# Viscoelasticity

Viscoelasticity is the study of materials which have a time-dependent strain that exhibit both viscous and elastic characteristics when undergoing deformation. Viscoelastic response is often used as a probe in polymer science, since it is sensitive to the material’s chemistry and microstructure.

The identification of the viscoelastic behavior is carried out by measuring the variation in viscosity $$(\mu)$$ as a function of the strain rate $$(\dot{\gamma})$$; the inverse magnitude of the viscosity is called fluidity.

The viscosity (and consequently the fluidity) are properties that vary with temperature, so that in the case of a viscoelastic fluid the viscosity depends on both the temperature and the strain rate, whereas for a purely viscous fluid the viscosity depends exclusively on temperature.

## Rheological behavior of viscoelastic materials

In viscoelastic materials, the viscosity understood as a constant of proportionality between stress and strain speed depends on the strain rate and then by time. Depending on the change of strain rate versus stress inside a material, the viscosity can be categorized as having a linear, non-linear, or plastic response.

The viscosity of a viscoelastic material consists of two types of contribution:

1. the shear viscosity, which is the ratio between the shear stress and the strain speed;
2. the extensional viscosity (or elongational viscosity), which is the relationship between perpendicular stresses and the strain speed.

When a material exhibits a linear response (the stress is linearly proportional to the strain rate), it is categorized as a Newtonian material.

If the material exhibits a non-linear response to the strain rate, it is categorized as Non-Newtonian fluid.

There is also a compelling case where the viscosity decreases as the shear/strain rate remains constant. A material which exhibits this type of behavior is known as thixotropic. Besides, when the stress is independent of this strain rate, the material exhibits plastic deformation.

Some properties of viscoelastic materials are the following:

• if the stress remains constant, the deformation grows with time; this phenomenon is called “creep“;
• if the deformation is kept constant, the stress decreases with time; this phenomenon is known as “stress relaxation“;
• the rigidity of the material depends on the speed of application of the load;
• if a cyclic load is applied, a hysteresis occurs (a periodic delay), with consequent dissipation (in the form of heat) of mechanical energy; representing the load cycle in a stress-strain diagram, the loss of mechanical energy is equal to the area of the path that represents the load cycle; this loss of mechanical energy does not occur in elastic materials, which resume their original shape once the load is removed;
• the rebound speed of an object as a result of a collision with a viscoelastic material is less than the speed of the object before the collision;
• the acoustic waves (as well as those vibrational) undergo an attenuation, due to energy dissipation due to the hysteresis of load-unload cycles;
• during the rolling of a viscoelastic material, the effects of rolling friction are characterized by sliding friction effects.