If the unit of time is seconds and the unit of length is millimeters, what unit must be chosen for the mass so that the force is the same as Newton’s?

To do this, you must do the following. If X is a new unit of mass and its relative value is compared to kilograms (X = a Kg):

N = (a Kg) mm/s^2 = (a Kg) 10e-3 m/s^2 = (10e-3 (a) (Kg.m/s^2) = (10e-3 a)(N)

The quantity (10 e-3 a) must be equal to one to obtain the force based on Newton. Therefore, the new unit of mass in this case should be 1000 kg or one ton.

Because Abaqus usually works with the density, for a material such as steel, the density must be entered in tons per cubic millimeter.

7800 Kg/m^3 = 7800 . 10^-3 ton/10^9 mm^3 = (7800). 10^-12 ton/mm^3

Poor selection of consistent units sometimes causes problems for the analyst. Consider the following example.

If mass is in kilograms and length is in millimeters, the unit of time b sec can be obtained in such a way that the force is obtained in Newtons:

Therefore, the coefficient must be  equal to one.

That is, in this consistent but unsuitable system, the unit of time will be  

In special cases, such as geological problems where very large masses travel very short distances over very long periods of time – for example, the movement of the Earth’s crust over 100 million years – it is best to use the following consistent units.

If the meter unit is selected for length, the necessary operations can be easily performed to identify the force unit.

This change of units makes analysis and modeling easier.