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- Title
AN EVOLUTIONARY ELASTOPLASTIC PLATE MODEL DERIVED VIA Γ-CONVERGENCE.
- Authors
LIERO, MATTHIAS; MIELKE, ALEXANDER; Brezzi, F.
- Abstract
This paper is devoted to dimension reduction for linearized elastoplasticity in the rate-independent case. The reference configuration of the three-dimensional elastoplastic body has a two-dimensional middle surface and a positive but small thickness. Under suitable scalings we derive a limiting model for the case in which the thickness of the plate tends to 0. This model contains membrane and plate deformations (linear Kirchhoff-Love plate), which are coupled via plastic strains. We establish strong convergence of the solutions in the natural energy space. The analysis uses an abstract Γ-convergence theory for rate-independent evolutionary systems that is based on the notion of energetic solutions. This concept is formulated via an energy-storage functional and a dissipation functional, such that energetic solutions are defined in terms of a stability condition and an energy balance. The Mosco convergence of the quadratic energy-storage functional follows the arguments of the elastic case. To handle the evolutionary situation the interplay with the dissipation functional is controlled by cancellation properties for Mosco-convergent quadratic energies.
- Subjects
ELASTOPLASTICITY; MATHEMATICAL models; STOCHASTIC convergence; HYSTERESIS; FUNCTIONALS; STRUCTURAL plates; DEFORMATIONS (Mechanics)
- Publication
Mathematical Models & Methods in Applied Sciences, 2011, Vol 21, Issue 9, p1961
- ISSN
0218-2025
- Publication type
Article
- DOI
10.1142/S0218202511005611