## General Mechanical

#### TB Hill-Orthotropic plasticity with Hill’s criterion

• cheng089413
Subscriber

Hello everyone,

I am trying to understand why and how the Hill's model can be combined with Bilinear Isotropic (BISO) hardening rule. Since BISO can only define one yield strength and its tangent modulus, why Hill can be combined with it. If BISO was combined with Hill, in which direction of the yield strength the BISO defines?

I am also thinking about the example given by Ansys that a Hill's model is combined with BISO. Since Hill is for anisotropic material, why only the elastic properties of x axis is defined? Will that lead to an error?

If i wanna define the hardening rule for all directions, can anyone advise me what to make it happen?

• Mike Rife
Ansys Employee

Hi cheng089413

Please see section 4.4.2.1.2 here:  https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v201/en/ans_mat/amp8sq21dldm.html%23matRIPtheory

Using the Hill's criteria is a isotropic elastic, anisotropic plastic strain model.  You can add it to the BKIN model as you have shown; then the Hill's material model inputs are scale factors that define the yield strength in the differing directions.

Mike

• cheng089413
Subscriber

Hi Mike,

I understand Hill is an anisotropic plastic strain model, which indicates different behavior in different material axes. However BISO (bilinear isotropic hardening) can only define only one yield stress (sigma zero), as shown in the figure below, while the anisotropic material has three different yield stresses along its anisotropic axes. That is why I am confused how the BISO or BKIN can add to Hill model.

I am thinking do you mean the yield stress (sigma zero) is the yield stress used in Hill model and it does not represent the yield stress of any axes? If it is so, then i get it. If it is the case, can you advise me how to assign a value for the yield stress (sigma zero) appropriately?

• Mike Rife
Ansys Employee

cheng089413 did you review the help section I pasted?  The BISO model defines the Yield but then the Hill defines scale factors for the yield in the differing directions.

• cheng089413
Subscriber

Hello Mike,

Yes I read the instructions you pasted. Sorry i was dumb but now i kind of get what you meant. You were saying Hill model is only for isotropic elastic material and in this way BISO is certainly able to be added to with only one yield strength (sigma zero) needed to be defined. So the material has to be isotropic in elastic phase but anisotropic for plastic phase.

I am tring to simulate an orthotropic nonlinear material. I have defined an orthotropic elastic material and I am wondering how to use Hill and any one of the plasticity model to simulate its plastic behavior? If it is possible, I was asking in previous posts what should be sigma zero defined in Hill. Bc there are three orthotropic planes for orthotropic elastic material and thus there should be three tangent moduli and yield strengths.

Eason

• cheng089413
Subscriber

Hi Mike,

Now i get it that in Ansys the Hill model doesn't work for my case. Bc it cannot support orthotropic material. Now i can only use TB ANISO to define this material behavior. May I ask what hardening rule is used for TB ANISO? Is it isotropic or kinematic?