Conserving algorithms for frictionless and full stick friction dynamic contact problems using the direct elimination method

This is the peer reviewed version of the following article: [Agelet de Saracibar C, Di Capua D. Conserving algorithms for frictionless and full stick friction dynamic contact problems using the direct elimination method. Int J Numer Methods Eng. 2018;113:910–937. https://doi.org/10.1002/nme.5693], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5693. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In this paper, conserving time-stepping algorithms for frictionless and full stick friction dynamic contact problems are presented. Time integration algorithms for frictionless and full stick friction dynamic contact problems have been designed in order to preserve the conservation of key discrete properties satisfied at the continuum level. Energy and energy-momentum preserving algorithms for frictionless and full stick friction dynamic contact problems, respectively, have been designed and implemented within the framework of the direct elimination method, avoiding the drawbacks linked to the use of penalty-based or Lagrange multipliers methods. An assessment of the performance of the resulting formulation is shown in a number of selected and representative numerical examples, under full stick friction and slip frictionless contact conditions. Conservation of key discrete properties exhibited by the time stepping algorithm is shown.Peer ReviewedPostprint (author's final draft