Modeling and numerical treatment of elastic rods with frictionless self-contact

In this paper we present a hyperelastic rod model that takes into account self-contact forces. The model is based on Cosserat rod theory that incorporates shear, elongation, flexure and twist deformations. The problem of avoiding self-penetration of parts of the rod is handled by the introduction of...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2009-10, Vol.198 (47), p.3751-3764
Main Authors: Chamekh, Mourad, Mani-Aouadi, Saloua, Moakher, Maher
Format: Article
Language:English
Subjects:
Augmented Lagrangian method
Computational techniques
Contact distance
Elastic rods
Exact sciences and technology
Finite element
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Mechanical contact (friction...)
Penalty method
Physics
Self-contact
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
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Summary:In this paper we present a hyperelastic rod model that takes into account self-contact forces. The model is based on Cosserat rod theory that incorporates shear, elongation, flexure and twist deformations. The problem of avoiding self-penetration of parts of the rod is handled by the introduction of a contact distance function and the incorporation of associated contact forces. We present a penalty method for the treatment of the multi-valued and non-differentiable contact law. We also describe an augmented Lagrangian formulation of this problem. We then give the details of the finite-element discretization of the elastic rod self-contact problem as well as some numerical examples.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2009.08.005