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

Paroni, Roberto; Tomassetti, Giuseppe
July 2011
Continuum Mechanics & Thermodynamics;Jul2011, Vol. 23 Issue 4, p347
Academic Journal
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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