On the domain space for constitutive laws in linear viscoelasticity (Q1058381)

The implication of certain phenomenological restrictions, attributed to Boltzmann for viscoelastic solids, on the class of admissible kernels a in the general constitutive law, \(\tau (t)=\int^{t}_{-\infty}a(t- s)\gamma (t,s)\quad ds,\) for an isotropic, incompressible linearly viscoelastic fluid is investigated. It is found that the only admissible non-function contribution to the kernel is that which corresponds to the Newtonian fluid. In particular, fluids of higher grades are excluded. Stability considerations are also used to reach the latter conclusion.