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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 81
Constitutive Error Estimator for the Control of Contact Problems involving Friction J.Ph. Combe, F. Louf and J.P. Pelle
Laboratoire de Mécanique et Technologie, ENS Cachan / CNRS / Université Paris 6, Cachan, France Full Bibliographic Reference for this paper
J.Ph. Combe, F. Louf, J.P. Pelle, "Constitutive Error Estimator for the Control of Contact Problems involving Friction", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 81, 2001. doi:10.4203/ccp.73.81
Keywords: contact, friction, Coulomb's law, bipotential, constitutive relation error estimator, finite elements.
Summary
Unilateral contact problems are found in many fields of structural
calculation. For these nonlinear simulations, it is essential to
evaluate the errors made due to the numerical approximations and
iterative algorithms involved in nonlinear calculations. For this
kind of problem, few research works have proposed a
posteriori error estimators to evaluate space discretization
errors. An error estimator based on stress recovery was proposed
in [7]. However, its computation involves a penalty
parameter inside the estimator, which is a major disadvantage.
More recently, an extension of the error in constitutive relation
to frictionless contact problems was proposed in [1].
The aim of this paper is to extend this study to the case of
contact involving Coulomb friction. This extension is based on a
formulation of the constitutive relation for unilateral contact
with friction using a bipotential [2] and on a specific
modeling of the contact zone as a whole mechanical entity, with
its own variables designated by
First, we consider the static problem of two elastic bodies in
unilateral contact with friction along their common boundary
The concept of error in constitutive relation is based on the partitioning of the equations of the reference problem into two sets. The first set contains the admissibility conditions, i.e. the kinematic constraints and the equilibrium equations. The second set contains the constitutive relations:
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and where ![]() ![]()
Then, the error in constitutive relation is defined by:
In order to compute the error in constitutive relation, we need to
derive a set of admissible fields
In this paper, the estimator is computed on several examples. Finally, we show how the concept of error in constitutive relation enables us to build an error indicator to evaluate the quality of the numerical solution to the problem and, thus, to separate the global error into an error due to this iterative scheme and an error due to the spatial discretization. Such a separation is necessary to develop methods of adaptive calculation which are robust. References
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