Cones of material response functions inone-dimensional and anisotropiclinear viscoelasticity

摘要

Viscoelastic materials have non-negative relaxation spectra. This property implies thatviscoelastic response functions satisfy certain necessary and sufficient conditions. Theseconditions can be expressed in terms of each viscoelastic response function rangingover a cone. The elements of each cone are completely characterized by an integralrepresentation. The 1 : 1 correspondence between the viscoelastic response functions isexpressed in terms of cone-preserving mappings and their inverses. The theory coversscalar- and tensor-valued viscoelastic response functions.