A Kelvin–Voigt material, also called a Voigt material, is the most simple model viscoelastic material showing typical rubbery properties. It is purely elastic on long timescales (slow deformation), but shows additional resistance to fast deformation. The model was developed independently by the British physicist Lord Kelvin in 1865 and by the German physicist Woldemar Voigt in 1890.
Definition
right|frame| Schematic representation of Kelvin–Voigt model.
The Kelvin–Voigt model, also called the Voigt model, is represented by a purely viscous damper and purely elastic spring connected in parallel as shown in the picture.
If, instead, 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:
:<math> \varepsilon_\text{Total} = \varepsilon_{\rm S} = \varepsilon_{\rm D }. </math>
where the subscript D indicates the stress-strain in the damper and the subscript S indicates the stress-strain in the spring. Similarly, the total stress will be the sum of the stress in each component:
:<math> \sigma_\text{Total} = \sigma_{\rm S} + \sigma_{\rm D}. </math>
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:
:<math>\sigma (t) = E \varepsilon(t) + \eta \frac {d\varepsilon(t)} {dt},</math>
or, in dot notation:
:<math>\sigma = E \varepsilon + \eta \dot {\varepsilon},</math>
where E is a modulus of elasticity and <math>\eta</math> is the viscosity. The equation can be applied either to the shear stress or normal stress of a material.
Effect of a sudden stress
[[Image:Kelvin deformation 2.png|right|frame|Dependence of dimensionless deformation
upon dimensionless time under constant stress]]
If we suddenly apply some constant stress <math>\sigma_0</math> to Kelvin–Voigt material, then the deformations would approach the deformation for the pure elastic material <math> \sigma_0/E</math> with the difference decaying exponentially: