The “analogue gravity formalism”, an interdisciplinary theoretical schemedeveloped in the past for studying several non relativistic classical and quantum systemsthrough effective relativistic curved space-times, is here applied to largely deformableelastic bodies described by the nonlinear theory of solid mechanics. Assumingthe simplest nonlinear constitutive relation for the elastic material given bya Kirchhoff-St Venant strain-energy density function, it is possible to write for the perturbationsan effective space-time metric if the deformation is purely longitudinal anddepends on one spatial coordinate only. Theoretical and numerical studies of the correspondingdynamics are performed in selected cases and physical implications of theresults obtained are finally discussed.
An analog of Einstein's general relativity emerging from classical finite elasticity theory: analytical and computational issues
Cherubini C;Filippi S
2013-01-01
Abstract
The “analogue gravity formalism”, an interdisciplinary theoretical schemedeveloped in the past for studying several non relativistic classical and quantum systemsthrough effective relativistic curved space-times, is here applied to largely deformableelastic bodies described by the nonlinear theory of solid mechanics. Assumingthe simplest nonlinear constitutive relation for the elastic material given bya Kirchhoff-St Venant strain-energy density function, it is possible to write for the perturbationsan effective space-time metric if the deformation is purely longitudinal anddepends on one spatial coordinate only. Theoretical and numerical studies of the correspondingdynamics are performed in selected cases and physical implications of theresults obtained are finally discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
