Mathematical Models and Methods in Applied Sciences (M3AS)
Inserted: 24 sep 2015
Last Updated: 15 mar 2017
We consider the dynamic evolution of a linearly elastic-perfectly plastic plate subject to a purely vertical body load. As the thickness of the plate goes to zero, we prove that the three-dimensional evolutions converge to a solution of a certain reduced model. In this limit model admissible displacements are of Kirchhoff-Love type. Moreover, the motion of the body is governed by an equilibrium equation for the stretching stress, a hyperbolic equation involving the vertical displacement and the bending stress, and a rate-independent plastic flow rule. Some further properties of the reduced model are also discussed.
Keywords: Functions of Bounded Deformation, Prandtl-Reuss plasticity, perfect plasticity, thin plates, Dynamic evolution