Kelvin–Voigt material

A Kelvin–Voigt material, also called a Voigt material, is a viscoelastic material having the properties both of elasticity and viscosity. It is named after the British physicist and engineer Lord Kelvin and after German physicist Woldemar Voigt.

The Kelvin–Voigt model, also called the Voigt model, can be represented by a purely viscous damper and purely elastic spring connected in parallel as shown in the picture.

If we connect these two elements in series we get a model of a Maxwell material.

Since the two components of the model are arranged in parallel, the strains in each component are identical:

Similarly, the total stress will be the sum of the stress in each component:

From these equations we get that in a Kelvin–Voigt material, stress σ, strain ε and their rates of change with respect to time t are governed by equations of the form:

where E is a modulus of elasticity and ${\displaystyle \eta }$ is the viscosity. The equation can be applied either to the shear stress or normal stress of a material.

If we suddenly apply some constant stress ${\displaystyle \sigma _{0}}$ to Kelvin–Voigt material, then the deformations would approach the deformation for the pure elastic material ${\displaystyle \sigma _{0}/E}$ with the difference decaying exponentially:

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