User login


You are here

If periodic boundary conditions do not respect stress continuity at the boundary....

Hi everybody,

have you ever tried to implement in Abaqus periodic boundary conditions?

I am doing this. Particularly, I am applying PBC to unit cells constituted of a clay particle in an epoxy matrix.

When I apply PBC in case of transverse shear, I have convergence problems using Abaqus standard,

so I have to use an algorithm of stabilization but because of this one

I have to renounce to the stress continuity between opposite boundaries of the unit cell.

Do you think this is normal or I am doing some mistakes?

I hope hearing from you soon.




The convergence difficulties are due to the strip of cohesive elements used to model the gallery between the two platelet of the clay

 particle. Before the first cohesive element in the gallery breaks, in the case of transverse shear under PBC, the analysis fails.

If I use the algorithm of stabilization of Abaqus standard the analysis does not fail

but stress continuity between opposite boundaries of the unit cell is not respected.

tedvaughan's picture

Hi Cecilia,

Are you using viscous regulaization for your cohesive regions? This usually helps with the convergence of cohesive elements.  In my micromechanical models I've implement cohesive elements for transverse shear loading and I haven't seen any problems with the PBC's 

Also, be careful how you define your fracture energy as depending on what scale your working with (nano/micro) in abaqus you may need to scale your definition of the fracture energy accordingly.  If the fracture energy is too small...abaqus might not be able to cope with such brittle behaviour.


Hi Ted,

 thank you very much for your answer.

I tried to use viscous regularization as you suggested me and I have found that I do not have any

problems in the stress continuity at opposite boundaries of the unit cell just if I use NLGEOM=NO.

So, if I use viscous regularization and NLGEOM=NO stress continuity is respected;

if I use viscous regularization and NLGEOM=YES stress continuity is not respected.

Have you found similar results?

Also, viscous regularization allows stresses to be outside cohesive curve limits, as if you are using

a cohesive curve different from that you specified. How do you justify this difference? Do you accept this difference

if it is low? But in this case why not accept the difference in stresses at opposite boundaries of the unit cell if this

 is low?

Thank you again.



P.S.: Un saluto a Limerick!!

tedvaughan's picture


I have not examined the case for NLGEOM=YES so I don't know.

The use of viscosity appears to be quite common in the implementation of cohesive elements and it's use is even suggested by ABAQUS manuals to aid convergence.  As far as I know, once the viscosity parameter is small compared to the size of the time increment, your results should not be greatly affected.  In my models I use 0.0002. Maybe you could test different viscosity parameters and see if they do alter the response

Also, I think the cohesive curve that governs the behaviour of the interface (which is probably linear??) is already an idealisation of physical behaviour of the interface and so deviating slightly from this I don't think is a big problem.  I think this is even less of an issue at the micro/nano scale as it is very difficult to obtain correct interfacial coheisve curves from experimental testing.




Hi Ted,

thanks for your reply.

I agree with you: is the deviation from the cohesive curve is low we can accept it.

In my case I have to use VISCOSITY=0.05 and I have a error=0.5%.

May be this is acceptable.

Thank you very much for your help.



tedvaughan's picture


This viscosity parameter is very high, it is usually in the order of 10e-4/10e-5 so you might need to check that.  It should be small compared to the characteristic time increment.


Subscribe to Comments for "If periodic boundary conditions do not respect stress continuity at the boundary...."

Recent comments

More comments


Subscribe to Syndicate