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An augmented Lagrangian technique combined with a mortar algorithm for modelling mechanical contact problems
Author(s) -
Cavalieri F.J.,
Cardona A.
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4391
Subject(s) - augmented lagrangian method , mortar , finite element method , penalty method , cartesian coordinate system , mortar methods , contact mechanics , representation (politics) , surface (topology) , mathematics , algorithm , projection (relational algebra) , contact force , lagrangian , mathematical analysis , geometry , mathematical optimization , mixed finite element method , structural engineering , engineering , materials science , classical mechanics , physics , politics , political science , law , composite material
SUMMARY A finite element formulation for three dimensional (3D) contact mechanics using a mortar algorithm combined with a mixed penalty–duality formulation from an augmented Lagrangian approach is presented. In this method, no penalty parameter is introduced for the regularisation of the contact problem. The contact approach, based on the mortar method, gives a smooth representation of the contact forces across the bodies interface, and can be used in arbitrarily curved 3D configurations. The projection surface used for integrating the equations is built using a local Cartesian basis defined in each contact element. A unit normal to the contact surface is defined locally at each element, simplifying the implementation and linearisation of the equations. The displayed examples show that the algorithm verifies the contact patch tests exactly, and is applicable to large displacements problems with large sliding motions.Copyright © 2012 John Wiley & Sons, Ltd.