A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence
Elisa Davoli
Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, ItalyMaria Giovanna Mora
Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy
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Abstract
The subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic–perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via Γ-convergence techniques that solutions to the three-dimensional quasistatic evolution problem of Prandtl–Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff–Love type and the stretching and bending components of the stress are coupled through a plastic flow rule. Some equivalent formulations of the limiting problem in rate form are derived, together with some two-dimensional characterizations for suitable choices of the data.
Cite this article
Elisa Davoli, Maria Giovanna Mora, A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 4, pp. 615–660
DOI 10.1016/J.ANIHPC.2012.11.001