You can change the model into standard and run a linear perturbation analysis. That would essentially give you the tangent stiffness. Not sure about acoustics under an uniaxial tensile test though.

Hello Dr. David Sziroczak ,

Thanks for the kind reply. I used explicit model because I also apply some temporal methods to detect necking, such as strain acceleration. So If I convert my model from explicit to static, does that cause a deviation in my temporal method results?

I am using both Al and steel specimens; at room temp and under quasi static loading conditions. From different resources, I understood that since they are not strain rate sensitive; hence, bifurcation analysis and perturbation analysis must yield the same result. Can you suggest me a comparative study on this issue?

Acoustic tensor is also an interesting concept here. Rice 1976 found that if the determinant of acoustic tensor is zero, then localized necking is observed in the form of shear band. After I obtain tangent modulus, I plan to calculate acoustic tensor in different directions. When I obtain zero or less determinant, I will detect the shear band. So, if I utilize standard model do you think I can carry out this procedure?

If you are interested in the algorithm, the main points are given in Akpama 2017.

Warm regards,

1) Rice, J. R. (1976). The localization of plastic deformation.

2) Akpama, H. K., Bettaieb, M. B., & Abed-Meraim, F. (2017). Localized necking predictions based on rate-independent self-consistent polycrystal plasticity: Bifurcation analysis versus imperfection approach. International Journal of Plasticity, 91, 205-237.

Hi Volkan Ili,

I am afraid that the answer to your first question is yes, the linear perturbation is purely static, so any dynamics/temporal effects are lost, you will see only the linear stiffness effects = the tangent modulus.

On the subject of comparing bifurcation and perturbation, I can't really suggest studies I'm afraid, and I'm not that familiar with your field to give you good advice without reading up on it. But I wish you good luck with your work!