3D elasto-plastic material model with piece-wise isotropic hardening (using Mises yield function)

Hello, 

I am a Master's student in the Technical University of Munich (TUM). I am currently doing my MSc Thesis, which is related to performing a finite element analysis (FEA) for a given geometry. I should be developing my own code in MATLAB to do that task.
 

The material model that I should be implementing in my FEA is: 3D elasto-plastic material model with piece-wise isotropic hardening (using Mises yield function).

 

This material matches this link in your manual: https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.5/books/gsx/ch05s02.html#gsx-elas-plas-behav 

(because I am given Young's Modulus (E), Poisson's ratio (v), and a list of plastic stresses & their corresponding "plastic" strains).

 

Luckily, so far in my work I was able to perform the meshing of my designed geometry, implement a linear elastic material, compute the elastic stiffness matrix for this 3D system, apply simple boundary conditions, and solve the system for the unknown displacements. 
 

Unfortunately, I have been having difficulties for a while now in going to the desired elasto-plastic material model (instead of the simple linear elastic that I currently have). In my literature research in this aspect, I also came across this very useful page from your manual:

https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/stm/default.htm?startat=ch04s02ath102.html

 

And there it describes exactly the material model that I want to implement. Quite unfortunately, some equations were not so clear to me & I am still struggling on how to do the coding implementation of that part.

I was really hoping that you can help me with the implementation of the desired material model.

I want to clarify that this work is done for educational purposes and to complete my degree. So, my work will be just a relatively small and simple code to specifically perform the desired task on the geometry I am working on. So, I do not think that there will be any conflict of interests in that regard.
 

Thank you in advance for your help and consideration.