For every beginner users, it is really strange that why quantities in Abaqus have no units. They get confused about the stress unit or when inputting parameters like Young Modulus, density…

Not only Abaqus, almost any finite element programs (Ansys, LS-Dyna…) do not consider the units of given quantities. It is the user’s responsibility to ensure that the given numbers have consistent units.

## Units in Abaqus

Abaqus has no units built into it except for rotation and angle measures. Therefore, the units chosen must be self-consistent, which means that derived units of the chosen system can be expressed in terms of the fundamental units without conversion factors.

### Consistent Units

Generally, any consistent system of units consists of some fundamental units such as Length (L), Mass (M) or Force (F), Time (T) as base units and the other units named derived units, which are formed by powers, products, or quotients of the base units and are potentially unlimited in number.

The International System of Units (SI) is an example of a self-consistent set of units. The fundamental units in the SI system are length in meters (m), mass in kilograms (kg), time in seconds (s), temperature in degrees Kelvin (K), and electric current in Amperes (A).

Combinations of base and derived units may be used to express other derived units. Definition of derived units is based on fundamental physical relations:

For example, A unit of force in the SI system is called a Newton (N):

Another example is the unit of energy, called a Joule (J):

## Choosing a suitable consistent system of units

Sometimes the standard units are not convenient to work with. For example, Young’s modulus is frequently specified in terms of MegaPascals (MPa) (or, equivalently, N/mm2), where 1 Pascal = 1 N/m2. In this case the fundamental units could be tonnes (1 tonne = 1000 kilograms), millimeters, and seconds.

There are numerous different sets of units that can be used when performing FE simulations. The best set of units will depend on the problem; typically, the most accurate results are obtained if the units are chosen such that the value s of the input quantities to the FE simulation are close to unity. By having the input quantities close to 1, the influence of round-off errors and truncation errors are reduced.

## Example

#### How Selecting Appropriate Unit System in Analyses

Let us see a practical example:

We have modeled a fullerene C60 in Abaqus and applied forces (distributed) to its ends (like a tension test). C60 has dimensions at the order of **nm** (1e-9 m). Our forces are also in **nN**.

E=1.16 **Tera-Pascal** = 1.16 e+12 **Pa**

How we can model this geometry in Abaqus?

What is the Young Modulus unit? What is the mass density unit?

Please think first 🙂

Modeling sub-micron quantities is not possible in Abaqus/CAE since geometric limits are set. It means that you cannot model a sphere of radius 1e-9 in Abaqus/CAE. Besides, if it was possible, due to the influence of round-off errors and truncation errors for very small values, the analysis will stop soon.

Therefore, we need to scale down the model and make the necessary changes in the material properties.

Remember the base units in SI: FLT=Force, Length and Time

For example, we select **nN** as force base unit, **nm** as length unit and **s** as time unit.

It means we will make our geometry saying all dimensions in **nm**.

Now, for Young Modulus, which is a kind of stress, we have:

So, we must enter Yong Modulus in 10^9 Pa:

We enter 1.16 e+3 as Young Modulus in Abaqus.

Remember that you are doing numerical calculation in Abaqus, and 3 mm and .003 m are different for computer; it needs more memory to save and doing calculates on .003 than 3.

## Reference Table for consistent systems of units

The following table provides examples of consistent systems of units. As points of reference, the mass density and Young’s Modulus of steel are provided in each system of units. “GRAVITY” is gravitational acceleration.

### Cautions When Using Imperial Units

The naming conventions are not as clear as in the SI system for imperial (American or English) units and they can cause confusion. Frequently it is not made clear in handbooks whether lb stands for lbm or lbf. You need to check that the values used make up a consistent set of units.

For example, 1 pound force (**lbf**) will give 1 pound mass (**lbm**) an acceleration of g **ft/sec2**, where g is the value of acceleration due to gravity. If we take pounds force, feet (ft), and seconds as fundamental units, the derived unit of mass is lbf sec2/ft. Since density is commonly given in handbooks as lbm/in3, it must be converted to lbf sec2/ft4 by

Two other units that cause difficulty are the slug, the mass that will accelerate at 1 **ft/sec^2** by 1 **lbf**, and the **poundal**, which we define it as the force required to accelerate 1 lbm at 1 **ft/sec2**. Useful conversions are

1 slug = **g** x lbm

and

1 lbf = **g** x poundals

where **g** is the magnitude of the acceleration due to gravity in **ft/sec2**.

**Quiz Time!**

How can we convert the SI units for specific heat capacity (J/kg-K) and Thermal Conductivity (W/m-K) in to consistent units when we model the geometry in mm? In other words, what is the conversion factor for these quantities when we model in mm?