Abstract
We prove the existence of a dual pairing between admissible stress and displacement fields in the context of Hencky plasticity. We apply this to show (i) that an extremal displacement field exists whenever the safe load condition holds; and (ii) that any extremal stress and displacement fields are related by a “saddle point condition,” expressing in weak form the constitutive hypothesis of Hencky plasticity.
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Communicated by A. V. Balakrishnan
Supported in part by NSF postdoctoral fellowship grant MCS-7919146 A01.
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Kohn, R., Temam, R. Dual spaces of stresses and strains, with applications to Hencky plasticity. Appl Math Optim 10, 1–35 (1983). https://doi.org/10.1007/BF01448377
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DOI: https://doi.org/10.1007/BF01448377