Generalized Hooke's law for isotropic second gradient materials

Details Generalized Hooke's law for isotropic second gradient materials Generalized Hooke's law for isotropic second gradient materials

2010-08-17

arxiv.org/abs/1008.2879v1

Physics

Mathematical Physics

20 pages

Scientific paper

In the spirit of Germain the most general objective stored elastic energy for a second gradient material is deduced using a literature result of Fortun\'e & Vall\'ee. 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.

Affiliated with

Also associated with

No associations

Rating

Generalized Hooke's law for isotropic second gradient materials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized Hooke's law for isotropic second gradient materials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Hooke's law for isotropic second gradient materials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-397856