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An Analog of Einstein’s General Relativity Emerging from Classical finite elasticity Theory:Analytical and Computational Issues

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Communications in Computational Physics 2013年第8期14卷 801-818页

作者： C.Cherubini S.Filippi Nonlinear Physics andMathematicalModeling Lab University Campus Bio-MedicoI-00128Via A.del Portillo 21RomeItaly International Center for Relativistic Astrophysics-I.C.R.A. University of Rome“La Sapienza”I-00185 RomeItaly

The“analogue gravity formalism”,an interdisciplinary theoretical scheme developed in the past for studying several non relativistic classical and quantum systems through effective relativistic curved space-times,is here applied to largely deformable elastic bodies described by the nonlinear theory of solid *** the simplest nonlinear constitutive relation for the elastic material given by a Kirchhoff-St Venant strain-energy density function,it is possible to write for the perturbations an effective space-time metric if the deformation is purely longitudinal and depends on one spatial coordinate *** and numerical studies of the corresponding dynamics are performed in selected cases and physical implications of the results obtained are finally discussed.

关键词： finite elasticity general relativity analogue gravity finite elements method

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Nonlinear elastic constitutive relations of residually stressed composites with stiff curved fibres

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Applied Mathematics and Mechanics(English Edition) 2022年第10期43卷 1515-1530页

作者： M.H.B.M.Shariff J.Merodio R.Bustamante Department of Mathematics Khalifa University of Science and TechnologyAbu Dhabi127788United Arab Emirates Departamento de Matemática Aplicada a las TIC ETS de Ingeniería de Sistemas InformaticosUniversidad Politecnica de MadridMadrid28031Spain Departamento de Ingeniería Mecánica Universidad de ChileBeauchef 851Santiago CentroSantiago8370448Chile

Mechanical models of residually stressed fibre-reinforced solids,which do not resist bending,have been developed in the ***,in some residually stressed fibre-reinforced elastic solids,resistance to fibre bending is significant,and the mechanical behavior of such solids should be ***,in this paper,we model the mechanical aspect of residually stressed elastic solids with bending stiffness due to fibre curvature,which up to the authors’knowledge has not been mechanically modeled in the *** proposed constitutive equation involves a nonsymmetric stress and a couple-stress *** invariants are used in the constitutive equation,where each spectral invariant has an intelligible physical meaning,and hence they are useful in experiment and analysis.A prototype strain energy function is ***,we use this prototype to give results for some cylindrical boundary value problems.

关键词： fibre-reinforced solid residual stress bending stiffness spectral invariant second gradient finite elasticity

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