Abstract
We prove the existence of a displacement field and of a stress field that satisfy the dynamical equation for continuous media and the Prandtl-Reuss constitutive law of elasto-perfect plasticity. First we obtain the existence of a displacement rate in a space of functions of bounded deformation, where the constitutive law is satisfied in an integral form, then we show that one can choose a good representative for the stress in such a way that the Prandtl-Reuss law is satisfied almost everywhere with respect to the deformation measure.
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Communicated by D. Kinderlehrer
Work done while the first author was a guest of Sonderforschungsbereich 123 at Heidelberg University.
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Anzellotti, G., Luckhaus, S. Dynamical evolution of elasto-perfectly plastic bodies. Appl Math Optim 15, 121–140 (1987). https://doi.org/10.1007/BF01442650
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DOI: https://doi.org/10.1007/BF01442650