UMAT: Jacobian Matrix for elastic and plastic materials

If you need linear elastic or Mises plastic UMAT and related CAE models please visit this link:
www.engssoft.com/elastic-plas...
In this playlist, we started with a video about plasticity theory, in the next video we described computational plasticity to introduce a numerical algorithm to solve plasticity equations. The last video of this playlist shows how to write a plastic UMAT. But before writing a UMAT, understanding and derivation of Jacobian matrix is a crucial step which is described in this video. In this video you can find out:
Concept and necessity of Jacobian matrix 00:00
Jacobian matrix for linear elastic materials 01:14
Jacobian matrix for plastic materials 01:50

[@ArkonPT]

This is amazing, great job producing the video. These topics are really hard to understand so material like this really helps!

[@nanbolkeza8296]

Awesome video, it helps me understand the theme. More videos and growth to you

[@ritAmad]

It is amazing how much knowledge you hold 👏🏻

[@hcdeng1283]

Thank you for your great video.

[@magedqasem7403]

Great video

[@structurelearninghub3340]

Can you provide reference to learn continuum mechanics to understand in detail

[@hcdeng1283]

I have compared the final Tangential stiffness at 7:31 with the one in the Section 5.6.2 of the book "Nonlinear Finite Elements for Continua and Structures, 2nd Edition" written by Ted Belytschko. The conclusion is that the Q and R are slightly different, but the Tangential stiffness at 7:31 shows better convergence than Ted Belytschko's one.

[@engineering_software]

You can find the formulas in Dunne book.

[@fractureandfatigueofmateri6283]

Very nice video. Well done. Could you make a video showing an example of the final partial derivative? You have shown a relation between stress variation and strain variation. There is a double contracted product n : delta strain and trace (delta strain). How to perform these derivatives? Do I carry out the operation first and then apply the partial derivative ?Many thanks!

[@hschan9423]

Thanks for the great video series. I am stuck at 6:01. The derivation seems not making sense. Could you elaborate?

[@hschan9423]

Sorry, I got this now. But at 6:48, what is trial strain (equation)? And why is it equal to strain?

[@sidharthr4463]

@@hschan9423 How you got the expression at 6:01 ?

[@mehmetcizer]

hi, how the plastic properties of wood are described in abaqus, Can you help or guide me on this? I can't find data or an example, I can't test it, I need to analyze in abaqus.

[@magedqasem7403]

When will you upload the last part of this video?

[@engineering_software]

kzbin.info/www/bejne/moLVpJqbiN-gnKM

[@awfsea]

what if in 2d condition, how the constitutive will be?

[@engineering_software]

For plane strain and axisymmetric conditions the relations and coding are the same just the number of stress and strain components are 4. But for plane stress condition the relations are a bit different.