Linear Rheological Models at Small Strains

Abstract

Rheology is a discipline studying relaxation processes in materials and, related to them, the way how materials dissipate energy. Substantial dissipation may typically arise in sudden change of external load (in solids) or, conversely, in a long lasting constant load (like in fluids), or in combination of both. The distinction between solids and fluids is, from the purely mechanical viewpoint, not much lucid. For example, in geophysics, rocks are considered as fluids because they cannot permanently withstand a constant shear load. But they manifest its fluidic character only in observation time scale of millions of years, while in the man’s observation time scale of years, they are well solid, as we all know from our everyday experience. Actually, this paradox is counted in a so-called Deborah number (sometimes denoted by the Hebrew letter ‘daleth’, $\daleth$) defined as a ratio between the relaxation time and the observation time. The difference between solids and fluids is thus reflected by this number: large $\daleth \gg 1$ means that the medium can be well understood as solid while small $0<\daleth \ll 1$ indicates rather a fluid.

The mountains flowed before the Lord.

Prophetess Judge Deborah ($\sim$1200 BC)

$T \grave{\alpha } \ \,\pi \acute{\alpha }\nu \tau \alpha \ \,`\!\rho \epsilon \tilde{\iota }$ ($\sim$everything flows)

Heraclitus of Ephesus (535–475 BC)