TY - JOUR

T1 - Contact between spheres and general surfaces

AU - Gay Neto, Alfredo

AU - Pimenta, Paulo de Mattos

AU - Wriggers, Peter

N1 - Funding Information: The first author acknowledges FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) under the grant 2016/14230-6 and CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) 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 Universités in the year of 2016 on a leave from the University of São Paulo and to CNPq for its support under the grant 303091/2013-4 . Publisher Copyright: © 2017 Elsevier B.V. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017/9/28

Y1 - 2017/9/28

N2 - 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.

AB - 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.

KW - Contact

KW - Finite element method

KW - Master–slave

KW - Sphere

KW - Surface

UR - http://www.scopus.com/inward/record.url?scp=85032020189&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2017.09.016

DO - 10.1016/j.cma.2017.09.016

M3 - Article

AN - SCOPUS:85032020189

VL - 328

SP - 686

EP - 716

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -