Introduction to the Abaqus Hysteresis Model
In this article, I will show how to use the Abaqus *Hysteresis model. The specific focus is on when to use Hybrid elements. Note that this is the Bergstrom-Boyce model, which is discussed in more details in a theory article and a graphical article.
First note that the *Hysteresis model is not available in Abaqus/Explicit!
High Poisson’s Ratio Materials
If we run an Abaqus/Standard simulation with element type C3D8 and the following material model:
*Hyperelastic, Yeoh
0.10, -0.05, 0.01, 0.05, 0, 0
*Hysteresis
6.4, 1.5e8, 7.5,-0.7, 0.05
Then we get the following error:
***ERROR: THE INITIAL BULK MODULUS OF 40.000 EXCEEDS 100 TIMES THE INITIAL
SHEAR MODULUS OF 0.20000 (THE INITIAL POISSON RATIO 0.49750 EXCEEDS
0.495) FOR THE HYPERELASTIC MATERIAL NAMED MAT. HOWEVER, A HYBRID
TYPE ELEMENT IS NOT USED. THIS MAY CAUSE CONVERGENCE PROBLEMS. IT IS
RECOMMENDED THAT YOU CHANGE THE ELEMENT TYPE TO A HYBRID ELEMENT;
HOWEVER YOU CAN ALSO CONVERT THIS ERROR MESSAGE TO A WARNING MESSAGE
BY SETTING THE ENVIRONMENT VARIABLE NONHYBRID_INCOMPRESS TO WARNING
OR BY ADDING *DIAGNOSTICS, NONHYBRID=WARNING TO THE INPUT FILE (NOT
RECOMMENDED).
If we switch to C3D8H elements, it instead fails with the following error message:
***ERROR: HYBRID ELEMENTS CAN BE USED WITH THE HYSTERESIS MODEL ONLY WHEN THE
ACCOMPANYING HYPERELASTICITY IS FULLY INCOMPRESSIBLE.
To fix this problem you need to make the hyperelastic model fully incompressible by setting D1=0 (instead of 0.05):
*Hyperelastic, Yeoh
0.10, -0.05, 0.01, 0, 0, 0
*Hysteresis
6.4, 1.5e8, 7.5, -0.7, 0.05
With this change and with hybrid elements, the simulation will run fine!
Low Poisson’s Ratio Materials
For “low Poisson’s ratio” materials, for example:
*Hyperelastic, Yeoh
0.10,-0.05, 0.05, 0.11, 0, 0
*Hysteresis
6.4, 1.5e8, 7.5, -0.7, 0.05
The *Hysteresis model works just fine.
Final note
In most cases it is better to use the Abaqus PRF model, for example the Yeoh-Power-Law Flow model, or the PolyUMod Three Network Viscoplasticity (TNV) model than the *Hysteresis model.
