Conditions for convexity of the isotropic function of the second-rank tensor

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.