# Viscoelasticity and Hyperelastic model, history and difference

Actually, I see some papers use viscoelasticity or hyperelastic model for the same materials. It seems to me that those models were invented in different eras, and the hyperelastic is a newer model than viscoelasticity. Am I right?

What's the difference?

What is the best way to decide which model to use when we want to simulate a material?

• For the first part, you got it almost right, but i think the seconde question is a way to broad and really difficult to answer. It is rather material science than engineering. Oct 15 '18 at 19:39
• It pretty much depends on what property you are interested in....you can have an analysis of some rubber component where you use an hyperelastic model to compute its stress or deformation, maybe strain rate is important so you need a viscoelastic material. They are not mutually exclusive you can find visco-hyperelastic models in the literature. I pretend to answer this question later today (maybe tomorrow), in the meanwhile can you cite those papers you were talking about? Oct 15 '18 at 20:44
• @user190081, You explanation is very clear. Thank you very much. Oct 16 '18 at 20:49

The hyperelastic and viscoelastic material models are both constitutive relations that relate:

• Stress and strain, in the case of hyperelasticity.
• Stress, strain and strain rate, in the case of viscoelasticity.

They are both empirical models, which means that you typically need to run experiments to find the necessary parameters to fit each model (there are some ways to find elastic properties from first principles, but I'm gonna leave that discussion aside).

Hyperelastic models (as the name implies) deal with elastic materials - those which deform when a load is applied, and return to their original shape after the load is released. Unlike Hookean elastic models, which have a linear strain-stress relationship, hyperelastic models have a non-linear relationship: One common example of simulations using hyperelastic models are about rubbers seals or gaskets: In viscoelastic models the strain-stress relationship will be dependent on the strain-rate (how fast you deform the material) and time, and the loading and unloading paths are not the same: If your constitutive model for viscoelasticity includes creep behavior you may also have permanent deformation: The choice of one model over the other depends on what problem are you trying to solve. Are you interested in the strain-stress response when you change the rate of deformation? Are you interested in creep or stress relaxation? Both models are not mutually exclusive, you can create an visco-hyperelastic model (or use those in the literature) if you need it.

Let's look at some (very rough) definitions:

1) Viscoelasticity = elastic behavior that changes if the rate of application of the load is changed or, if the load is kept fixed, the change in the elastic behavior of a material over time.

2) Hyperelasticity = rate/time-independent elastic behavior beyond linear elasticity

Of course, elastic behavior means that once the load is removed the material returns to its original state (given enough time for viscoelastic materials or instantaneously for hyperelastic materials).

Typically, when engineers talk about viscoelasticity they mean "linear" viscoelasticity, i.e, the material is linear elastic even though the elastic moduli may depend on the rate of loading or on time. You can also have hyperelastic viscoelastic materials which are more commonly known as nonlinear viscoelastic materials.

Hyperelastic materials (such as St. Venant-Kirchhoff materials) and linear viscoelastic materials were both initially explored in the mid-1800s. So they are approximately the same age.

The choice of material model depends on:

1) The amount of strain you expect: large strains -> hyperelastic, small strains -> linear elastic

2) The effect of loading rate: rate-dependent-> viscoelastic, rate-independent -> elastic (linear or hyper)

• Thank you for the answer, I was wondering what do you mean about loading rate? Do you mean temperature or residual stress or others? Thank you very much. Oct 16 '18 at 20:23
• These models are independent of temperature (unless one adds extra features). Loads in mechanics means forces/tractions. Loads are typically applied over a period of time and the derivative to load wrt time is the loading rate. Oct 17 '18 at 2:02