Week - 1 - Consistency of units

1. Aim: To show the detailed calculation for the conversion of units - SI unit to g/mm/ms unit system.

2. Objectives: 

• To study the different unit systems.
• To prepare a table of different unit system with the conversion factor.

3. Theory:

As different industries use different system of units, there is need to maintain the consistency of units. LS-DYNA doesn't have a default system of units. The user needs to input material properties and physical dimensions according to a consistent system of units as per the requirements. The following the inputs given to convert into respective unit systems:

• Mass = 1 kg
  Length =  1 m
  Time =  1 s
  Force = 1 N
  Stress = 1 Pa (N/m2)
  Energy = 1 Nm (J)
  Density = 1 kg/m3
  Young's Modulus = 210 GPa = 210 x 10^9 Pa
  Velocity = 56.33 Km/hr = 15.65 m/s ((56.33 x1000)/3600)
  Gravity = 9.8 m/s2

4. Calculation:

The conversion from kg/m/s to g/mm/ms is explained below:

1 kg = 1000 g or 1 g = 0.001 kg

1 m = 1000 mm or 1 mm = 0.001 m

1 s = 1000 ms or 1 ms = 0.001 s

Force = 1 N (kgm/s2) = > (1000 g x 1000 mm)/(1000 ms x 1000 ms) = 1 
Stress = 1 Pa (N/m2) = > (1000 g x 1000 mm)/(1000 ms x 1000 ms x 1000 mm x 1000 mm) = 10^-6 = 1 MPa (N/mm2)
Energy = 1 Nm (J) => 1N x 1000 mm = 10^3 = 1 mJ as 1 J = 1000 mJ
Density = 1 kg/m3 => 1000 g/(1000 mm x 1000 mm x 1000 mm) = 10^-6 
Young's Modulus = 210 GPa = 210 x 10^9 Pa = (210 x 10^9)/(1000 mm x 1000 mm) = 210 x 1000 = 2.1 x 10^5 
Velocity = 56.33 Km/hr = 15.65 m/s ((56.33 x1000)/3600) = (15.65 x 1000 mm)/(1000 ms) = 15.65 
Gravity = 9.8 m/s2 = (9.8 x 1000 mm)/(1000 ms x 1000 ms) = 9.8 x 10^-3

5. Results:

The other conversions are mentioned in the following table:

Mass	Length	Time	Force	Stress	Energy	Density	Youngs's Modulus	Velocity	Gravity
kg	m	s	N	Pa	J = Nm	kg/m3	2.10E+11	15.65	9.8
kg	cm	ms	1.00E+04	1.00E-02	1.00E-04	1.00E-06	2.10E+03	1.57E+00	9.80E-04
kg	cm	s	1.00E-02	1.00E-02	1.00E-04	1.00E-06	2.10E+09	1.57E+03	9.80E+02
g	mm	ms	N	1000000 Pa or 1 MPa	0.0001 J or 1 mJ	1.00E-06	2.10E+05	15.65	9.80E-03
g	cm	s	0.00001 N (1 dyne)	0.000000001 Pa (1 dyne/cm2)	0.0000001 J (1 erg)	1.00E-03	2.10E+12	1565	980
g	cm	us	1.00E+07	100000000000 Pa or 100 GPa	1.00E-05	1.00E-03	2.10E+00	1.56E-03	9.80E-10
g	mm	s	1.00E-06	Pa	1.00E-09	1.00E-06	2.10E+11	1.56E+04	9.80E+03
ton	mm	s	N	1000000 Pa or 1 MPa	0.0001 J or 1 mJ	1.00E-12	2.10E+05	1.56E+04	9.80E+03
slug	ft	s	4.448 (N)	47.880 Pa	4.448 J	515.3787 (kg/m3)	1.01E+13	4.7701 (m/s)	2.9870 (m/s2)
kg	mm	s	1.00E-03	1000 Pa or 1 KPa	1.00E-06	1.00E-09	2.10E+08	1.57E+04	9.80E+03
g	cm	ms	10	0.1 MPa	0.1	1.00E-03	2.10E+06	1.56	9.80E-04
kg	mm	ms	1000	1.00E+09	J	1.00E-09	2.10E+02	1.57E+01	9.80E-03

 6. Conclusion:

All the conversion factors are calculated and mentioned in the result table. The detailed calculation from kg/m/s to g/mm/ms is explained. Hence, in LS - DYNA the input properties can be feeded into the respective unit systems.