Spherical indentation- load-displacement graph

[unnikrishnany]

Hi all,

I am have just started working on abaqus standard/explicit. I am trying to solve an elastic-plastic spherical indentation problem using axisymmetric model. The indenter is taken as analytical rigid and the specimen is considered as PMMA polymer which is deformable. I am using Drucker-prager as the yield criterion for plasticity with the suboption as drucker-prager hardening. The input data is as follows:
friction angle=15, flow stress ratio=1, dilation angle= 15.
I am attempting an indentation with a displacement(u2) of 2mm given to the indenter. The load -displacement graph that i could get is linearly increasing upto a displacement of about 1.5mm after that the curve is not climbing up. I am not able to think of a reason for this. I am attaching the image of the graph.

Kindly help me in solving this.

Thanking you in advance

Unnikrishnan

 

[adfergusson]

What other analysis have you done so far? At the least I think you'll need to do (if you have not already done so):

1) Use analytical solution to determine stress components as a function of depth and your materials using hertz contact (e.g. use AMES contact stress calculator and the links to additional solutions for stress components Link
2) A mesh convergence study using linear elastic material model with an implicit solver and very small loads/displacements (otherwise it will crash and/or element aspect ratios will cause headaches), an important factor to consider is that , for example, your peak shear stress values will converge at a larger element size than the peak stresses in the direction of the plane you are indenting (e.g. sigma 11 and 22 where 3 is the direction of indentation). The results from calculation done in 1) will inform you as to why this happens.

Once you get the same result from Abaqus and analytical solutions as outlined above, move to explicit and make sure your explicit and implicit runs give you the same result. Once thats done, then start playing about with plasticity models and their parameters. If you've done all this then can you be more specific about what your concerns are? Based on what you've said about your model I'd guess that the apparent softening is a result of plastic flow, but seeing as you've chosen a material model that incoprorates plasticity I don't see why this would be surprising?

 

[unnikrishnany]

thanks adfergusson.

AMES calculator was really helpful in understanding the problem.
Your suggestions have helped me learn more about the problem and about Abaqus.
As if now since I have just started I am not trying plasticity models. I will work on some elastic models to get myself familiarized.
Thanks a lot.
Do reply if I further post some doubts here.
Cheers.