Week - 1 - Consistency of units

L S Dyna Units:

LS-DYNA doesn't have a default system of units. User needs to input material properties and physical dimensions according to a consistent system of units as per their choice. This warrants that to use LS-DYNA in different circumstances, users have to be conversant with converting quantities from one system of units to another.

Few systems of units are described as given below:

• Kg cm ms
• Kg cm s
• gm mm ms
• kg m s
• g cm s
• g cm s
• g mm s
• ton mm s
• slug ft s
• kg mm s
• g cm ms
• kg mm ms

Values of some measurements are given as below:

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

Detailed Calculation:

Here we will see conversion of above measurements with conversion factor.

• Detailed calculation for conversion from SI unit to gm/mm/ms unit system can be as given below:

MASS: 1kg = 1000 gm, Conversion factor = 1 * 1000 = 10³

LENGTH: 1m = 1000 mm, Conversion factor = 1 * 1000 = 10³

TIME: 1s = 1000 ms, Conversion factor = 1 * 1000 = 10³

FORCE: 1N = 1 (Kg * m) / S²

= 1 (1000 gm * 1000 mm) / (1000 ms) ²

= (1 gm*mm)/ ms²

Conversion factor = 1

STRESS: 1Pa = 1 N / m² = {(1 Kg * m) / S²} / m²

= {(1000gm * 1000mm) /1000000 ms²} / 1000000mm²

= {(10⁶ gm mm)/ 10⁶ ms²} / 10⁶ mm²

= (1 gm mm)/ms² / 10⁶ mm²

= (10^-6 gm)/mm * ms²

Conversion factor = 10^-6

ENERGY: 1Nm = {1 (Kg * m) / S²} * m

= {1 (1000 gm * 1000 mm) / (1000 ms) ²} * 1000mm

= {1 (10⁶ gm * mm) / (10⁶ ms ²} * 10³ mm

= 1{(gm * mm) / ms ²}* 10³ mm

= 1{(gm * mm) / ms ²} * 10³ mm

= 10³(gm * mm²) / ms ²

Conversion factor =10³

DENSITY: 1Kg/m3 = 1000 gm / (1000mm)³

= 1000 gm / 10⁹ mm³

= 10³ gm / 10⁹ mm³

= 10^-6 gm /mm³

Conversion factor =10^-6

YOUNG'S Modulus: 210GPa = 210 * 1000 N / mm²

= {210 * 1000 (Kg * m) / S²}/ mm²

= {210 * 1000 (1000 gm * 1000 mm) / (1000 ms) ²} / mm²

= {210 * 1000 (1 gm * mm) /ms ²} / mm²

= (210 * 10³ gm * mm) / mm² * ms²

= 210 * 10³ gm / mm * ms²

Conversion factor =10³

VELOCITY: 56.33KMPH = (56.33 * 1000 m) / H

= (56.33 * 10⁶ mm) / 3600 * 1000 s

= (56.33 * 10⁶ mm) / 36 * 10⁵ ms

= 15.6472 mm/ ms

For Factor, taking Round figure of 15.6472 is 15. So Prime Factors are 5 and 3.

• To get 5 in RHS, divide it by 3.12944.
• To get LHS, divide it by 3.12944.
• By division of 3.12944 , we get LHS = 18 and RHS = 5
• So, RHS = 5 / 18

Conversion factor =5/18

GRAVITY: 9.8m/s2 = 9.8 (1000mm) / (1000 ms) ²

= 9.8 (10³ mm) / 10⁶ms²

= 9.8 *10^-3 mm /ms²

Conversion factor =10^-3

Units	Mass	Length	Time	Force	Stress	Energy	Density	Young’s Modulus	Velocity	Gravity
Kg cm ms	1 Kg	102cm	103ms	10-4kg cm/ms2	10-8kg /cm*ms2	10-2kg*cm2/ms2	10-6kg/cm3	2100kg/cm*ms2	1.56472 cm/ms	9.8*10-4 cm/ms2
Kg cm s	1 Kg	102cm	1s	102kg*cm/s2	10-2kg/cm*s2	104kg*cm2/s2	10-6kg/cm3	210*107kg/cm*s2	1564.72 cm/s	9.8*102 cm/s2
gm mm ms	103 gm	103mm	103ms	1gm*mm/m10-8kg	10-6 gm/mm*ms2	103gm*mm2/ms2	10-6gm/mm3	210*103gm/mm*ms2	15.6472 mm/ms	9.8*10-3 mm/ms2
kg m s	103 gm	1m	1s	1kg*m/s2	1 kg/m*s2	1 kg*m2/s2	1kg/m3	210*109N/m2	15.6472 m/s	9.8 m/s2
gm cm s	103 gm	102cm	1s	105gm*cm/s2	10 gm/cm*s2	107gm*cm2/s2	10-3gm/cm3	210*1010gm/cm*s2	1564.72cm/s	9.8*102 cm/s2
gm cm μs	103 gm	102cm	106μs	10-7gm*cm/μs2	10-11gm/cm*μs2	10-5gm*cm2/μs2	10-3gm/cm3	2.1gm/cm*μs2	15.6472 *10-4cm/μs	9.8*10-10 cm/μs2
gm mm s	103 gm	103mm	1s	106gm*mm/s2	1gm/mm*s2	109gm*mm2/s2	10-6gm/mm3	210*1011gm/mm*s2	156472 mm/s	9.8*103 mm/s2
ton mm s	10-3 gm	103mm	1s	1 ton mm/s2	10-6ton /mm*s2	103ton*mm2/s2	10-12ton/mm3	210*103ton/mm*s2	156472 mm/s	9.8*103 mm/s2
slug ft s	0.068 slug	3.28 ft	1s	0.2246 slug*ft /s2	0.0208slug/ft*s2	0.7366slug*ft2/s2	1.93*10-3slug/ft3	4.368*slug/ft*s2	51.322 ft/s	32.144 ft/s2
kg mm s	1 Kg	103mm	1s	103kg mm/s2	10-3kg/mm*s2	106kg*mm2/s2	10-9kg/mm3	210*106kg/mm*s2	156472 mm/s	9.8*103 mm/s2
gm cm ms	103 gm	102cm	103ms	10-1 gm cm/ms2	10-5gm/cm*ms2	10gm*cm2/ms2	10-3gm/cm3	210*104gm/cm*ms2	1.56472 cm/ms	9.8*10-4 cm/ms2
kg mm ms	1 Kg	103mm	103ms	10-3 kg*mm/ms2	10-9kg/mm*ms2	1kg*mm2/ms2	10-9 kg/mm3	210kg/mm*ms2	15.6472 mm/ms	9.8*10-3 mm/ms2

Conclusion:

As we know that L S Dyna has no own unit system, so we have to convert each units as per requirements.

We can convert units with help of conversion factor very easy and fast.

So above conversion should always keep in mind and when ever we need ,we must convert units with help of conversion factor.

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Thanks & Regards,

Dharmesh Joshi