Symmetry groups in nonlinear elasticity: an exercise in vintage mathematics

Pages: 435 - 456, Volume 8, Issue 1, January 2009

doi:10.3934/cpaa.2009.8.435       Abstract        Full Text (247.5K)       Related Articles

Annie Raoult - Laboratoire MAP5, Université Paris Descartes and CNRS, 45 rue des Saints Pères, 75006 Paris, France (email)

Abstract: This manuscript aims at characterizing energy densities and constitutive laws of transversely isotropic materials, orthotropic elastic materials and materials with non orthogonal families of fibers. It makes explicit references to results that are scattered over the literature and, although said to be well-known, are not always easy to locate. Direct proofs that are thought to be new and simplified expressions of constitutive laws for materials with two preferred directions are given.

Keywords:  Nonlinear elasticity, constitutive laws, symmetry groups, anisotropy, transverse isotropy, orthotropy, fibers
Mathematics Subject Classification:  74A20, 74B20, 74E10

Received: March 2008;      Revised: August 2008;      Published: October 2008.