TAGGED: constitutivelaws, largedeformation


December 14, 2021 at 6:35 amrsadiwaSubscriber
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) [1]
(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) [2][3][4]
(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?
[1] ANSYS theory manual.
[2] Hencky's elasticity model and linear stressstrain relations in isotropic finite hyperelasticity , Xiao et al
[3] On H. Hencky’s Approximate StrainEnergy Function for Moderate Deformations, L. Anand
[4] 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.

December 19, 2021 at 11:41 pmrsadiwaSubscriber

December 29, 2021 at 1:47 pmJohn DoyleAnsys EmployeeHave you considered the references listed in the Bibliography at the end of the MAPDL Theory Manual?
[2]Bathe, K. J.(1996).Finite Element Procedures.Upper Saddle River, NJ:PrenticeHall.
[3]Biot, M. A.(1965).Mechanics of Incremental Deformation.Hoboken, NJ:Wiley.
[5]Cook, R. D.(1981).Concepts and Applications of Finite Element Analysis (2nd ed.).Hoboken, NJ:Wiley.

January 25, 2022 at 4:09 amrsadiwaSubscriberHey jjdoyle,
I looked up the references you mentioned and they did not help. The closest help I found was in [2] but even that was just a passing comment on the use of logarithmic strain and Cauchy stress, with no equations or attached reference.
[2]Bathe, K. J.(1996).Finite Element Procedures.Upper Saddle River, NJ:PrenticeHall

January 29, 2022 at 12:52 pmpeteroznewmanSubscriberI don't work for ANSYS, I just use their products.
A lefthand screw thread is NOT equivalent to a righthand screw thread, but both are useful.
Users need to know not to screw a lefthand screw thread into a righthand threaded hole.
Why does a user need to know if ANSYS uses a left stretch tensor or a right stretch tensor?

February 10, 2022 at 10:06 pmJohn DoyleAnsys EmployeeI 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.

February 13, 2022 at 8:28 pmrsadiwaSubscriberHey 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.

 You must be logged in to reply to this topic.
Boost Ansys Fluent Simulations with AWS
Computational Fluid Dynamics (CFD) helps engineers design products in which the flow of fluid components is a significant challenge. These different use cases often require large complex models to solve on a traditional workstation. Click here to join this event to learn how to leverage Ansys Fluids on the cloud, thanks to Ansys Gateway powered by AWS.
Earth Rescue – An Ansys Online Series
The climate crisis is here. But so is the human ingenuity to fight it. Earth Rescue reveals what visionary companies are doing today to engineer radical new ideas in the fight against climate change. Click here to watch the first episode.
Ansys Blog
Subscribe to the Ansys Blog to get great new content about the power of simulation delivered right to your email on a weekly basis. With content from Ansys experts, partners and customers you will learn about product development advances, thought leadership and trends and tips to better use Ansys tools. Sign up here.
 Saving & sharing of Working project files in .wbpz format
 Solver Pivot Warning in Beam Element Model
 Understanding Force Convergence Solution Output
 An Unknown error occurred during solution. Check the Solver Output…..
 What is the difference between bonded contact region and fixed joint
 whether have the difference between using contact and target bodies
 The solver engine was unable to converge on a solution for the nonlinear problem as constrained.
 User manual
 Colors and Mesh Display
 material damping and modal analysis

3820

2607

1853

1244

600
© 2023 Copyright ANSYS, Inc. All rights reserved.