A Simple Derivation of Representations for Non‐Polynomial Constitutive Equations in Some Cases of Anisotropy

Abstract A method is developed allowing to establish irreducible representations for anisotropic non‐polynomial constitutive equations. The case when a constitutive equation takes the form of an explicit relation between two symmetric second order tensoers is considered in detail. Transitions from the most general anisotropy to particular cases of anisotropy are established. As an example the transition from the general non linear forms to the case of classical linear elasticity is given. It appears that for the considered case of tensor functions the irreducible representations for the non‐polynomial case are similar to those concerning a polynomial function. This similarity disappears for functions involving a larger number of arguments.