Abstract
This paper is devoted to confronting two different approaches to the problem of dynamical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs’ system enables one to derive admissible hyperbolic boundary conditions. Using variational methods, we show the well-posedness of this problem in a suitable weak measure theoretical setting. Thanks to the property of finite speed propagation, we establish a new regularity result for the solution in short time. Finally, we prove that this variational solution is actually a solution of the hyperbolic formulation in a suitable dissipative/entropic sense, and that a partial converse statement holds under an additional time regularity assumption for the dissipative solutions.
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Babadjian, JF., Mifsud, C. Hyperbolic Structure for a Simplified Model of Dynamical Perfect Plasticity. Arch Rational Mech Anal 223, 761–815 (2017). https://doi.org/10.1007/s00205-016-1045-4
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DOI: https://doi.org/10.1007/s00205-016-1045-4