How to Expand the PEEQ formula of mohr-Cuolomb and Write VUSDFLD

[SKSA]

Hello Altruistic People,
I believe everyone is fine. Let me explain something, I want to vary Angle of Internal friction and Cohesion with PEEQ. So I want to write VUSDFLD. Here, I don't understand that how to expand the PEEQ of Mohr-Cuolomb. I mean what could be the final solution of PEEQ in terms of strain components and stress components. Can you please give me some idea how to calculate it mathematically?
Thank you.

 

[FEA way]

It can be also written like this:

where ϵ^p is a plastic strain tensor.

 

[SKSA]

Where the cohesion 'c' has gone? Is the determinant of strain tensor in last term?
Also, Can you please share some reference? I really need this.

 

[FEA way]

This is just a general formula for equivalent plastic strain, not related to any specific plasticity model. Those brackets represent the norm (of the tensor). The formula is expanded in an equivalent way to the one for von Mises stress. The picture is from "The Finite Element Method for Three-Dimensional Thermomechanical Applications" by G. Dhondt but there are many other similar references, also specifically about computational plasticity.

 

[SKSA]

Excellent! I have a quick query to you. I am using Mohr Coulomb Hardening. I gave input angle of internal friction that is varying with PEEQ. And this PEEQ I used the following formula in this attached picture. So, My question is that does the ABAQUS calculate PEEQ based on Mohr Coulomb or thr formula I am providing here?

 

[FEA way]

According to the "Mohr-Coulomb Plasticity" documentation chapter, PEEQ is calculated in a specific way (including cohesion yield stress) for this material model. You can use a different formula independent of that to create custom output (even without subroutines - just using scripting or built-in postprocessing tools: Create Field Output From Fields or Operate on XY data). Then it would be good to compare it with PEEQ calculated by Abaqus for other material models (like classical metal plasticity).