A note on viscoelastic bodies whose material properties depend on the density

In this note, we study the response of a viscoelastic body whose stress relaxation modulus and creep compliance depend on the density of the body in such a manner that the stress and strain appear linearly in the constitutive equation. Such models would be useful to study the response of porous viscoelastic bodies undergoing small deformations, as the moduli depend on the porosity, and hence the density. We study the problem of tension-torsion of cylinders of arbitrary cross-section within the context of this constitutive relation.

Automated summary

The note discusses the response of a viscoelastic body with stress relaxation modulus and creep compliance depending on body density, resulting in linear stress and strain in the constitutive equation. Such models are useful for studying porous viscoelastic bodies undergoing small deformations where moduli vary with porosity and density. The tension-torsion problem of cylinders with arbitrary cross-section is specifically examined within this constitutive relation.