KelvinVoigtModell

The Kelvin-Voigt model (Kelvin-Voigt-Modell) is a simple rheological model for viscoelastic materials consisting of a spring and a dashpot in parallel. The spring has elastic modulus E; the dashpot has viscosity η. Because they are in parallel, both elements experience the same strain ε(t) and the total stress σ(t) is the sum of the individual stresses: σ = E ε + η dε/dt.

Constitutive relations for this model express the relationship between stress and strain. Under a constant strain ε0, the stress is σ(t) = E ε0 + η dε/dt, and since dε/dt = 0 for a maintained strain, σ = E ε0, independent of time. Under a constant applied stress σ0, the strain evolves according to dε/dt + (E/η) ε = σ0/η. With an initial strain ε(0) = 0, the solution is ε(t) = (σ0/E)(1 − exp(−E t / η)). The strain approaches σ0/E as time grows, so the model exhibits creep but no stress relaxation under constant strain.

In the frequency domain, the Kelvin-Voigt model has a complex modulus E*(ω) = E + i ω η, implying a storage modulus E and a loss modulus η ω. The single time constant is τ = η / E, reflecting the balance between elastic and viscous responses.

Applications and limitations: The model serves as a basic representation of viscoelastic damping in polymers and biological tissues and is often used as a building block in more complex models (for example, generalized Kelvin-Voigt or the Standard Linear Solid). It cannot capture stress relaxation under constant strain, non-linear effects, or large deformations; more sophisticated models are required for precise data fitting.