A viscoelastic material is one in which the stress induced is proportional to the rate of strain in the material.

Viscoelastic material models are frequently used to describe the behaviour of human tissue.

Commonly used viscoelastic models are the Kelvin-Voight and Maxwell models.

Viscous materials, like honey, resist Shear flow and Strain linearly with time when a Stress is applied.
Elastic materials strain instantaneously when stretched and just as quickly return to their original state once the stress is removed.
Viscoelastic materials have elements of both of these properties and, as such, exhibit time dependent strain.
Whereas elasticity is usually the result of bond stretching along crystallographic planes in an ordered solid, viscoelasticity is the result of the diffusion of atoms or molecules inside of an amorphous material


In the nineteenth century, physicists such as Maxwell and Kelvin experimented with creep and recovery of Glasses, Metals, and Rubbers.
Viscoelasticity was further examined in the late twentieth century when Synthetic_polymers were engineered and used in a variety of applications.
Viscoelasticty calculations depend heavily on the Viscosity variable, η.
The inverse of η is also known as Fluidity, φ.
The value of either can be derived as a function of temperature or as a given value (ie for a dashpot).
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.
When a material exhibits a linear response it is categorized as a Newtonian_material.
In this case the stress is linearly proportional to the strain rate.
If the material exhibits a non-linear response to the strain rate, it is catagorized as Non-Newtonian_fluid.
There is also an interesting case where the viscosity decreases as the strain rate increases.
A material which exhibits this type of behavior is known as thixotropic . In addition, when the stress is independent of this strain rate, the material exhibits plastic deformation.
Many viscoelastic materials exhibit Rubber like behavior explained by the Thermodynamic theory of polymer elasticity.
Some examples of viscoelastic materials include amorphous polymers, semicrystalline polymers, biopolymers, and metals at very high temperatures.
A viscoelastic material has the following properties: "Hysteresis is seen in the Stress-strain_curve."

Elastic Behavior Versus Viscoelastic Behavior

Unlike purely elastic substances, a viscoelastic substance has an elastic component and a viscous component.
The Viscosity of a viscoelastic substance gives the substance a strain rate dependent on time.
Purely elastic materials do not dissipate energy (heat) when a load is applied, then removed.
However, a viscoelastic substance loses energy when a load is applied, then removed.
Hysteresis is observed in the stress-strain curve, with the area of the loop being equal to the energy lost during the loading cycle.
Since viscosity is the resistance to thermally activated plastic deformation, a viscous material will lose energy through a loading cycle.
Plastic deformation results in lost energy, which is uncharacteristic of a purely elastic materials reaction to a loading cycle.
Specifically, viscoelasticity is a molecular rearrangement.
When a stress is applied to a viscoelastic material such as a Polymer, parts of the long polymer chain change position.
This movement or rearrangement is called Creep.
Polymers remain a solid material even when these parts of their chains are rearranging in order to accompany the stress, and as this occurs, it creates a back stress in the material.
When the back stress is the same magnitude as the applied stress, the material no longer creeps.
When the original stress is taken away, the accumulated back stresses will cause the polymer to return to its original form.
The material creeps, which gives the prefix visco-, and the material fully recovers, which gives the suffix -elasticity.

Types of viscoelasticity

Linear viscoelasticity is when the function is separable in both creep response and load.
All linear viscoelastic models can be represented by a Volterra equation connecting stress and Strain.

Nonlinear viscoelasticity is when the function is not separable.
It is usually happens when the Deformations are large or if the material changes its properties under deformations.