Learning Forum

[yipxx043]

Hi All,

I am reading up on the JH2 model for ceramics and trying to understand how the plastic strain increment is calculated. From literature, it says, "the plastic strain increment is the plastic strain during a cycle of integration". I'm assuming that's integrating the equivalent plastic strain rate, but then how does LS-DYNA compute the equivalent plastic strain rate using the JH2 model?

I found another resource says that for the JH2 model, the plastic strain incremement can also be computed via the current equivalent stress state and the radial return algorithm. If that's the case, where does the hardening modulus get derived from in the JH2 model, if at all? 

Clarification is greatly appreciated.

PY

[Jim Day]

You don't mention which references you have. Google mat110_mat241_papers.tar and download that file. There's an archive of papers therein that may be helpful.

[yipxx043]

Hi Jim,

Thank you for your response. My apologies. I am referencing Holmquist and Johnson's papers, "Response of boron carbide subjected to large strains, high strain rates, and high pressures (1999)" and "An improved computational constitutive model for brittle materials (1994)". They both explicitly state " delta_eps_p (equivalent plastic strain increment) is the plastic strain during a cycle of integration". So I am curious what is being integrated from an LS-DYNA implementation perspective. Is it the equivalent plastic strain that is in the 1999 paper and we integrate that? Or is a radial return algorithm used to obtain the equivalent plastic strain?

I will look at the other resources that I found via Google that you provided.

Thanks,

Peter

[yipxx043]

Hi Jim,

Your resources provided the answer I was looking for. 

Much appreciated!

Peter

[Jim Day]

Hi, Peter. For the benefit of other customers that may be reading this, what was the answer that you found?

[yipxx043]

Hi Jim,

My apologies. From the Implementation of the Johnson-Holmquist I (JH-2) Constitutive Model Into DYNA3D by George A. Gazonas paper, it explicitly says in the algorithm procedure that they compute the equivalent plastic strain rate which I assumed is the traditional formulation and verified with other papers in the resources you provided. The LS-DYNA Support link here (https://www.dynasupport.com/tutorial/computational-plasticity/radial-return), still confuses me because I am sure if you did take a radial return approach, you can have it compute the equivalent plastic strain increment and then use that to update the equivalent plastic strain at each integration cycle. Do you have any input as to know which one LS-DYNA chooses and when/why? 

[Jim Day]

Thanks, Peter. I have nothing to add to what's shown in Table 1.