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From non-linear elasticity to linear elasticity with initial stress via Γ-convergence

Paroni, Roberto and Tomassetti, Giuseppe (2011) From non-linear elasticity to linear elasticity with initial stress via Γ-convergence. Continuum Mechanics and Thermodynamics (in press). ISSN 0935-1175. eISSN 1432-0959. Article.

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DOI: 10.1007/s00161-011-0184-y


We consider a initially stressed hyperelastic body in equilibrium in its undeformed configuration under a system of dead loads. We give sufficient conditions on the stored energy which guarantee that when the loads undergo a small perturbation, the energy functional Γ converges, after some re-scaling, to the energy functional of linear elasticity with initial stress. We also show, under stronger conditions, that quasi-minimizers of the non-linear problem converge to a minimizer of the incremental problem.

Item Type:Article
ID Code:6170
Uncontrolled Keywords:Initial stress, incremental elasticity
Subjects:Area 08 - Ingegneria civile e Architettura > ICAR/08 Scienza delle costruzioni
Divisions:001 Università di Sassari > 01 Dipartimenti > Architettura e pianificazione
Publisher:Springer Berlin / Heidelberg
Copyright Holders:© Springer-Verlag 2011
Deposited On:21 Jun 2011 11:06

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