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The obstacle problem for an elastoplastic body

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Abstract

The obstacle problem for elastoplastic bodies is considered within the framework of general existence results for unilateral problems recently presented by Baiocchiet al. Two models of plasticity are considered: one is based on a displacement-plastic strain formulation and the second, a specialization of the first, is the standard Hencky model. Existence theorems are given for the Neumann problem for a body constrained to lie on or above the half-space {x∈ℝ3:x 3≤0}. For hardening materials the displacements are sought in the Sobolev spaceH 1(Ω, ℝ3) while for perfectly plastic materials they are sought in BD(Ω), the space of functions of bounded deformation. Conditions for the existence of solutions are given in terms of compatibility and safe load conditions on applied loads.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Cape Town, 7700, Rondebosch, Republic of South Africa

    B. D. Reddy

  2. Dipartimento di Matematica, Università di Pavia, Strada Nuova 65, 27100, Pavia, Italy

    F. Tomarelli

Authors
  1. B. D. Reddy
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  2. F. Tomarelli
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Communicated by D. Kinderlehrer

This work was initiated while B. D. Reddy was on leave at the Istituto di Analisi Numerica del CNR, Pavia, Italy. The hospitality of that institution is gratefully acknowledged, as is the award of an FRD sabbatical grant. F. Tomarelli was partially supported by IAN and GNAFA of CNR, and by Ministero della Pubblica Istruzione.

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Reddy, B.D., Tomarelli, F. The obstacle problem for an elastoplastic body. Appl Math Optim 21, 89–110 (1990). https://doi.org/10.1007/BF01445159

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