Stiffness Non-Linearity of Viscoplastic Material Models

Problem Statement

Sometimes multi-network viscoplastic material models produce stress-strain curves that look bi-linear (or multilinear), and may not have the correct stiffness non-linearity. Here is one example stress-strain curve for the PolyUMod® TNV model.

➡️In this article I will show you how you can make this prediction look smoother (and more realistic).

Stiffness non-linearity example

Solution: How to Improve the Stiffness Non-Linearity

In the Bergstrom-Boyce (BB), Three Network (TN), and Three Network Viscoplastic (TNV) models the parameter mm controls how much the strain rate influences the stress-strain response (see this article for more info about this). It turns out that if you select a lower value for mm, then the stress-strain curve gets  a more rounded (smoother) non-linearity in the pre-yield region. This, however, is not the preferred way to fix the problem of a bi-linear looking response since it also changes the strain-rate dependence of the model.

Another way to tailor the stiffness non-linearity in the pre-yield region is to add more networks to the viscoplastic material model. This is not so great either since it makes the material model calibration more difficult and also slows down the FE simulation speed.

Instead, the best way to fix this problem is to activate yield evolution. In the following figure I used exactly the same material model as above, except that I activated yield evolution. It looks better, doesn’t it?

Improved stiffness non-linearity

All I did was to change the yield stress values for the 2 networks from being fixed values to being variables that evolve with plastic strain. In this case, Network 1 initially had tauHat=3.4 MPa, and I changed it so that it has an initial value of tauHat=0.85 MPa and then evolves to 0.85*4=3.4 MPa once when the plastic strain reaches a value of 0.01. The variable FFF specifies the factor 4, and the variable epsF specifies the transition strain. Similarly for Network 2, I changed the tauHat value from 13.6 MPa to have an initial value of 3.4 MPa and then evolves to 3.4*4=13.6 MPa once the plastic strain reaches a value of 0.02. That’s it!

Summary: You can change the predicted stiffness non-linearity in the pre-yield region using the yield evolution options in the PolyUMod viscoplastic material models.

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