Viscoelasticity

Definition

Consider a material point with strain history $\varepsilon(s)$, $s \le t$, and stress $\sigma(t)$ at time $t$. The material is viscoelastic if its constitutive equation gives $\sigma(t)$ as a functional of the past strain history $\{\varepsilon(s) : s \le t\}$ that satisfies:

1. causality: $\sigma(t)$ depends only on $\varepsilon(s)$ for $s \le t$;
2. fading memory: strain at times far in the past has a vanishing effect on the present stress;
3. rate dependence: the response depends on the rate of loading, so that the material shows creep under constant stress and stress relaxation under constant strain.

It is linear viscoelastic if moreover the functional is linear in the history and does not change under a shift of time.