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Finite deformation frictional mortar contact using a semi‐smooth Newton method with consistent linearization
Author(s) -
Gitterle Markus,
Popp Alexander,
Gee Michael W.,
Wall Wolfgang A.
Publication year - 2010
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.2907
Subject(s) - linearization , lagrange multiplier , newton's method , contact force , constraint algorithm , quadratic equation , mathematics , augmented lagrangian method , bilinear interpolation , kinematics , nonlinear system , mathematical analysis , control theory (sociology) , mathematical optimization , computer science , classical mechanics , geometry , physics , statistics , quantum mechanics , control (management) , artificial intelligence
Abstract A two‐dimensional, finite deformation frictional contact formulation with Coulomb's law is presented. The approach considers multibody contact and is based on a mortar formulation. The enforcement of contact constraints is realized with dual Lagrange multipliers. These alternative multiplier spaces are constructed in a way that the multipliers can easily be eliminated from the global system of equations by static condensation such that the system size does not increase. Friction kinematic variables are formulated in an objective way and enter non‐smooth complementarity functions for expressing the contact constraints. An active set strategy is derived by applying a semi‐smooth Newton method, which treats contact nonlinearities, material and geometrical nonlinearities in one single iterative scheme. By further carrying out a consistent linearization for both normal and frictional contact forces and constraints, a robust and highly efficient algorithm for linear and higher‐order (quadratic) interpolation is achieved. Efficiency of the proposed method and quality of results are demonstrated in several examples. Copyright © 2010 John Wiley & Sons, Ltd.