Kelvin–Voigt Creep Response Calculator

Example data table

Example values shown for quick reference.

These rows illustrate how lower η or higher t increases creep toward σ/E.

Kelvin–Voigt creep response guide

1) What the model represents

The Kelvin–Voigt element combines an elastic spring and a viscous dashpot in parallel. It is a simple way to describe primary creep where strain rises quickly, then gradually levels off. The calculator translates stress, stiffness, and viscosity into time‑dependent strain for design checks.

2) Creep under constant stress

For a step stress σ applied at t = 0, the strain follows ε(t) = (σ/E)(1 − e^−t/τ) + ε₀. The asymptotic strain is σ/E, so the spring sets the final deformation. The dashpot controls how fast you approach that limit.

3) The time constant τ = η/E

The characteristic time τ links viscosity η and modulus E. After one τ, the strain reaches about 63% of its final value. After three τ, it is near 95%. Use this to estimate how long a creep test should run.

4) Compliance and creep rate

The calculator reports creep compliance J(t) = ε(t)/σ (when ε₀ = 0). Early in time, the creep rate is highest and decays exponentially. A larger η lowers the initial rate and stretches the curve in time. A larger E reduces the vertical scale by lowering σ/E.

5) Typical parameter scales

Polymers and biological tissues often have lower E and moderate η, giving noticeable creep over seconds to hours. Metals at room temperature can behave as if η is extremely large, so primary creep may be small in short tests. Always keep units consistent: Pa, Pa·s, and seconds.

6) Interpreting microstrain output

Microstrain (με) is strain multiplied by one million. Engineers prefer microstrain for small deformations in structures and coupons. If results look unrealistic, recheck stress units and any initial strain offset.

7) Data entry and conversions

This tool accepts stress and modulus units from Pa up to GPa, and viscosity units from Pa·s up to GPa·s. Internally, everything converts to SI before computing τ, ε(t), and J(t). Time can be entered in seconds, minutes, hours, or days for convenience.

8) When to use and when not to

Kelvin–Voigt fits materials that show delayed elastic strain under sustained loading. It cannot represent a long‑term constant creep rate, so it is not a full secondary‑creep model. If your measurements show linear strain growth at long times, consider generalized chains or other rheologies.

FAQs

1) What inputs most strongly affect the curve?

Modulus E sets the final strain level σ/E, while viscosity η sets the time constant τ = η/E. Increasing stress σ raises the whole curve proportionally.

2) Why does the strain approach a limit?

In this model, the spring is always engaged, so it enforces a bounded deformation. As time increases, dashpot flow slows and the strain tends toward σ/E.

3) What does the initial strain ε₀ mean?

ε₀ is an optional offset used when a specimen already has pre‑strain, seating strain, or a defined reference shift. Set ε₀ to zero for a pure step‑load creep response.

4) How do I pick realistic η values?

Start from literature values for your material class, then fit η and E to measured ε(t) data. If creep happens too fast in the calculator, η is likely too small for that modulus.

5) Can I use this for temperature effects?

Indirectly. Temperature changes both E and η, often strongly. Run the calculator with temperature‑specific parameters taken from experiments or material datasheets.

6) Why is unit consistency so important?

τ depends on η/E, so mixing MPa with Pa·s without conversion can shift τ by factors of one million. Use the built‑in unit selectors to avoid scaling mistakes.

7) Does Kelvin–Voigt model secondary creep?

No. Kelvin–Voigt predicts a decreasing creep rate that approaches zero. Secondary creep needs models that allow an approximately constant long‑term strain rate.