A multi-scale FEM-BEM formulation for contact mechanics between rough surfaces

  • Jacopo BonariEmail author
  • Maria R. Marulli
  • Nora Hagmeyer
  • Matthias Mayr
  • Alexander Popp
  • Marco Paggi
Original Paper


A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface interactions at the macro-scale with a boundary element method (BEM) for the solution of the contact problem at the micro-scale. The BEM is used at each integration point to determine the normal contact traction and the normal contact stiffness, allowing to take into account any desirable kind of rough topology, either real, e.g. obtained from profilometric data, or artificial, evaluated with the most suitable numerical or analytical approach. Different numerical strategies to accelerate coupling between FEM and BEM are discussed in relation to a selected benchmark test.


Contact mechanics Roughness Finite element method Boundary element method Multi-scale method 



The authors would like to acknowledge funding from the MIUR-DAAD Joint Mobility Program 2017 to the project “Multi-scale modelling of friction for large scale engineering problems”. The project has been granted by the Italian Ministry of Education, University and Research (MIUR) and by the Deutscher Akademischer Austausch Dienst (DAAD) through funds of the German Federal Ministry of Education and Research (BMBF).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.IMT School for Advanced Studies LuccaLuccaItaly
  2. 2.Institute for Mathematics and Computer-Based SimulationUniversity of the Bundeswehr MunichNeubibergGermany

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