Past exam of the quantum condensed matter course of the University of Cambridge / 2008 / Section A / A3 / a / Solution

A linear viscoelastic fluid responds linearly to small imposed strain histories but retains memory of earlier deformation. For shear strain $\gamma (t)$ and a relaxed initial state, Boltzmann superposition givesHere $G(t)$ is the causal relaxation modulus, the stress following a unit step strain. Doubling a sufficiently small strain history doubles the stress, and responses to added histories add. Elasticity stores deformation energy; viscosity dissipates it. Linearity is an amplitude approximation, not an assertion that the material has no relaxation times.