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Viscoelastic materials have non-negative relaxation spectra. This propertyimplies that viscoelastic response functions satisfy certain necessary andsufficient conditions. It is shown that these conditions can be expressed interms of each viscoelastic response function ranging over a cone. The elementsof each cone are completely characterized by an integral representation. The1:1 correspondences between the viscoelastic response functions are expressedin terms of cone-preserving mappings and their inverses. The theory coversscalar and tensor-valued viscoelastic response functions

Cones of material response functions in 1D and anisotropic linear viscoelasticity