Week - 1 - Consistency of Units

Challenge- Consistency of Units-

Aim- The aim of this challenge is to convert the given SI unit values of given quantities to gm/mm/ms units & also to prepare consistent unit system table for different unit system.

All parameters are converted to their respective unit system with SI Unit system as standard (kg,m,s)

Calculation of the conversion from SI unit to g,mm,ms

SI UNIT SYSTEM (Kg,m,s)	Conversion to (g,mm,ms)
Mass 1 kg	1000 g
Length 1 m	1000 mm
Time 1 s	1000 ms
Force 1N	1N=1mass*1acceleration
	=1kg*1m/s2
	=(1000g*1000mm)/(1000ms)2
	=106*10-6(g*mm)/ms2
	=1(g*mm)/ms2
	Coversion factor=1
Stress 1Pa	1Pa=1N/m2
	= {1kg*(1m/s2)}/m2
	=1kg/(m*s2)
	=1000g/{1000mm*(1000ms)2}
	=10-6g/(mm*ms2)
	Coversion factor=10-6
Energy 1J	1J=1Nm=(1kg*1m/s2)*m=1(kg*m2/s2)
	={1000g*(1000mm)2}/(1000ms)2
	=(109g*mm2)/(106ms2)
	=103(g*mm2/ms2)
	Coversion factor=103
Density 1 Kg/m3	1 Kg/m3=1000g/(1000mm)3
	=10-6g/mm3
	Coversion factor=10-6
Young's modulus 210GPa	210 GPa=210e9kg/(m*s2)
	We already calculate during stress that 1kg/(m*s2)=10-6g/(mm*ms2)
	so, 210e9kg/(m*s2)= 210e9*10-6g/(mm*ms2)
	=210e3 or 210*103 g/(mm*ms2)
	Coversion factor=103
Velocity 56.33 Kmph	56.33Kmph=56.33*{106mm/(3600*1000ms)}
	=15.647 mm/ms
	Coversion factor= 0.2778
Gravity 9.8 m/s2	9.8 m/s2= 9.8*1000mm/(1000ms)2
	= 9.8*10-3mm/ms2
	Coversion factor=10-3

Table with all parameters under repective unit system

Unit System	Mass	Length	Time	Force	Stress	Energy	Density	Young's Modulus	Velocity 56.33 Kmph	Gravity
SI Unit Kg m s	1 kg	1 m	1 s	1kg*m/s2	1kg/(m*s2)	1kg*m2/s2	1 Kg/m3	210e9kg/(m*s2)	15.647 m/s	9.8 m/s2
Kg cm ms	1 kg	102 cm	103 ms	10-4kg*cm/ms2	10-8kg/(cm*ms2)	10-2 kg*cm2/ms2	10-6 Kg/cm3	2100 kg/(cm*ms2)	1.5647 cm/ms	9.8*10-4 cm/ms2
Coversion factor	-	-	-	10-4	10-8	10-2	10-6	10-8	0.1	10-4
Kg cm s	1 kg	102 cm	1 s	102 kg*cm/s2	10-2kg/(cm*s2)	104 kg*cm2/s2	10-6 Kg/cm3	210e7kg/(cm*s2)	1564.7 cm/s	9.8*102 cm/s2
Coversion factor	-	-	-	102	10-2	104	10-6	10-2	102	102
g mm ms	103 g	103 mm	103 ms	1 g*mm/ms2	10-6g/(mm*ms2)	103 (g*mm2/ms2)	10-6 g/mm3	210*103g/(mm*ms2)	15.647 mm/ms	9.8*10-3mm/ms2
Coversion factor	-	-	-	1	10-6	103	10-6	10-6	1	10-3
g cm s	103 g	102 cm	1 s	105 g*cm/s2	10 g/(cm*s2)	107 g*cm2/s2	10-3 g/cm3	210e10 g/(cm*s2)	1564.7 cm/s	9.8*102 cm/s2
Coversion factor	-	-	-	105	10	107	10-3	10	102	102
g cm μs	103 g	102 cm	106 μs	10-7 g*cm/μs2	10-11g/(cm*μs2)	10-5 g*cm2/μs2	10-3 g/cm3	2.10 g/(cm*μs2)	15.647*10-4 cm/μs	9.8*10-10 cm/μs2
Coversion factor	-	-	-	10-7	10-11	10-5	10-3	1011	10-4	10-10
g mm s	103 g	103 mm	1 s	106 g*mm/s2	1 g/(mm*s2)	109 g*mm2/s2	10-6 g/mm3	2.10e11 g/(mm*s2)	15647 mm/s	9.8*103 mm/s2
Coversion factor	-	-	-	106	1	109	10-6	1	103	103
ton mm s	10-3 ton	103 mm	1 s	1 ton*mm/s2	10-6 ton/(mm*s2)	103 ton*mm2/s2	10-12 ton/mm3	210e3 ton/(mm*s2)	15647 mm/s	9.8*103 mm/s2
Coversion factor	-	-	-	1	10-6	103	10-12	10-6	103	103
slug ft s	0.068 slug	3.28 ft	1 s	0.2246 slug*ft/s2	0.0208 slug/(ft*s2)	0.7366 slug*ft2/s2	1.93*10-3 slug/ft3	4.368e9 slug/(ft*s2)	51.322 ft/s	32.144 ft/s2
Coversion factor	-	-	-	0.2246	0.0208	0.7366	1.93*10-3	0.0208	3.279	3.28
kg mm s	1 kg	103 mm	1 s	103 kg*mm/s2	10-3 kg/(mm*s2)	106 kg*mm2/s2	10-9 kg/mm3	210e6 kg/(mm*s2)	15647 mm/s	9.8*103 mm/s2
Coversion factor	-	-	-	103	10-3	106	10-9	10-3	10-3	103
g cm ms	103 g	102 cm	103 ms	10-1 g*cm/ms2	10-5 g/(cm*ms2)	10 g*cm2/ms2	10-3 g/cm3	210e4 g/(cm*ms2)	1.5647 cm/ms	9.8*10-4 cm/ms2
Coversion factor	-	-	-	10-1	10-5	10	10-3	10-5	0.1	10-4
kg mm ms	1 kg	103 mm	103 ms	10-3 kg*mm/ms2	10-9 kg/(mm*ms2)	1 kg*mm2/ms2	10-9 kg/mm3	210 kg/(mm*ms2)	15.647 mm/ms	9.8*10-3 mm/ms2
Coversion factor	-	-	-	10-3	10-9	1	10-9	10-9	1	10-3

Conclusion-

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 has to be conversant with converting quantities from one system of units to another.