We consider a residually-stressed, uniform hyperelastic body whose stored energy is quadratic with respect to the Green–St. Venant strain. We show that, in the limit of vanishing loads, suitable minimizing sequences converge to the unique minimizer of the energy functional of linear elasticity. We also deduce the standard stress-strain relations for linear elasticity with residual stress.
Paroni, R., Tomassetti, G. (2009). A variational justification of linear elasticity with residual stress. JOURNAL OF ELASTICITY, 97(2), 189-206 [10.1007/s10659-009-9217-1].
A variational justification of linear elasticity with residual stress
TOMASSETTI, GIUSEPPE
2009-01-01
Abstract
We consider a residually-stressed, uniform hyperelastic body whose stored energy is quadratic with respect to the Green–St. Venant strain. We show that, in the limit of vanishing loads, suitable minimizing sequences converge to the unique minimizer of the energy functional of linear elasticity. We also deduce the standard stress-strain relations for linear elasticity with residual stress.File in questo prodotto:
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