Contact between spheres and general surfaces

authored by: Alfredo Gay Neto, Paulo de Mattos Pimenta, Peter Wriggers
Abstract: This work presents a mathematical model to establish the weak form and tangent operator contributions due to contact between spherical surfaces and general surfaces. Normal and friction components are included, such as dissipative actions. The main concern herein is the proper consideration of the kinematics of the spherical surface and its influence on contact forces, including the appropriate description of the spherical motion by gap functions in normal and tangential directions. This leads to the possibility of dealing with complex kinematics of rolling or alternating rolling/sliding of the spherical surface, mapping its motion on another general surface. To achieve that, the model is based on rotational and translational degrees of freedom used to map the motion of contacting surfaces. One may employ such strategy for interactions between spheres and rigid or flexible bodies, modeled using finite element meshes. As examples, parameterizations of rigid and flexible surfaces are proposed and used. Practical applications are shown, with usage of beam and shell finite elements, experiencing contact interactions.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Universidade de Sao Paulo
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 328
Pages: 686-716
No. of pages: 31
ISSN: 0045-7825
Publication date: 28.09.2017
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2017.09.016 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{4b3599f6e85648ef9c5351acdb5fdb64,
title = "Contact between spheres and general surfaces",
abstract = "This work presents a mathematical model to establish the weak form and tangent operator contributions due to contact between spherical surfaces and general surfaces. Normal and friction components are included, such as dissipative actions. The main concern herein is the proper consideration of the kinematics of the spherical surface and its influence on contact forces, including the appropriate description of the spherical motion by gap functions in normal and tangential directions. This leads to the possibility of dealing with complex kinematics of rolling or alternating rolling/sliding of the spherical surface, mapping its motion on another general surface. To achieve that, the model is based on rotational and translational degrees of freedom used to map the motion of contacting surfaces. One may employ such strategy for interactions between spheres and rigid or flexible bodies, modeled using finite element meshes. As examples, parameterizations of rigid and flexible surfaces are proposed and used. Practical applications are shown, with usage of beam and shell finite elements, experiencing contact interactions.",
keywords = "Contact, Finite element method, Master–slave, Sphere, Surface",
author = "{Gay Neto}, Alfredo and Pimenta, {Paulo de Mattos} and Peter Wriggers",
note = "Funding Information: The first author acknowledges FAPESP (Funda{\c c}{\~a}o de Amparo {\`a} Pesquisa do Estado de S{\~a}o Paulo) under the grant 2016/14230-6 and CNPq (Conselho Nacional de Desenvolvimento Cient{\'i}fico e Tecnol{\'o}gico) under the grant 308190/2015-7 . The second author expresses his acknowledgments to the Alexander von Humboldt Foundation for the Georg Forster Award that supported multiple stays at the Universities of Duisburg–Essen and Hannover in Germany in the triennium 2015–2017, to the French and Brazilian Governments for the Chair CAPES-Sorbonne during his stay at Sorbonne Universit{\'e}s in the year of 2016 on a leave from the University of S{\~a}o Paulo and to CNPq for its support under the grant 303091/2013-4 . Publisher Copyright: {\textcopyright} 2017 Elsevier B.V. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",
year = "2017",
month = sep,
day = "28",
doi = "10.1016/j.cma.2017.09.016",
language = "English",
volume = "328",
pages = "686--716",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}