velocityGradientTensor.velocityGradientTensor edit page

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

See also

tensor strainRateTensor spinTensor