How to implement an integral over a volume expression in a user subroutine Umat

[Lemine]

Hello,

I want to implement the expression below in Abaqus analysis using the Umat subroutine.
Matrix1 and Matrix2 are seconde order tensor
A is a forth order tensor
The : represent the contracted product
Omega is the geometry
How this can be implemented Thanks in advance for your response

 

[IceBreakerSours]

It has been a very long time since I did this so my response may not be helpful.

Now, if you have the expression in index format, then I think you just write the code for that. Let's pretend the equation was Stress_ij = C_ijkl * Strain_kl. Since kl is repeated on the right, the product on the right is a contraction. Two tensors on the right - one 4th order and one second order tensor produce a second order tensor on the left.

Looking at your equation, I am guessing Matrix 1 and Matrix 2 must contract the 4th order tensor A to a scalar which you are want to sum up over the volume. I don't think you need to compute the integral over the volume because the computation will be performed at each integration point in the UMAT (otherwise, the code will become expensive - which may or may not be okay in your case, I don't know). You could do the integration in a post-processing script.

*********************************************************
Are you new to this forum? If so, please read these FAQs:

http://www.eng-tips.com/faqs.cfm?fid=376

http://www.eng-tips.com/faqs.cfm?fid=1083

 

[Lemine]

Thanks a lot, Dear IceBreakerSours for your response, Yes absolutely the result is a scalar and I want to sum up the expression over the volume, Matrix 1 and Matrix 2 are expressions of stress tensor so after processing I know their values in the structures,and the 4th order tensor is also known, How can I do the integration in a post-processing script Thanks in advance for your help.

 

[Lemine]

Hello FEA Engineers, Any idea about this topic Thanks in advance for your help !