Journal
MATHEMATICS AND MECHANICS OF SOLIDS
Volume 16, Issue 3, Pages 334-346Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1081286510397228
Keywords
fractional heat conduction law; fractional thermoelasticity; generalized thermoelasticity; variational principle; uniqueness and reciprocal theorems
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Two general models of fractional heat conduction for non-homogeneous anisotropic elastic solids are introduced and the constitutive equations for thermoelasticity theory are obtained, uniqueness and reciprocal theorems are proved and the convolutional variational principle is established and used to prove a uniqueness theorem with no restriction on the elasticity or thermal conductivity tensors except for symmetry conditions. The dynamic coupled, Lord-Shulman, Green-Naghdi and fractional coupled thermoelasticity theories result as limit cases. The reciprocity relation in the case of quiescent initial state is found to be independent of the order of differintegration.
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