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PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru and M.L. Romero
An Augmented Lagrange Method to Solve Large Deformation Three-Dimensional Contact Problems
M. Tur, J. Albelda, E. Giner and J.E. Tarancón
Department of Mechanical Engineering and Materials, Universidad Politécnica de Valencia, Spain
M. Tur, J. Albelda, E. Giner, J.E. Tarancón, "An Augmented Lagrange Method to Solve Large Deformation Three-Dimensional Contact Problems", in B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru, M.L. Romero, (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 262, 2010. doi:10.4203/ccp.93.262
Keywords: contact, Lagrange multiplier, mortar, large deformation, finite element, convergence.
In recent years, the mortar finite element method has been successfully applied to solve contact problems using non-conforming discretizations of the bodies in contact. Unlike the classical node-to-segment approach, the mortar method prevents locking or over-constraint and it allows the optimal convergence rate of the error to be obtained [1,2,3,4].
In this work an implementation of the mortar method is proposed to solve three-dimensional contact problems in the context of large deformations. The contact constraints and non-linear equilibrium equations are derived from the augmented Lagrange method which is a C1 continuous functional. This method was first used by Pietrzak and Curnier  for node-to-segment contact formulations. Newton's method is used to solve the non-linear system of equations. As the proposed formulation is based on the mortar method, the constraints are imposed in a weak integral sense. In order to compute the contact integrals, we use an inexact numerical quadrature that facilitates the linearization of the contact variables (gap, normal, etc.) and reduces the computational cost.
In the numerical examples we show that, although the contact integrals are not exact, the optimal convergence rate of the discretization error is still preserved. We have performed the full linearization of the equilibrium equations and good quadratic convergence is obtained in the numerical examples.
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