 ## General Mechanical

• rsadiwa
Subscriber

I have been digging into the ANSYS theory manual to get the constitutive model used in ANSYS. I figured out that ANSYS uses a linear relation between the Cauchy stresses and right logarithmic strain

σ = D.ln(U) 

(D here is the linear constitutive matrix, and U is the right stretch tensor) I verified that ANSYS uses this model by simulating in both ANSYS and my own Matlab FEA code and matching the results for multiple cases.

I have tried to look up the theoretical and experimental basis for using this constitutive law in literature. I did not find the exact same relation cited in any paper. I however discovered the Hencky elastic model which uses a linear relationship between Kirchoff stresses and left logarithmic strain.

J.σ = D.ln(V) 

(V here is the left stretch tensor, J is the determinant of the deformation gradient tensor F)

This model has been extensively researched and has both a theoretical and experimental basis for using it. Both these models are NOT equivalent, which can be proven easily.

My question is why does ANSYS use this particular model, and what is the theoretical/experimental background to it?

 ANSYS theory manual.

 Hencky's elasticity model and linear stress-strain relations in isotropic finite hyperelasticity , Xiao et al

 On H. Hencky’s Approximate Strain-Energy Function for Moderate Deformations, L. Anand

 Henky's elasticity model with the logarithmic strain measure: a study on Poynting effect and stress response in torsion of tubes and rods, Bruhns et. al.

• rsadiwa
Subscriber

• John Doyle
Ansys Employee
Have you considered the references listed in the Bibliography at the end of the MAPDL Theory Manual?
Bathe, K. J.(1996).Finite Element Procedures.Upper Saddle River, NJ:Prentice-Hall.
Biot, M. A.(1965).Mechanics of Incremental Deformation.Hoboken, NJ:Wiley.
Cook, R. D.(1981).Concepts and Applications of Finite Element Analysis (2nd ed.).Hoboken, NJ:Wiley.
• rsadiwa
Subscriber
Hey jjdoyle,

I looked up the references you mentioned and they did not help. The closest help I found was in  but even that was just a passing comment on the use of logarithmic strain and Cauchy stress, with no equations or attached reference.
Bathe, K. J.(1996).Finite Element Procedures.Upper Saddle River, NJ:Prentice-Hall

• peteroznewman
Subscriber
I don't work for ANSYS, I just use their products.
A left-hand screw thread is NOT equivalent to a right-hand screw thread, but both are useful.
Users need to know not to screw a left-hand screw thread into a right-hand threaded hole.
Why does a user need to know if ANSYS uses a left stretch tensor or a right stretch tensor?
• John Doyle
Ansys Employee
I received this tip from a reliable source:
The log strain tensors ln(U) and ln(V) only differ by a rotation. ln(U) is natural for use with the corotational formulation.
• rsadiwa
Subscriber
Hey jjdoyle, thanks for the response. Actually I was more concerned about the stress measure (J.¤âvs ¤â) most academic sources use J.¤â(Kirchoff stresses) instead of ¤â(true stresses)-which is what is used in ANSYS. 