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Functions of bounded deformation

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Abstract

We study the space BD(Ω), composed of vector functions u for which all components εij=1/2(u i, j+u j, i) of the deformation tensor are bounded measures. This seems to be the correct space for the displacement field in the problems of perfect plasticity. We prove that the boundary values of every such u are integrable; indeed their trace is in L 1 (Γ)N. We show also that if a distribution u yields ɛ ij which are measures, then u must lie in L p(Ω) for p≦N/(N−1).

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Authors and Affiliations

  1. Laboratoire d'Analyse Numérique, Université de Paris-Sud, Orsay

    Roger Temam & Gilbert Strang

  2. Department of Mathematics, Massachusetts Institute of Technology, USA

    Roger Temam & Gilbert Strang

Authors
  1. Roger Temam
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  2. Gilbert Strang
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The second author gratefully acknowledges the supprot of the National Science Foundation.

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Temam, R., Strang, G. Functions of bounded deformation. Arch. Rational Mech. Anal. 75, 7–21 (1980). https://doi.org/10.1007/BF00284617

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  • DOI: https://doi.org/10.1007/BF00284617

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