8 Replies Latest reply on Sep 19, 2008 1:16 PM by Chris Frye

# Cosmosworks Orthotropic Material Poisson Ratios

Is it the major or minor Poisson ratio that should be entered into Cosmosworks for FEA of orthotropic materials?
• ###### Cosmosworks Orthotropic Material Poisson Ratios
I found this in the Cosmos Knowledge Base:

For orthotropic materials, the Young's Moduli (EX, EY, EZ) and Poisson's Ratios (NUXY, NUYZ, NUZX) have to be defined.
----

So it is using all the values , not minor or major.
• ###### Cosmosworks Orthotropic Material Poisson Ratios
Mr. Cuenca,
you have not understood correctly the question of Mr. Martinez.
Each of the three Nusselt module components (XY,XZ,YZ) has its 'major' and 'minor' version. Only one of them need to be defined because the other one is defined by the constitutive equations of the material. But it is necessary to know which one of the two versions Cosmos expects to receive from the user.
I hope that somebody knows the answer.
Leonardo Presciuttini
• ###### Cosmosworks Orthotropic Material Poisson Ratios
Well... I do not understand the question of the "major or minor Poisson ratio that should be entered into Cosmosworks for FEA of orthotropic materials".

By definition, an orthotropic material has at least 2 orthogonal planes of symmetry, where material properties are independent of direction within each plane. Such materials require 9 independent variables (i.e. elastic constants) in their constitutive matrices.

In contrast, a material without any planes of symmetry is fully anisotropic and requires 21 elastic constants, whereas a material with an infinite number of symmetry planes (i.e. every plane is a plane of symmetry) is isotropic, and requires only 2 elastic constants.

Now you can have "linear" orthotropic materials or "non-linear" orthotropic materials. Look at all the material inside COSMOS Works Help related to linear and not linear analysis of orthotropic materials and I believe you will see there the answers to your question. On a linear orthotropic material you do not define major or minor mechanical properties, all you define is the properties in the three mutually perpendicular directions. For exaple Elastic Modulus in the X, Y, and Z directions or Poisson's Ratio in the X, Y, and Z directions. For non-linear materials it is a little more complex and there are cases where some orthotropic materials do not have Elactic Modulus, nor Poisson's Ratio (like it is the case of some hyperelastic composites particularly if they incorporate layers of elastic weaved fabrics).

If you need to analyze non-linear materials I believe you will need COSMOS ADVANCED PROFESSIONAL (is what we use) since I believe that the standard COSMOS Works do not have the non-linear analysis module active. Modeling material non-linearities (no-linear relationships between stress and strain) will require modeloing of plasticity, creep and maybe even thermopalsticity problems.

Look inside the Help for COSMOS for Material Models, Linear Elastic Orthotropic Materials and also for non-linear Material Models, Hyperelasticity (Mooney, Ogden, Blatz), Plasticity (von Misses, Tresca, Drucker) Viscoelasticity, Creep, Nitinol. But all of this will only be available if you have non-linear fucntionality open on your software.

• ###### Cosmosworks Orthotropic Material Poisson Ratios
I don't understand this question either, but here are the Poisson ratio definitions for an orthotropic material:

http://en.wikipedia.org/wiki/Poisson's_ratio

In any way, the easiest way to find out is to set up a simple uniaxial tension model and try the different values to see what happens.
• ###### Cosmosworks Orthotropic Material Poisson Ratios
Dear Martinez,
things like Posson'r ratio in the three principal directions do not exist.
The constitutive flexibility matrix of an orthotropic material has its non-diagonal terms of the form -nuyx/Ey. It must be -nuyx/Ey=-nuxy/Ex. Therefore in the gneral case nuyx<>nuxy. And so for nuzx and nuzy too. But you need to specify only one value of each couple, since the other one comes from the values of Ex, Ey, and Ez. From this fact comes the need to specify if you are giving the major or the minor values.
Regards.
• ###### Cosmosworks Orthotropic Material Poisson Ratios
Dear Mr. Presciuttini,

During my days at colleage, they indicate to me that by definition, an orthotropic material has at least 2 orthogonal planes of symmetry, where material properties are independent of direction within each plane. Such materials require 9 independent variables (i.e. elastic constants) in their constitutive matrices.

By convention, the 9 elastic constants in orthotropic constitutive equations of their matrices are comprised of 3 Young's modulii Ex, Ey, Ez, the 3 Poisson's ratios nyz, nzx, nxy, and the 3 shear modulii Gyz, Gzx, Gxy. (This is correct assuming that Hoke's Law for orthotropic materiasl in Compliace Form still correct this days... one never know... and has been some years since I get my graduation...).

For Orthotropic material, such as wood, or some composites, Poisson's ratio is different in each direction (x, y and z axis) the relation between Young's modulus and Poisson's ratio in the Complaince Matrix is described as follows:

(Vyx / Ey) = (Vxy / Ex)

(Vzx / Ez) = (Vxz / Ex)

(Vyz / Ey) = (Vzy / Ex)

Where Ei is the Youg's Modulus alon axis i
Vjk is a Poisson's Ratio in Plane jk

Again either I do not undertud the question or I am wrong (which is possible).

• ###### Cosmosworks Orthotropic Material Poisson Ratios
Dear Mr. Martinez,
you are 100% correct. What is missing is the conclusion:
Vyx<>Vxy
Vzx<>Vxz
Vyz<>Vzy
which element of each couple do you provide (beyond the 3 E's and the three G's)?
Regards
• ###### Cosmosworks Orthotropic Material Poisson Ratios
What is the problem? Cosmosworks material GUI specifically requests the information. It asks for NUXY, NUYZ, NUXZ. It does not ask for NUYX, NUZY, or NUZX. That's because they are calculated.