Journal of Siberian Federal University. Mathematics & Physics / Conditions for Convexity of the Isotropic Function of the Second-rank Tensor

Full text (.pdf)
Issue
Journal of Siberian Federal University. Mathematics & Physics. 2011 4 (2)
Authors
Sadovskii, Vladimir M.
Contact information
Sadovskii, Vladimir M. : e-mail:
Keywords
isotropic tensor function; convexity; invariants; nonlinear elasticity; plasticity
Abstract

For a scalar function, depending on the invariants of the second-rank tensor, condition of convexity and strong con-vexity 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..

Pages
265-272
Paper at repository of SibFU
https://elib.sfu-kras.ru/handle/2311/2293