Adaptive finite element techniques for frictional contact problems involving large elastic strains

doi:10.1016/S0045-7825(97)00169-2

Computer Methods in Applied Mechanics and Engineering

Volume 151, Issues 3–4, 20 January 1998, Pages 593-603

https://doi.org/10.1016/S0045-7825(97)00169-2 Get rights and content

Abstract

Adaptive finite element methods have been developed over the last ten years for engineering problems in solid and fluid mechanics. They provide a tool for accurate and reliable analysis which is needed in many applications. The use of these techniques within contact problems is advantageous since the contact area is not known a priori and thus element sizes cannot be estimated beforehand. Furthermore, high gradients of stresses can occur in the contact interface which then need a sufficient refinement of the mesh for an accurate analysis.

Within this work an adaptive finite element method is developed for large strain problems of two or more deformable bodies being in frictional contact. For this purpose we discuss new error indicators and error estimators related to the contact area. Based on these quantities and the known estimates for the solid body, a numerical method is constructed which allows automatic mesh refinement.

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Adaptive finite element techniques for frictional contact problems involving large elastic strains

Abstract

Comput. Methods Appl. Mech. Engrg.

Adv. Eng. Software

Comput. Struct.

Error estimates for adaptive finite element computations

SIAM J. Numer. Anal.

Validation of a posteriori error estimators by numerical approach

Int. J. Numer. Methods Engrg.

Formulation of unilateral contact between two elastic bodies undergoing finite deformation

C.R. Acad. Sci. Paris

Mathematical Elasticity

The return mapping method for the integration of friction constitutive relations

Comput. Struct.

Solution of Variational Inequalities in Mechanics

Adaptive finite element methods for the obstacle problem

Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods