Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 465, Issue 2107, Pages 2177-2196Publisher
ROYAL SOC
DOI: 10.1098/rspa.2008.0530
Keywords
stress concentration; constitutive behaviour; elastic material
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In the spirit of Germain the most general objective stored elastic energy for a second gradient material is deduced using a literature result of Fortune & Vallee. Linear isotropic constitutive relations for stress and hyperstress in terms of strain and strain-gradient are then obtained proving that these materials are characterized by seven elastic moduli and generalizing previous studies by Toupin, Mindlin and Sokolowski. Using a suitable decomposition of the strain-gradient, it is found a necessary and sufficient condition, to be verified by the elastic moduli, assuring positive definiteness of the stored elastic energy. The problem of warping in linear torsion of a prismatic second gradient cylinder is formulated, thus obtaining a possible measurement procedure for one of the second gradient elastic moduli.
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