Parameters for linear Drucker Prager

[Mario_Aero92]

Hi,

I want to model the compression of a polymer cylinder. For that purpose, I want to use a linear Drucker Prager yield criterion with no hardening and a non-associative flow rule. 

I have seen that in Abaqus the linear Drucker Prager requires the introduction of three parameters: friction angle, flow stress ratio and dilation angle. 
The flow stress ratio I will set it to 1, assuming that the yield surface in the deviatoric plane is a circle. 

I know the value of friction angle from other experiments. Also I have the value of the compression yield stress.

Therefore, my question is: how can I calculate the value of dilation angle from the parameters that I have, i. e. friction angle and compression yield stress? Is it possible?

Thank you in advance!

 

[StefCon]

Can this help you?
Link

I tried this myself and get the wrong angle (because my true plastic poissons ratio is wrong (because the transverse strain is wrong). Is it absolutely necessary to measure the transverse strain or can it be calculated?

 

[Mario_Aero92]

Hi!

Thank you for the answer. I actually found this document in the internet too, but I still cannot understand how to obtain the dilation angle. Anyways, in principle I do not have that value of plastic Poisson ratio so I cannot use it.

 

[StefCon]

Hi,
I am afraid I don't know much about Drucker-Prager. Can you explain what the dilation angle is? Is it described in the linked document?

Best regards,

 

[Mario_Aero92]

Hi,

Yes, the dilation angle is basically related to the direction of the plastic flow. It is the direction of the differential plastic strain with respect to the yield surface in the meridional plane. When associated plastic flow is assumed, then the dilation angle is equal to the friction angle.

I think the ABAQUS Analysis User's Manuel contains a very good explanation about the DP yield criterion.

Best Regards,

 

[StefCon]

Are you talking about "Beta" or "Psi"?

tan(Beta)= µ = (3.*(((3.**0.5)*(S/T))-1.))

where Ss is the shear yield stress
and St is the tensile yield stress

I think calculation of Psi requires either the transverse strain or a known plastic poissons ratio.

Anyone else?

 

[Mario_Aero92]

According to Abaqus User's manual, beta would be friction angle and Psi would be the dilation angle.

That expression is correct, but as I said I Have the value of beta.