It's not a recent article, but maybe you can look into this :

http://www.sciencedirect.com/science/article/pii/S0022509600000612

Also, writing a subroutine requires that you translate your constitutive equations in coding. The main difficulty is to find the name ABAQUS uses for state variables, like plastic deformation or Von Mises stress for example. My best advice is to look into ABAQUS documentation. If you have access to the hotline/help center site, browse it, there may be examples of how to implement this kind of effects.

It's not a recent article, but maybe you can look into this :

http://www.sciencedirect.com/science/article/pii/S0022509600000612

Also, writing a subroutine requires that you translate your constitutive equations in coding. The main difficulty is to find the name ABAQUS uses for state variables, like plastic deformation or Von Mises stress for example. My best advice is to look into ABAQUS documentation. If you have access to the hotline/help center site, browse it, there may be examples of how to implement this kind of effects.

Thank you so much @ Etienne Lebard

In ABAQUS, you have two subroutines to define user materials. If you plan to use ABAQUS/Standard solver, you need to write a UMAT. But if you plan to use ABAQUS/Explicit, you need to write a VUMAT.

The main difference between these two user subroutines is that you must define the Jacobian matrix in the UMAT subroutine.

You can find some examples of material user subroutines in the ABAQUS documentation.

@ Dear Correia

Thank you for your answer. Could you please explain VUMAT more! I should find it in documentation part by this name? "VUMAT".

Have you done this simulation before?

@Dear Arabzadeh

than you for your help.

I think the first subroutine can be helpful, but the second one is related to the composite material and I have doubt to be related to my work. Anyway, thank you again

Perhaps you will find more informations on UMAT and VUMAT subroutines in the enclosed file.

@correria Thank you