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Numerical solution of a contact problem with unilateral constraint and history-dependent penetration

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Abstract

A numerical method is presented for a mathematical model which describes the frictionless contact between a viscoplastic body and an obstacle, the so-called foundation. The process is quasistatic, and the contact is modeled with normal compliance and unilateral constraint, in such a way that the stiffness coefficient depends on the history of the penetration. A solution algorithm is discussed and implemented. Numerical simulation results are reported, illustrating the mechanical behavior related to the contact condition.

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Acknowledgments

This work was supported by a the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No. 295118. The work of the second author was also supported by grants from the Simons Foundation.

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Authors and Affiliations

  1. Laboratoire de Mathématiques et Physique, Université de Perpignan Via Domitia, 52 Avenue Paul Alduy, 66860, Perpignan, France

    Mikael Barboteu & Mircea Sofonea

  2. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    Weimin Han

Authors
  1. Mikael Barboteu
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  2. Weimin Han
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  3. Mircea Sofonea
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Correspondence to Weimin Han.

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Barboteu, M., Han, W. & Sofonea, M. Numerical solution of a contact problem with unilateral constraint and history-dependent penetration. J Eng Math 97, 177–194 (2016). https://doi.org/10.1007/s10665-015-9804-z

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  • DOI: https://doi.org/10.1007/s10665-015-9804-z

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