Simulation unit : make sure your units are coherent

[hugtalbot]

Dear SOFA community,

We often get the follow question "what are the unit used in SOFA? What are the unit of my simulation ?".
This aims at clarifying this.

Unit definition

Checking the units of your simulation is very good practice. The fact is that SOFA makes no assumption on the unit in a simulation. This means that you - as a user - are in charge of the choice of the units. However, these units must remain coherent in your scene file.

"you chose the units" : what does it mean?

Yes, as a user, you do choose the unit:

• SOFA being a simulation engine relying on the Finite Element Method (FEM), it often requires to load a mesh. Your mesh defines the positions of mesh nodes. These positions are given in a .. LENGTH unit
• you also specify a time step (dt) which is given in a .. TIME unit
• if your simulated bodies have a mass, you may define a total mass, given in a .. MASS unit

Let's take an example. Let's say that:

• you use a mesh in mm, mm is now your LENGTH unit
• you define a time step of 0.001s meaning that second is your TIME unit
• you define a total mass of your object of 1 kg meaning that kg is your MASS unit

If you use a linear elastic model on a tetrahedral mesh (TetrahedronFEMForceField), how should we now define the Young's Modulus?
The unit of the Young's Modulus is : MASS / (TIME²⋅LENGTH)

• in the IS unit, the Young's Modulus should be expressed in ➡️ kg / ( s²⋅m) = [kg⋅m/s²] / m² = N / m² = Pa
• using the units of our example, the Young's Modulus should be expressed in ➡️ kg / ( s²⋅mm) = [kg⋅mm/s²] / mm² = mN / mm² = kPa

If your object is a rubber, and its Young's modulus amounts : 3 MPa (mega-pascal) = 3 ·10⁶ Pa. But using the units of our example, the value you should set in your simulation file is : youndModulus=3000 since it corresponds to 3 · 10³ kPa

Note that the forces computed in your simulation would therefore be in mN!
Does this makes sense?

Keep it simple

In many countries, the International System of Units is often used. To keep things simple, you may want to use these units. Just, as always, make sure to use this convention everywhere in your scene file to remain coherent 👍