Branch of physics that aims to describe, explain, measure, and study the mechanical phenomena that occur in materials when they are deformed.
In this sense, rheology studies the deformation and flow of materials.
The primary objective of a rheological study of a material is therefore the search for a relationship that defines its mechanical behavior.
It is usually indicated with the name of constitutive equation or also rheological equation of state of the material considered and links the dynamic quantities (stress) to the kinematic ones (strain).
A material’s nature (liquid, semi-solid, or solid) can be classified based on its response to an external stress. The material can flow, deform partially, or remain unchanged.
At the end of the external stress, three responses can occur from the material in question:
- A continuous, infinite, no longer recoverable deformation: the material flows (liquid)
- A deformation that remains totally or partially after the stress is removed: plastic or viscoelastic materials
- A deformation that is completely recovered at the end of the stress: elastic materials.
Deformation of a solid:A solid subjected to an external force F tangential to its surface A, undergoes a deformation γ proportional to the applied stress.
Si definisce sforzo di taglio τ la forza per unità di superficie:
Real solids, under the effect of a stress τ, undergo a deformation g which are linked to each other through the following relationship (Hooke’s law)
Deformation of a liquid:
Consider an infinitesimal fluid element and apply a tangential force F to its surface.
In this case, the applied stress produces a time-varying deformation, i.e., it produces slip.
We can imagine the fluid element as a deck of cards: the top card moves at maximum speed, while the bottom card, resting on the surface, is stationary.
We will therefore have a distribution or variation of velocity along the vertical y-axis (the thickness of the deck), i.e., we will have a velocity gradient.
We will therefore talk about laminar flow in which infinitesimal layers of fluid flow over each other.
Let’s define the velocity gradient:
There is a linear proportionality between the applied stress and the velocity gradient to which the fluid element is subjected:
Where η is the viscosity of the liquid, or its resistance to flow.
Viscosity thus defined is called dynamic viscosity.