Abstract
This paper deals with dimension reduction in linearized elastoplasticity in the rate-independent case. The reference configuration of the elastoplastic body is given by a two-dimensional middle surface and a small but positive thickness. 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 which are coupled via plastic strains. The convergence analysis is based on an abstract Γ-convergence theory for rate-independent evolution formulated in the framework of energetic solutions. This concept is based on an energy-storage functional and a dissipation functional, such that the notion of solution is phrased in terms of a stability condition and an energy balance.
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Both authors wish to thank Martin Brokate, Pavel Krejčí and Alexander Mielke for insightful discussions. T. Roche thanks the Weierstrass Institute for Applied Analysis and Stochastics Berlin, where part of the work was conducted, for its kind hospitality. T. Roche was supported by the Bavarian Network of Excellence through its graduate program ‘TopMath’ and the TUM Graduate School through its Thematic Graduate Center ‘TopMath’.
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Liero, M., Roche, T. Rigorous derivation of a plate theory in linear elastoplasticity via Γ-convergence. Nonlinear Differ. Equ. Appl. 19, 437–457 (2012). https://doi.org/10.1007/s00030-011-0137-y
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DOI: https://doi.org/10.1007/s00030-011-0137-y