IJPAM: Volume 93, No. 6 (2014)

SECOND-ORDER STRESS RELATIONS FOR
HYPERELASTIC CONSTRAINED MATERIALS

Maria Luisa Tonon
Department of Mathematics ``Giuseppe Peano''
University of Turin
Via Carlo Alberto 10, Turin, 10123, ITALY


Abstract. In this paper the second-order stress relations for hyperelastic internally constrained materials are derived, both for the Cauchy stress and the two Piola-Kirchhoff stresses. In our approach the constitutive equations are obtained by the corresponding finite constitutive equations by means of suitable expansions. In contrast to the classical approach, our method guarantees the accuracy required by a second-order theory. For incompressible isotropic materials explicit stress relations are derived and compared with those used in classical theory, in order to show that only our constitutive equations are accurate to second order of approximation.

Received: March 28, 2014

AMS Subject Classification: 74B20, 74A10

Key Words and Phrases: hyperelastic constrained materials, second-order stress relations

Download paper from here.




DOI: 10.12732/ijpam.v93i6.8 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 6
Pages: 813 - 833

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).