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# Elastic and Plastic deformation gradients in AB Viscoplastic model

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(@melly)
Active Member
Joined: 1 month ago

Dr. Jorgen,

I am trying to write a VUMAT to implement the  Arruda-Boyce viscoplastic model. After assuming linear elasticity at the beginning of the analysis, the total deformation gradient (F) can be easily obtained from defgradNew.

I am a little bit confused about how to decompose F into its elastic and plastic components. Should I obtain the plastic components from the state variables and then, of course, find the elastic part via the product of F and the inverse of the plastic part?

How about the plastic flow rate, the rate of the plastic deformation, time-derivative of the deformation gradient, and the strain softening. How to incorporate these to capture the material response?

My reference is Chapter 8 of your book (Mechanics of Solid Polymers).

Thank you very much,

Warm regards,

Melly

11 Replies Posts: 3835
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(@jorgen)
Member
Joined: 2 months ago

Good question. You need to save either the elastic or the plastic components of F as state variables. I typically save Fp. Then you need to write an equation for the time-derivative of Fp, and calculate Fp at time t+dt. Once you have Fp at t+dt, you can calculate Fe at t+dt, which you can use to calculate the new stress at t+dt.

Best of luck,
Jorgen (@melly)
Joined: 1 month ago

Active Member
Posts: 19

@jorgen

I appreciate. Let me try and figure it out.

The time derivative of Fp is given in the book (Equation 8.38). I believe the deviatoric part of stress driving the plastic flow required to get the rate of plastic deformation is calculated from the Fe at time t. I also believe that I don't have to explicitly state the time increment dt as it is taken care of by Abaqus.

Suppose the Fp  (t+dt) = Fp(t) + dtFp(time-derivative), How about the total F(t+dt) so that I can get Fe(t+dt).

Thank you very much.

Warm regards,

Melly. Posts: 3835
Moderator
(@jorgen)
Member
Joined: 2 months ago

The total F(t+dt) is provided by Abaqus, so you can calculate Fe(t+dt) once you have calculated Fp(t+dt).

-Jorgen Posts: 19
(@melly)
Active Member
Joined: 1 month ago

Dr. Jorgen,
Many many thanks. I realized that the total F at the beginning and at the end of the time step is given by defgradOld and defgradNew, respectively.

Regards,
Melly. Posts: 19
(@melly)
Active Member
Joined: 1 month ago

Dr. Jorgen,

Once again, I appreciate your guidance. It means everything to my research.

I have written the code for AB viscoplastic model. I must have missed a few important details as there is an excessive distortion of elements.

The only part of the code that I borrowed is the one that utilizes Jacobi method for eigen values and vectors (In order to calculate the Hencky strain).

If you have a minute, kindly have a look at my code (attached) and (if possible) give me some hints on where I could be wrong.

Warm regards,

Melly

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