Unit Conversion for Consistency of Units in LS Dyna

Objective:

To write the given measurements according to the given system of units and to mention the conversion factors for the same.

Value of the following measurements are given as follows:

• MASS - 1kg
• LENGTH - 1m
• TIME - 1s
• FORCE -1N
• STRESS - 1Pa
• ENERGY - 1Nm
• DENSITY - 1Kg/m3
• YOUNG'S Modulus - 210GPa
• Velocity - 56.33KMPH
• GRAVITY - 9.8m/s2

System of units:

1. Kg cm ms
2. Kg cm s
3. gm mm ms
4. kg m s
5. g cm s
6. g cm us
7. g mm s
8. ton mm s
9. slug ft s
10. kg mm s
11. g cm ms
12. kg mm ms

Detailed calculation for conversion from SI unit to gm/mm/ms unit system needs to be shown and a table for the remaining units need to be created with the unit systems as rows and measured quantities as columns.

Procedure:

1. As asked in the question a detailed calculation for conversion from SI unit to gm/mm/ms unit system is shown below.

Mass

1 kg = 1000 grams

Length

1 m = 1000 mm

Time

1 second = 1000 milli-seconds

Force

`F =m*a = kg*m/s^2`

`1kg*m/s^2 = 10^3g * (10^3mm)/(10^6ms^2)` = `1g*(mm)/(ms^2)`

Therefore,

`1 N = 1 g*(mm)/(ms^2)`

Stress

Stress = Force / Unit Area

1 Pa = 1 N/m^2

`1 Pa = 1g*(mm)/(ms^2)/10^6mm^2`

Therefore,

`1Pa = 10^-6 g/(mm*ms^2)`

Energy

`1 Nm = 1 g*(mm)/(ms^2) * (10^3) mm`

Therefore

`1Nm = 10^3 g*(mm^2)/(ms^2)`

Density

`1(kg)/m^3 = 10^3 g / (10^9mm^3)`

Therefore:

`1(kg)/m^3 = 10^-6 g/(mm^3)`

Young's Modulus

`210 GPa = 210 * 10^9 Pa = 210 *10^9 * 10^-6 g*(mm)/(ms^2)/mm^2`

Therefore:

`210 GPa = 210 * 10^3 g/(mm*ms^2)`

Velocity

`56.33 (km)/h = (56.33* 10 ^6 mm) / (3.6 * 10^6 ms)`

Therefore

`56.33 (km)/h = 15.64722 (mm)/ms`

Gravity

`9.8m/s^2 = 9.8 * 10^3 (mm) / (10^6 ms^2)`

Therefore:

`9.8m/s^2 = 9.8 * 10^-3 (mm)/(ms^2)`

The quantities in their corrresponding unit systems are shown bellow:

