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Representations for implicit constitutive relations describing non-dissipative response of isotropic materials
, U. Saravanan, K.R. Rajagopal
Published in Birkhauser Verlag AG
2017
Volume: 68
   
Issue: 6
Pages: 1 - 14
Abstract
A methodology for obtaining implicit constitutive representations involving the Cauchy stress and the Hencky strain for isotropic materials undergoing a non-dissipative process is developed. Using this methodology, a general constitutive representation for a subclass of implicit models relating the Cauchy stress and the Hencky strain is obtained for an isotropic material with no internal constraints. It is shown that even for this subclass, unlike classical Green elasticity, one has to specify three potentials to relate the Cauchy stress and the Hencky strain. Then, a procedure to obtain implicit constitutive representations for isotropic materials with internal constraints is presented. As an illustration, it is shown that for incompressible materials the Cauchy stress and the Hencky strain could be related through a single potential. Finally, constitutive approximations are obtained when the displacement gradient is small. © 2017, Springer International Publishing AG.
About the journal
JournalZeitschrift fur Angewandte Mathematik und Physik
PublisherBirkhauser Verlag AG
ISSN00442275
Open AccessNo