Question of Example umat_nh_ttb_simple.F about ttb HOT 7 CLOSED

Yes, after redefine the DDSDDE, STRESS and detF1 in that code, everything works.

Fine, thanks for testing it out!

Since I was trying to understand the DDSDDE by comparing my derivations with yours, and still have a couple question. I have read the document you mentioned, but that file doesn't help me much to compute DDSDDE from dS/dE. Therefore, I am wondering if you still have the derivation documents for this neo-hookean model implementation?

Giving support for this library is one thing - I'll always try to help you! But I don't have the time (at least not now) to support you with your tensor calculations in detail. A little hint: All the FEA packages calculate a geometric tangent for you (a.k.a. "initial stress stiffness"), and for some historical reasons in updated lagrange formulations they are requesting a so-called Jaumann rate of Kirchhoff or Cauchy stress. I think (!) the main reason behind this is to obtain symmetric tangent matrices for both the constitutive part inside UMAT and the internal calculated geometric stiffness.

Have a look at the pdf file inside this repo from @mholla https://github.com/mholla/hitchhikers-guide-to-abaqus - I think this will be helpful to you!

All the best,
Andreas

from ttb.

No, I have not tested it because I have no Abaqus license as I wrote in your other Issue.

For Abaqus, don't use asarray or T%a6b6 - Abaqus has different voigt notation than this toolbox. Use asabqarray instead. ...that is already the case for this example.

Regarding tangent calculation, see this document (section Neo-Hooke material): https://imechanica.org/files/Writing%20a%20UMAT.pdf

from ttb.

You mean this example does not work in Abaqus? Wow, thanks for reporting. I'll take a look on Monday. However, I can only double check the code - that's all I can do.

FYI: I created a subroutine for MSC.Marc (hypela2 example files), then took the umat header and pasted the code from my tested (!) hypela2 file. My goal was to make this toolbox also available for Abaqus users...

from ttb.

I think I found the error. Please rename the output variables from s to STRESS and D to DDSDDE. Will push a fix on Monday. It seems that I forgot to rename the output variables from Marc's HYPELA2 to Abaqus UMAT 😊

from ttb.

Yes, after redefine the DDSDDE, STRESS and detF1 in that code, everything works. Since I was trying to understand the DDSDDE by comparing my derivations with yours, and still have a couple question. I have read the document you mentioned, but that file doesn't help me much to compute DDSDDE from dS/dE. Therefore, I am wondering if you still have the derivation documents for this neo-hookean model implementation?

Also, I am wondering what's the difference between dya and cdya, literally you have explained it, but I didn't find any definition if I google "crossed dyadic product". While I have derivation written in tensor form, I just don't know when should I use dyadic and when should I use "crossed dyadic", since I didn't expand the tensors into indices notation. For me, all dyadic-like products look all like standard dyadic product.

from ttb.

Also, I am wondering what's the difference between dya and cdya, literally you have explained it, but I didn't find any definition if I google "crossed dyadic product". While I have derivation written in tensor form, I just don't know when should I use dyadic and when should I use "crossed dyadic", since I didn't expand the tensors into indices notation. For me, all dyadic-like products look all like standard dyadic product.

Please have a look at the readme file:

• Dyadic Product C(i,j,k,l) = A(i,j) B(k,l) written as C = A.dya.B
• Crossed Dyadic Product C(i,j,k,l) = (A(i,k) B(j,l) + A(i,l) B(j,k))/2 written as C = A.cdya.B

Again, I can't help you when to use dyadic or outer products and crossed dyadic products. You have to know which product you would like to use.

One example for crossed dyadic products are tensor derivatives w.r.t. the Tensor itself: https://en.wikipedia.org/wiki/Tensor_derivative_(continuum_mechanics)#Derivative%20of%20a%20second-order%20tensor%20with%20respect%20to%20itself

EDIT:

... dya and cdya, literally you have explained it, but I didn't find any definition if I google "crossed dyadic product"

Yes, the wording dyadic and crossed dyadic product is indeed not very common. We spoke about dyadisches Produkt and verschränkt-dyadisches Produkt (german) at my university (Graz University of Technology, Austria) and I translated both terms to english. Sometimes the dyadic product is called Tensor product (NumPy) numpy.tensordot(a, b, axes=0), others call it Kronecker Product as a generalization of the outer vector product.

A little example:

With crossed-dyadic product (cdya) I refer to a operation which flips indices of a fourth order tensor and is used frequently in derivatives of a (symmetric) tensor w.r.t. the tensor itself.

I4_ijkl = d C_ij / d C_kl = (Eye_ik Eye_jl + Eye_il Eye_kl) / 2

A double contraction of this fourth-order identity tensor with a symmetric second-order tensor results in the same second-order tensor itself.

C_ij = I4_ijkl : C_kl

Again, this is just a very brief, incomplete and small example...

from ttb.

This issue was closed by my pull-request, feel free to open it again.

from ttb.