Units	Mass	Length	Time	Force	Stress	Energy	Density	Young's Modulus	Velocity	Gravity
Kg cm ms	1 kg	100 cm	1000 ms	`10^-4 kg*(cm)/(ms^2)`	`10^-8 (kg)/(cm*ms^2)`	`10^-2 (kg)*(cm^2)/(ms^2)`	`10^-6 (kg)/(cm)^3`	`2100 kg/(cm*ms^2)`	`156.4*10^-2 (cm)/(ms)`	`9.8 * 10^-4 (cm/ms^2)`
Kg cm s	1 kg	100 cm	1 s	`10^2 kg*(cm)/(s^2)`	`10^-2 (kg)/(cm*s^2)`	`10^4 (kg)*(cm^2)/(s^2)`	`10^-6 (kg)/(cm)^3`	`210*10^7 kg/(cm*s^2)`	`1564.722 (cm)/s`	`980 (cm)/(s^2)`
g mm ms	1000 g	1000 mm	1000 ms	`1 g*(mm)/(ms^2)`	`10^-6 g/(mm*ms^2)`	`10^3 g*(mm^2)/(ms^2)`	`10^-6 (g)/(mm)^3`	``210*10^3 g/(mm*ms^2)`	`15.647 (mm)/(ms)`	`9.8*10^-3 (mm)/(ms^2)`
kg m s	1 kg	1 m	1 s	`1kg*(m)/(s^2)`	`1 (kg)/(m*s^2)`	`1 (kg)*(m^2)/(s^2)`	`1 (kg)/m^3`	`210* 10^9 kg/(m*s^2)`	`15.64 m/s`	`9.8 m/(s^2)`
g cm s	1000 g	100 cm	1 s	`10^5 g*(cm)/(s^2)`	`10 g/(cm*s^2)`	`10^7 g*(cm^2)/(s^2)`	`10^-3 (g)/(cm)^3`	`210*10^10 g/(cm*s^2)`	`1564.7 (cm)/s`	`980 (cm)/s^2`
g cm `mu`s	1000 g	100 cm	`10^6` `mu`s	`10^-7 g*(cm)/(s^2)`	`10^-11 g/(cm*mus^2)`	`10^-5 g*(cm^2)/(mus^2)`	`10^-3 (g)/cm^3`	`210*10^-2 g/(cm*mus^2)`	`15.647 * 10^-4 (cm)/(mus)`	`9.8 *(10^-10) (cm)/(mus^2)`
g mm s	1000 g	1000 mm	1 s	`10^6 g*(mm)/(s^2)`	`1 g/(mm*s^2)`	`10^9 g*(mm^2)/(s^2)`	`10^-6 (g)/mm^3`	`210*10^9 g/(mm*s^2)`	`15647.2 (mm)/s`	`9.8 *10^3 m/(s^2)`
ton mm s	0.001 ton	1000 mm	1 s	`1"ton"*(mm)/s^2`	`10^-6 "ton"/(mm*s^2)`	`10^3 "ton"*(mm^2)/(s^2)`	`10^-12 ("ton")/mm^3`	`210*10^3 "ton"/(mm*s^2)`	`51.33 (ft)/s`	`9.8 *10^3 (mm)/(s^2)`
slug ft s	0.068 slug	3.28 ft	1 s	`0.224 slug*(ft)/s^2`	`0.020 (slug)/(ft*s^2)`	`0.731 "slug"*(ft^2)/(s^2)`	`1.92*10^-3 (slug)/ft^3`	`4.35*10^9 (slug)/(ft*s^2)`	`15647.2 (mm)/s`	`32.144 (ft)/(s^2)`
kg mm s	1 kg	1000 mm	1 s	`1000 kg*(mm)/(s^2)`	`10^-3 (kg)/(mm*s^2)`	`10^6 (kg)*(mm^2)/(s^2)`	`10^-9 (kg)/mm^3`	`210*10^6 kg/(mm*s^2)`	`15647.22 (mm)/s`	`9.8*10^3 (m)/s^2`
g cm ms	1000 g	100 cm	1000 ms	`0.1 g*(cm)/(ms^2)`	`10^-5 g/(cm*ms^2)`	`10 g*(cm^2)/(ms^2)`	`10^-3 (g)/cm^3`	`210*10^4 g/(cm*ms^2)`	`1.564 (cm)/(s^2)`	`9.8*10^-4 (cm)/s^2`
kg mm ms	1 kg	1000 mm	1000 ms	`10^-3 kg*(mm)/(ms^2)`	`10^-9 (kg)/(mm*ms^2)`	`1 (kg)*(mm^2)/(ms^2)`	`10^-9 (kg)/mm^3`	`210 kg/(mm*ms^2)`	`15.647 (mm)/ms`	`9.8*10^-3 (mm)/(ms^2)`

Conversion units:

To convert the given value in (kg m s) to the required units, the conversion values are shown below:

Units	Mass	Length	Time	Force	Stress	Energy	Density	Young's Modulus	Velocity	Gravity
Kg cm ms	1	100	1000	0.0001	0.00000001	0.01	0.000001	0.00000001	0.027765	0.0001
Kg cm s	1	100	1	100	0.01	10000	0.000001	0.01	27.77777	100
g mm ms	1000	1000	1000	1	0.000001	1000	0.000001	0.000001	0.277774	0.001
kg m s	1	1	1	1	1	1	1	1	0.27765	1
g cm s	1000	100	1	100000	10	10000000	0.001	10	27.77738	100
g cm `mu`s	1000	100	1000000	1E-07	1E-11	0.00001	0.001	1E-11	2.78E-05	1E-10
g mm s	1000	1000	1	1000000	1	1000000000	0.000001	1	277.7774	1000
ton mm s	0.001	1000	1	1	0.000001	1000	1E-12	0.000001	0.911237	1000
slug ft s	0.068	3.28	1	0.224	0.02	0.731	0.00192	0.020714286	277.7774	3.28
kg mm s	1	1000	1	1000	0.001	1000000	1E-09	0.001	277.7777	1000
g cm ms	1000	100	1000	0.1	0.00001	10	0.001	0.00001	0.027765	0.0001
kg mm ms	1	1000	1000	0.001	1E-09	1	1E-09	0.000000001	0.277774	0.001

Result:

• The given measurements were converted according to the given system of units and the mention the conversion factors for the same are mentioned.
• Calculation for one conversion is shown extensively.

Learning outcomes:

• Importance of unit conversion in LS Dyna
• Conversion units to convert from kg m s.