Anelasticity

Anelasticity is a delayed but recoverable strain response caused by relaxation of internal degrees of freedom. After a small imposed stress is removed, the strain can return to its original value over a finite time rather than instantaneously. Under oscillatory loading, this delay causes a phase lag and dissipation, measured by a loss modulus or loss tangent. Stress-induced redistribution of interstitial impurities in a metal gives the Snoek effect. This solid-state response is distinct from an approximation to fluid mass conservation carrying a similar name.

The Snoek effect is anelasticity caused by stress-induced redistribution of mobile interstitial defects among differently oriented sites in a crystal. An applied stress favors orientations whose local distortion best accommodates it. At low frequency the atoms can track that bias and provide additional relaxed compliance; at high frequency their populations are nearly frozen. Dissipation is largest between these regimes. For a weak single relaxation, the loss tangent has the approximate shape $\Delta \omega \tau /[1+(\omega \tau {)}^2]$, with $\tau ={\tau }_0{e}^{E_a/(k_{B}T)}$ for thermally activated hopping. The peak is near $\omega \tau =1$. This describes a standard mechanism for interstitial impurities in body-centred cubic metals, not every damping mechanism in every alloy. ^[ref]