A viscoelastic material is one in which:

• hysteresis is seen in the stress-strain curve.
• stress relaxation occurs: step constant strain causes decreasing stress
• creep occurs: step constant stress causes increasing strain

Viscoelastic material models are frequently used to describe the behaviour of (soft) human tissue, plastics, soil, etc. Commonly used viscoelastic models are the Kelvin material and Maxwell material. Each model can be represented by springs and dashpots set in combinations of series and parallel elements.

Overview

Early scientists defined matter as a solid, liquid, or gas. They found that some materials fit in more than one of these phases. For instance, honey is a good example of a material with the physical properties of both a solid and a liquid. If one allows honey to flow from a container and then quickly tips the container up, a portion of the honey will be pulled back into the container. Liquids don’t typically respond to tensile force or pulling force. Scientists defined this material as viscoelastic because it exhibited the characteristics of a viscous liquid and an elastomeric solid. Silly putty, chewing gum, and polyurethane memory foam are also examples of viscoelastic materials.

Almost all polymers exhibit viscoelastic behavior. Polymers (and other viscoelastic materials) behave more like solids at low temperatures and fast deformation speeds. They are more like liquids at high temperatures and slow deformation speeds.

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:

$\backslash epsilon(t)=\; \backslash frac\; \{\; \backslash sigma(t)\; \}\{\; E\_\{inst,creep\}\; \}+\; \backslash int\_0^t\; K(t-t^\backslash prime)\; \backslash sigma(t^\backslash prime)\; d\; t^\backslash prime$

or

$\backslash sigma(t)=\; E\_\{inst,relax\}\backslash epsilon(t)+\; \backslash int\_0^t\; F(t-t^\backslash prime)\; \backslash epsilon(t^\backslash prime)\; d\; t^\backslash prime$

where

• t is time
• $\backslash sigma\; (t)$ is stress
• $\backslash epsilon\; (t)$ is strain
• $E\_\{inst,creep\}$ and $E\_\{inst,relax\}$ are instantaneous elastic moduli for creep and relaxation
• K(t) is the creep function
• F(t) is the relaxation function

Linear viscoelasticity is usually applicable only for small deformations.

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.

See also

• Creep
• Stress relaxation
• Hysteresis
• Biomaterial
• Biomechanics

Materials science | Non-Newtonian fluids | Continuum mechanics | Rubber properties

لزوجة مرنة | Viskoelastizität | Viscoelasticidad de polímeros | 粘弹性