Dureisseix, Anthony Gravouil, Michel RochetteAbstract:A multiscale strategy using model reduction for Frictional Contact computation is presented. This new approach aims to improve computation time of finite element simulations involving Frictional Contact between linear and elastic bodies. This strategy is based on a combination between the LATIN (LArge Time INcrement) method and the FAS multigrid solver. The LATIN method is an iterative solver operating on the whole time-space domain. Applying an a posteriori analysis on solutions of different Frictional Contact problems shows a great potential as far as reducibility for Frictional Contact problems is concerned. Time-space vectors forming the so-called reduced basis depict particular scales of the problem. It becomes easy to make analogies with multigrid method to take full advantage of multiscale information.
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A multiscale large time increment/FAS algorithm with time-space model reduction for Frictional Contact problems
International Journal for Numerical Methods in Engineering, 2013Co-Authors: Anthony Giacoma, David Dureisseix, Anthony Gravouil, Michel RochetteAbstract:A multiscale strategy using model reduction for Frictional Contact computation is presented. This new approach aims to improve computation time of finite element simulations involving Frictional Contact between linear and elastic bodies. This strategy is based on a combination between the LATIN (LArge Time INcrement) method and the FAS multigrid solver. The LATIN method is an iterative solver operating on the whole time-space domain. Applying an a posteriori analysis on solutions of different Frictional Contact problems shows a great potential as far as reducibility for Frictional Contact problems is concerned. Time-space vectors forming the so-called reduced basis depict particular scales of the problem. It becomes easy to make analogies with multigrid method to take full advantage of multiscale information.
G. De Saxcé - One of the best experts on this subject based on the ideXlab platform.
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Three-dimensional finite element computations for Frictional Contact problems with non-associated sliding rule
International Journal for Numerical Methods in Engineering, 2004Co-Authors: Mohammed Hjiaj, Zhiqiang Feng, G. De SaxcéAbstract:This 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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On the modelling of complex anisotropic Frictional Contact laws
International Journal of Engineering Science, 2004Co-Authors: Mohammed Hjiaj, Zhiqiang Feng, G. De SaxcéAbstract:In this paper, the formulation of complex anisotropic Frictional models with orthotropic friction condition and non-associated sliding rule is discussed. The friction law is described by a superellipse, which allow to consider a wide range of convex friction condition by simply varying the roundness factor affecting the shape of the limit surface. The sliding potential is also a superellipse but with a different semi-axis ratio, which lead to a non-associated sliding rule. For bodies in Contact, the Signorini conditions can be formulated in terms of velocities and combined with the sliding rule to give the Frictional Contact law describing interfacial interactions. Its is shown that the Frictional Contact law as well as its inverse can be derived from the same scalar valued function called bi-potential. Due to the non-associated nature of the law, this relation is implicit. The advantage of the present formulation lies in the existence of stationary points of a functional, called bi-functional, that depends on both the displacements and the stresses.
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On the modelling of complex anisotropic Frictional Contact laws
International Journal of Engineering Science, 2004Co-Authors: Mohammed Hjiaj, G. De Saxcé, Zhiqiang Feng, Zenon MrózAbstract:International audienceIn this paper, the formulation of complex anisotropic Frictional models with orthotropic friction condition and non-associated sliding rule is discussed. The friction law is described by a superellipse, which allow to consider a wide range of convex friction condition by simply varying the roundness factor affecting the shape of the limit surface. The sliding potential is also a superellipse but with a different semi-axis ratio, which lead to a non-associated sliding rule. For bodies in Contact, the Signorini conditions can be formulated in terms of velocities and combined with the sliding rule to give the Frictional Contact law describing interfacial interactions. Its is shown that the Frictional Contact law as well as its inverse can be derived from the same scalar valued function called bi-potential. Due to the non-associated nature of the law, this relation is implicit. The advantage of the present formulation lies in the existence of stationary points of a functional, called bi-functional, that depends on both the displacements and the stresse
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an improved discrete element method based on a variational formulation of the Frictional Contact law
Computers and Geotechnics, 2002Co-Authors: Jérôme Fortin, Mohammed Hjiaj, G. De SaxcéAbstract:An improved algorithm based on the Contact dynamics approach is proposed. Like previous developed algorithms it involves two stages. In the first one (local stage) for each particle, forces are computed from the relative displacement using an interaction law, which models Frictional Contact and shock. In the second stage (global stage) Newton's second law is used to determine, for each particle, the resulting acceleration which is then time-integrated to find the new particle positions. This process is repeated for each time step until convergence is achieved. The two distinguishing features of the present algorithm are the local integration of the Frictional Contact law and the convergence criterion. By adopting a variational statement of the Frictional Contact law based on the bi-potential concept, the integration procedure is reduced to a single predictor-corrector step and a new convergence criterion is introduced. Both aspects significantly reduce the computing time and enhance the convergence. Numerical applications show the robustness of the algorithm.
