LS-Dyna Unit Consistency
Objective: Unit conversion for LS-DYNA. Conversion of SI units to gm/mm/ms unit system.
| SI units (Kg, m, s) | Converted units to gm, mm, ms |
| Mass 1 Kg | 1000 gm |
| Length 1m | 1000 mm |
| Time 1 s | 1000 ms |
| Force 1N |
Force =mass * acceleration `1N=(kg*m)/s^2` =`(1000gm*1000mm)/(1000^2 ms^2)` =`1(gm*mm)/(ms^2)` Conversion factor=1 |
| Stress 1Pa |
`Stress = (FORCE) / (AREA)` `1Pa = (1N)/(1m^2)` =`(kg*m/s^2)/m^2` =`(kg)/(m*s^2)` =`(1000gm)/(1000mm*1000^2ms^2` =`10^-6(gm)/(mm*ms^2)` Conversion factor= `10^-6` |
| Energy 1Nm |
`1J=1Nm=1 ((kg*m)/s^2)*m` =`1 (kg*m^2)/s^2` =`(1000gm*1000^2mm)/(1000^2ms^2)` =`10^3(gm*mm^2)/(ms^2` Conversion factor = `10^3` |
| Density 1kg/`m^3` |
Density =`(MASS)/(VOLUME)` =`1(kg)/(m^3` `(1000 gm)/(1000^3 mm^3)` =`10^-6(gm)/(mm^3)` Conversion factor = `10^-6` |
| Young's Modulus 210GPa |
210 GPa=`210e9 (kg)/(m*s^2)` Stress=`1(kg)/(m*s^2)=10^-6(gm)/(mm*ms^2)` =`210e9(kg)/(m*s^2)= 210e9*10^-6(gm)/(mm*ms^2)` =`210e3 or 210*10^3 (gm)/(mm*ms^2)` Conversion factor=103 |
| Velocity 56.33 Kmph |
56.33Kmph=`56.33*10^6(mm)/(3600*1000ms)` =15.647 `(mm)/(ms` Conversion factor= 0.2778 |
| Gravity 9.8 `m/s^2` |
`9.8 (m)/s^2= 9.8*(1000mm)/(1000^2ms^2` = `9.8*10^-3(mm)/(ms^2` Conversion factor = `10^-3` |
Table with all parameters under respective unit systems:
| 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 | `1(kg*m)/(s^2` | `1(kg)/(m*s^2)` | `1(kg*m^2)/(s^2` | `1 (kg)/(m^3` | `210e9 (kg)/(m*s^2)` | `15.647 m/s` | `9.8 m/(s^2` |
| Kg cm ms | 1 kg | `10^2 cm` | `10^3 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)` | `1.5647 (cm)/(ms` | `9.8*10^-4(cm)/(ms^2` |
| Conversion factor | - | - | - | `10^-4` | `10^-8` | `10^-2` | `10^-6` | `10^-8` | 0.1 | `10^-4` |
| Kg cm s | 1 kg | `10^2 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` | `210e7(kg)/(cm*s^2)` | `1564.7 (cm)/s` | `9.8*10^2 (cm)/s^2` |
| Conversion factor | - | - | - | `10^2` | `10^-2` | `10^4` | `10^-6` | `10^-2` | 102 | `10^2` |
| g mm ms | `10^3 g` | `10^3 mm` | `10^3 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` |
| Conversion factor | - | - | - | 1 | `10^-6` | `10^3` | `10^-6` | `10^-6` | 1 | `10^-3` |
| g cm s | `10^3 g` | `10^2 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` | `210e10 (g)/(cm*s^2)` | `1564.7 (cm)/s` | `9.8*10^2 (cm)/(s^2` |
| Conversion factor | - | - | - | `10^5` | 10 | `10^7` | `10^-3` | 10 | `10^2` | `10^2` |
| g cm μs | `10^3 g` | `10^2 cm` | `10^6 μs` | `10^-7 (g*cm)/(μs^2` | `10^-11(g)/(cm*μs^2)` | `10^-5 (g*cm^2)/(μs^2` | `10^-3 (g)/(cm^3` | `2.10 (g)/(cm*μs^2)` | `15.647*10^-4 (cm)/(μs` | `9.8*10^-10 (cm)/(μs^2` |
| Conversion factor | - | - | - | `10^7` | `10^-11` | `10^5` | `10^-3` | `10^11` | `10^-4` | `10^-10` |
| g mm s | `10^3 g` | `10^3mm` | 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` | `2.10e11 (g)/(mm*s^2)` | `15647 (mm)/s` | `9.8*10^3 (mm)/s^2` |
| Conversion factor | - | - | - | `10^6` | 1 | `10^9` | `10^-6` | 1 | `10^3` | `10^3` |
| ton mm s | `10^-3` ton | `10^-3` 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` | `210e3 (TON)/(mm*s^2)` | `15647 (mm)/s` | `9.8*10^3 (mm)/(s^2` |
| Conversion factor | - | - | - | 1 | `10^-6` | `10^3` | `10^-12` | `10^-6` | `10^3` | `10^3` |
| slug ft s | 0.068 slug | 3.28 ft | 1 s | `0.2246 (slug*ft)/(s^2` | `0.0208 (slug)/(ft*s^2)` | `0.7366 (slug*ft^2)/(s^2` | `1.93*10^-3 (slug)/(ft^3` | `4.368e9 (slug)/(ft*s^2)` | `51.322 (ft)/s` | `32.144 (ft)/(s^2` |
| Conversion factor | - | - | - | 0.2246 | 0.0208 | 0.7366 | `1.93*10^-3` | 0.0208 | 3.279 | 3.28 |
| kg mm s | 1 kg | `10^3` mm | 1 s | `10^3 (kg*mm)/s^2` | `10^-3 (kg)/(mm*s^2)` | `10^6 (kg*mm^2)/s^2` | `10^-9 (kg)/(mm^3` | `210e6 (kg)/(mm*s^2)` | `15647 (mm)/s` | `9.8*10^3 (mm)/(s^2` |
| Conversion factor | - | - | - | `10^3` | `10^-3` | `10^6` | `10^-9` | `10^-3` | `10^-3` | `10^-3` |
| g cm ms | `10^3` g | `10^2 cm` | `10^3`ms | `10^-1 (g*cm)/(ms^2` | `10^-5 (g)/(cm*ms^2)` | `10 (g*cm^2)/(ms^2` | `10^-3 (g)/(cm^3` | `210e4 (g)/(cm*ms^2)` | `1.5647 (cm)/(ms` | `9.8*10^-4 (cm)/(ms^2` |
| Conversion factor | - | - | - | `10^-1` | `10^-5` | 10 | `10^-3` | `10^-5` | 0.1 | `10^-4` |
| kg mm ms | 1 kg | `10^3` mm | `10^3` 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 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 have to be conversant with converting quantities from one system of units to another.