2018/10/31 by Francesco Maddalena, Danilo Percivale, Franco Tomarelli · 1 citation
Computer Science · Engineering · Mathematics · #Compatibility (geochemistry) #Contact Mechanics and Variational Inequalities #Elastic energy #Elasticity (physics) #Elasticity and Material Modeling #Hyperelastic material #Linear elasticity #Maxima and minima #Nonlinear Partial Differential Equations #Nonlinear elasticity #Nonlinear system #Traction (geology) #math.AP #math.OC
paper · pdf · doi:10.1007/s00205-019-01408-2
published as Arch. Rational Mech. Anal (2019)
openalex created_date 2018/10/12 · arxiv created 2019/03/13 · openalex publication_date 2019/06/20 · arxiv updated 2019/07/01 · openalex updated_date 2026/08/05
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.