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

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

2009-06-10

arxiv.org/abs/0906.1893v2

Physics

Condensed Matter

Materials Science

submitted to Proc. Roy. Soc. A

Scientific paper

Viscoelastic materials have non-negative relaxation spectra. This property implies that viscoelastic response functions satisfy certain necessary and sufficient conditions. It is shown that these conditions can be expressed in terms of each viscoelastic response function ranging over a cone. The elements of each cone are completely characterized by an integral representation. The 1:1 correspondences between the viscoelastic response functions are expressed in terms of cone-preserving mappings and their inverses. The theory covers scalar and tensor-valued viscoelastic response functions

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