[haapalm]

Hi,

I need to implement the following equation (attached) which involves a fourth order tensor. As far as I know these are not readily available in OpenFOAM.

What would be the best way to go about implementing a fourth order tensor and the corresponding operations in OpenFOAM?

I have looked into this: https://math.stackexchange.com/a/3026704
would that mean that I would implement it as a 9-by-9 Foam::vector of Foam::vectors?

Thank you for your help!
Matias

[Santiago]

That would be a bad idea. You just need to create a struct: follow the definition of the Tensor class

[haapalm]

Thank you for your answer. I am not sure what the struct would look like, would it simply contain 81 scalars?

As far as I see the tensor class inherits from the MatrixSpace class, would I need to do the same only with a 9-by-9 matrix?

Matias

[Santiago]

Originally Posted by haapalm

Thank you for your answer. I am not sure what the struct would look like, would it simply contain 81 scalars?

As far as I see the tensor class inherits from the MatrixSpace class, would I need to do the same only with a 9-by-9 matrix?

Matias

you can extend the VectorSpace class, in the same way Tensor does:

(...)
/* TENSOR 2nd rank*/
  template<class Cmpt>
  class Tensor
  :
      public VectorSpace<Tensor<Cmpt>, Cmpt, 9>
  {
(...)

Then implement all basic operations like transpose, inner-(outer) products, duals, etc....

[HPE]

Hi,

- I know arbitrary-order tensors and matrices are different in terms of their mathematical properties. But, is there any chance for you to designate your problem as a set of matrix operations, rather than tensor?
- If you can use matrices for your problem, I would use the class template: Matrix<Type> in OF.