Tensor linearity of two-dimensional isotropic functions in the plane problem of nonlinear theory of elasticity

It is shown that a nonlinear isotropic tensor function of the second rank in two-dimensional space, which is a power series in its tensor argument, is representable by a finite binomial tensor linear relation. Expressions of two coefficients of this relation are given in terms of an infinite set of coefficients of the original series and two independent invariants of the tensor argument. In relation to continuum mechanics, the reducibility of the constitutive relations in the plane problem of tensor nonlinear elasticity theory to the tensor linear connection of the corresponding second-order minors of stresses and strains is established.