A new representation for anisotropic viscoelastic functions

A new representation for viscoelastic functions, the tensor relaxation-creep duality representation, is introduced. The derivation of a tensor time-differential constitutive equation for anisotropic viscoelastic materials using this new presentation is presented. The relaxation-creep duality characteristic ingrained in the new representation enables the interconversion of viscoelastic functions, which is not possible with the conventional Prony series representation of viscoelastic functions. The new representation therefore offers a better representation of the physics of viscoelasticity leading to a reduced number of viscoelastic parameters required to describe a viscoelastic function. The new representation has been demonstrated on two anisotropic viscoelastic crystallographic systems: (i) the symmetric systems with material- and time-independent eigenvectors and (ii) the symmetric systems with material-dependent but time-independent eigenvectors.