# Poisson ratios for Orthotropic materials (composites)

• Arjan82
In summary, the speaker is a mechanical engineering student who is learning about composite materials for a project involving fluid structure interaction. They are trying to learn the basics and need to specify three Poisson ratios for an orthotropic material in the FEM software they are using. They have questions about the relationship between the Poisson ratios and how to derive the complete matrix of ratios. They also mention constraints that must hold for a real material and wonder if there are other checks they can do to ensure the consistency of their input dataset.
Arjan82
TL;DR Summary
For an orthotropic material (e.g. carbon reinforced polymer), how to derive the Poisson matrix from 3 values?
I'm new to composite materials. I've studied mechanical engineering but I am actually usually involved in hydrodynamics (in which I've done my masters). However for a project we do fluid structure interaction with composites, and as these things go, you cannot get away with the 'black box' approach (I wish I could sometimes...). So I'm trying to learn the basics.

In the FEM software I use I need to specify three Poisson ratios: ##\nu_{12},\ \nu_{23},\ \nu_{31}## (and also three E and three G moduli). It is orthotropic material (3 symmetry planes). I want to derive the other Poisson ratio's because I want to know if the supplier provided a consistent set of data.

Some questions:
1. ##\nu_{12}## gives me the strain in 2 direction from the strain in 1 direction, i.e. ##\epsilon_2 = -\nu_{12}\sigma_2/E_2##, correct?
2. But I believe in general, for orthotropic materials, ##\nu_{12}## is not equal to ##\nu_{21}##. Correct?
3. If indeed so, can I derive the complete matrix of all Poisson ratios from ##\nu_{12},\ \nu_{23},\ \nu_{31}##? And how?
4. There are al kinds of constrains that must hold for a real material, e.g. ##\Delta = 1-\nu_{12}\nu_{21}-\nu_{23}\nu_{32}-\nu_{31}\nu_{13}-2\nu_{21}\nu_{32}\nu_{13} > 0##, which is I believe the change in volume...? Are there more of these checks that I can do to find if my input dataset is consistent?

## 1. What is a Poisson ratio for Orthotropic materials?

A Poisson ratio is a measure of the ratio of lateral strain to axial strain when a material is subjected to a uniaxial stress. In the case of orthotropic materials, the Poisson ratio varies depending on the direction of the applied stress.

## 2. How are Poisson ratios for Orthotropic materials determined?

Poisson ratios for orthotropic materials are typically determined experimentally through mechanical testing. This involves subjecting the material to different types of stress and measuring the resulting strains in different directions.

## 3. What is the significance of Poisson ratios for Orthotropic materials in engineering?

Poisson ratios are important in engineering because they affect the mechanical properties of orthotropic materials, such as their stiffness and strength. They also play a role in determining the behavior of these materials under different types of loading.

## 4. Can Poisson ratios for Orthotropic materials be negative?

Yes, Poisson ratios for orthotropic materials can be negative. This occurs when the material experiences a transverse expansion when subjected to an axial stress, which is the opposite of what is typically observed in isotropic materials.

## 5. How do Poisson ratios for Orthotropic materials compare to those of isotropic materials?

Poisson ratios for orthotropic materials can vary significantly depending on the direction of the applied stress, whereas isotropic materials have a single, constant Poisson ratio. Additionally, orthotropic materials can have negative Poisson ratios, which is not possible in isotropic materials.

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