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Heat generation in plane strain compression of a thin rigid plastic layer

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Abstract

This paper presents a theoretical investigation into heat generation in the continued quasi-static plane strain compression of a thin metal strip between two rigid, parallel perfectly rough dies. The strip material is rigid perfectly plastic. The length of the dies is supposed to be much larger than the current strip thickness. The plastic work rate approaches infinity in the vicinity of perfectly rough friction surfaces. Since the plastic work rate is involved in the heat conduction equation, this significantly adds to the difficulties of solutions of this equation. In particular, commercial finite element packages are not capable of solving such boundary value problems. The present approximate solution is given in Lagrangian coordinates. In this case, the original initial/boundary value problem reduces to the standard second initial/boundary value problem for the nonhomogeneous heat conduction equation. Therefore, the Green’s function is available in the literature. An example is presented to illustrate the general solution.

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Authors and Affiliations

  1. Institute for Problems in Mechanics, 101-1 Prospect Vernadskogo, 119526, Moscow, Russia

    Sergei Alexandrov

  2. Department of Mathematics, Aberystwyth University, Penglais, Aberystwyth, SY23 3BZ, UK

    Wiktoria Miszuris

Authors
  1. Sergei Alexandrov
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  2. Wiktoria Miszuris
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Correspondence to Sergei Alexandrov.

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Alexandrov, S., Miszuris, W. Heat generation in plane strain compression of a thin rigid plastic layer. Acta Mech 227, 813–821 (2016). https://doi.org/10.1007/s00707-015-1499-8

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  • DOI: https://doi.org/10.1007/s00707-015-1499-8

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