Clarifying Abaqus units | How to choose right units in Abaqus?

For any beginner user, it is truly puzzling why quantities in Abaqus lack units. This often leads to confusion regarding stress units and when entering parameters such as Young’s Modulus, density, and more. This isn’t just an issue with Abaqus; nearly all finite element programs (including Ansys, LS-Dyna, and others) overlook the consideration of unit systems for provided quantities. Thus, it falls upon the user to ensure that the provided numerical values are accompanied by consistent units. To understand how units in Abaqus and how to appropriately select an Abaqus consistent unit system, I recommend reading this post. By the end of the post, the CAE assistant team has provided an Abaqus units table that can be quite helpful.

1. Abaqus units | A Comprehensive Overview of 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. Read this useful article in 4 minutes to get enough information about Abaqus units or units in Abaqus.

The different types of units are CGS system units, FPS system units, MKS system units, and SI units.

The CGS units are the centimeter-gram-second system of units. This metric system uses the unit of “centimeter” to denote the distance/length, gram is used as the basic unit to denote mass /weight, and “seconds” is used to denote time.

The FPS units are the foot-pound-second system of units. This metric system uses the foot as the standard unit of length, pound is set as the unit for denoting mass and force. Lastly, the second is used to denote time.

The MKS units are meter, kilogram, and second system of units. This metric system is used to denote the measurement of physical quantities. Here meter is used for denoting length, kilogram is used for denoting mass. It was known for setting the base for the SI units before they were redefined.

The SI unit is the most recent and modern type of metric system used throughout the world. It is often used as the standard unit of measurement. It mainly contains 7 units of measurement which are:

• ampere (symbol: A) – unit of electric current
• kelvin (symbol: K) – unit of temperature
• second (symbol: s) – unit of time
• meter (symbol: m) – unit of length
• kilogram (symbol: kg) – unit of mass
• candela (symbol: cd) – unit of luminous intensity
• mole (symbol: mol) – unit reflecting the amount of a substance

1.1. Abaqus consistent units

Generally, any consistent system of units consists of some fundamental units such as Length (L), Mass (M) or Force (F), and Time (T) as base units and the other units are 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), the 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. The 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):

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1.2. Choosing a suitable Abaqus consistent 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 values 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.

2. Example of Abaqus units | How to choose the right unit systems for analyses?

Let us see a practical example for choosing appropriate Abaqus units:
We have modeled a fullerene C60 in Abaqus and applied forces (distributed) to its ends (like a tension test). C60 has dimensions in 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 would 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 a numerical calculation in Abaqus, and 3 mm and .003 m are different for a computer; it needs more memory to save and do calculations on .003 than 3.

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