Solution (source code)

= 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> gives
$$
\sigma(t)=\int_{-\infty}^tG(t-s)\dot\gamma(s)\,ds.
$$
Here $G(t)$ 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.