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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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.
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