Strong Ellipticity Conditions for Orthotropic Bodies in Finite Plane Strain
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Necessary and sufficient conditions for strong ellipticity of the equilibrium equations governing finite plane deformations are established for the class of orthotropic and compressible hyperelastic materials. The conditions are then specialized to the case of an orthotropic material having the symmetry axes parallel to the principal directions of deformation. This case is relevant in experimental protocols employed in the characterization of constitutive relations of rubber-like materials and biological tissues. The classical conditions for infinitesimal linear elasticity and isotropic finite elasticity are recovered as particular cases.
KeywordsNonlinear elasticity Orthotropy Ellipticity condition Constitutive modeling
Mathematics Subject Classification (2010)74B20 74E10
We would like to acknowledge the financial support provided by the National Council for Scientific and Technological Development (CNPq) and the State of São Paulo Research Foundation (FAPESP). We are also grateful to the referees, who have provided detailed comments that lead to an expansion of the scope of this work and improvements in the presentation.
- 4.Gurtin, M.E., Fried, E., Anand, L.: The Mechanics and Thermodynamics of Continua. Cambridge University Press, Cambridge (2009) Google Scholar