New and minimal representations for isotropic constitutive equations of Rivlin–Ericksen fluids and hygrosteric materials

According to the well-known representation theorem in literature, isotropic symmetric tensor-valued functions of two symmetric tensor variables are expressible in terms of eight polynomial generators. Although it is irreducible, this representation can now be sharpened by presenting seven new polynomial generators. This new representation is further shown to be minimal with the fact that the number of polynomial generators for every representation should be at least seven. New and minimal representations are provided for isotropic constitutive equations of Rivlin–Ericksen fluids of grade two, hygrosteric materials, and elastoplastic granular media, and so forth.