Geodesic
Conditions for convexity of the isotropic function of the second-rank tensor
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 2, pp. 265-272

Voir la notice de l'article provenant de la source Math-Net.Ru

For a scalar function, depending on the invariants of the second-rank tensor, condition of convexity and strong convexity are obtained with respect to the components of this tensor in an arbitrary Cartesian coordinate system. It is shown that if a function depends only on the four invariants: three principal values of the symmetric part of a tensor and modulus of pseudovector of the antisymmetric part, these conditions are necessary and sufficient. A special system of convex invariants is suggested to construct potentials for the stresses and strains in the mechanics of structurally inhomogeneous elastic media, exhibiting moment properties.
Keywords: isotropic tensor function, convexity, nonlinear elasticity, plasticity.
Mots-clés : invariants 
@article{JSFU_2011_4_2_a13,
     author = {Vladimir M. Sadovskii},
     title = {Conditions for convexity of the isotropic function of the second-rank tensor},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {265--272},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2011_4_2_a13/}
}
TY  - JOUR
AU  - Vladimir M. Sadovskii
TI  - Conditions for convexity of the isotropic function of the second-rank tensor
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2011
SP  - 265
EP  - 272
VL  - 4
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2011_4_2_a13/
LA  - ru
ID  - JSFU_2011_4_2_a13
ER  - 
%0 Journal Article
%A Vladimir M. Sadovskii
%T Conditions for convexity of the isotropic function of the second-rank tensor
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2011
%P 265-272
%V 4
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2011_4_2_a13/
%G ru
%F JSFU_2011_4_2_a13
Vladimir M. Sadovskii. Conditions for convexity of the isotropic function of the second-rank tensor. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 2, pp. 265-272. http://geodesic.mathdoc.fr/item/JSFU_2011_4_2_a13/