A limit elastic energy for the pure traction problem is derived from re-scaled nonlinear energies of a hyperelastic material body subject to an equilibrated force field. We prove that the strains of minimizing sequences associated to re-scaled nonlinear energies weakly converge, up to subsequences, to the strains of minimizers of a limit energy, provided an additional compatibility condition is fulfilled by the force field. The limit energy is different from the classical energy of linear elasticity; nevertheless, the compatibility condition entails the coincidence of related minima and minimizers. A strong violation of this condition provides a limit energy which is unbounded from below, while a mild violation may produce unboundedness of strains and a limit energy which has infinitely many extra minimizers which are not minimizers of standard linear elastic energy. A consequence of this analysis is that a rigorous validation of linear elasticity fails for compressive force fields that infringe up on such a compatibility condition.
|Titolo:||The Gap Between Linear Elasticity and the Variational Limit of Finite Elasticity in Pure Traction Problems|
|Data di pubblicazione:||2019|
|Appare nelle tipologie:||01.01 - Articolo su rivista|
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|2019_MPT_ArchRationMechAnal_TheGapBetweenLinearElasticity.pdf||Documento in Post-print||Open Access Visualizza/Apri|