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Mathematical Problems in Engineering
Volume 2016, Article ID 6217679, 25 pages
Research Article

Discontinuous Deformation Analysis Coupling with Discontinuous Galerkin Finite Element Methods for Contact Simulations

1School of Mathematics and Statistics, Xidian University, Xi’an 710126, China
2School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received 1 August 2016; Revised 18 October 2016; Accepted 19 October 2016

Academic Editor: Gerardo Severino

Copyright © 2016 Yue Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A novel coupling scheme is presented to combine the discontinuous deformation analysis (DDA) and the interior penalty Galerkin (IPG) method for the modeling of contacts. The simultaneous equilibrium equations are assembled in a mixed strategy, where the entries are derived from both discontinuous Galerkin variational formulations and the strain energies of DDA contact springs. The contact algorithms of the DDA are generalized for element contacts, including contact detection criteria, open-close iteration, and contact submatrices. Three representative numerical examples on contact problems are conducted. Comparative investigations on the results obtained by our coupling scheme, ANSYS, and analytical theories demonstrate the accuracy and effectiveness of the proposed method.