| Autor: |
Maddalena, Francesco, Percivale, Danilo, Tomarelli, Franco |
| Rok vydání: |
2018 |
| Předmět: |
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| Zdroj: |
Arch. Rational Mech. Anal (2019) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s00205-019-01408-2 |
| Popis: |
A limit elastic energy for pure traction problem is derived from re-scaled nonlinear energy of an hyperelastic material body subject to an equilibrated force field. We show that the strains of minimizing sequences associated to re-scaled non linear 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 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 a limit energy with infinitely many extra minimizers which are not minimizers of standard linear elastic energy and whose strains are not uniformly bounded. A relevant consequence of this analysis is that a rigorous validation of linear elasticity fails for compressive force fields that do not fulfil such compatibility condition. |
| Databáze: |
arXiv |
| Externí odkaz: |
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