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 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.
Paroni, R., Tomassetti, G. (2011). From non-linear elasticity to linear elasticity with initial stress via Γ-convergence. CONTINUUM MECHANICS AND THERMODYNAMICS, 23(4), 347-361 [10.1007/s00161-011-0184-y].
From non-linear elasticity to linear elasticity with initial stress via Γ-convergence.
TOMASSETTI, GIUSEPPE
2011-01-01
Abstract
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 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.File | Dimensione | Formato | |
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