Fig. 1.

Phenomenological models for rheological analysis. The symbols represent (A) the solid (spring, shear modulus $G$) and (B) liquid (dashpot, viscosity $\eta$) behaviors, and the plots of their dependencies with angular frequency. The spring characterizes energy storage in the material, and the relationship between stress and strain is given by $\sigma =G∊.$ The dashpot characterizes the energy loss in the material and the relationship between stress and strain is given by $\sigma =\eta \frac{d∊}{\mathit{dt}}.$ The association of one spring and one dashpot in parallel gives rise to the Kelvin-Voigt model for a viscoelastic solid (C). The association in series represents the Maxwell model for a viscoelastic liquid (D). Both the Maxwell and Kelvin-Voigt models present only one relaxation time, $\tau =\eta /G$. The combination of an infinite number of Kelvin-Voigt blocks describes the model for soft glassy materials (E), characterized by a power law dependency of the complex shear modulus with the angular frequency. The power law dependency is also a signature of infinity time-scales present in the response. When $G^{\text{'}}>G\text{'}\text{'}$, a solid-like behavior is observed. When $G^{\text{'}}<G\text{'}\text{'}$ a liquid-like behavior is visualized.