class representing a velocity gradient tensor
The velocity gradient L is the rank 2 tensor of the spatial derivatives of the velocity field. Its symmetric part is the strainRateTensor, its skew symmetric part the spinTensor. Since solids are not compressible all velocity gradient tensors have trace 0.
Syntax
L = velocityGradientTensor(M)
L = velocityGradientTensor.uniaxial(d,e)
L = velocityGradientTensor.simpleShear(d,n,e)
L = velocityGradientTensor.pureShear(exp,comp,e)Input
| M | 3x3 matrix |
| d, n | vector3d |
| e | strain rate |
| exp | extension direction, vector3d |
| comp | compression direction, vector3d |
Output
| L | velocityGradientTensor |
Class Properties
| M | the tensor coefficients |
| rank | always 2 |
| CS | symmetry the coefficients refer to |
Example
L = velocityGradientTensor.simpleShear(vector3d.X,vector3d.Z)L = velocityGradientTensor (y↓→x)
rank: 2 (3 x 3)
0 0 2
0 0 0
0 0 0