Closed Form Equations for Elasticity Properties for Anisotropic Materials

In summary, the conversation revolves around finding a closed form solution for obtaining elasticity properties from a 6x6 anisotropic stiffness or compliance matrix. Relevant threads and an example for orthotropic material are provided. There are no new conclusions or information available at the moment.
  • #1
jester117
5
0
Hi all,

I'm wondering if anyone knows of a way to obtain elasticity properties (Ex, Ey, Ez, Gxy, Gxz, Gyz, vxy, vxz, vyz) from the terms of a 6x6 anisotropic stiffness or compliance matrix. I'm looking for a closed form solution, preferably. I would think that there should be a closed form solution but I'm not 100% certain so if anyone believes that

Here is a brief review of somewhat relevant threads on this site:
https://www.physicsforums.com/threads/elastic-modulus-of-an-anisotropic-crystal.397048/
https://www.physicsforums.com/threads/isotropic-crystals-anisotropic-crystals.554570/

And here is an example of the type of solution I'd like to see (note that this is for an orthotropic material):
http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/hooke_orthotropic.cfm

Thank you,

jester117
 
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  • #2
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
  • #3
I'm sorry to say that I don't have any new info. Plenty of my colleagues are stumped by this problem as well.

-jester117
 

1. What is the significance of closed form equations for elasticity properties for anisotropic materials?

Closed form equations provide a mathematical representation of the relationship between stress and strain in anisotropic materials. This allows for a better understanding of the mechanical behavior of these materials and aids in the design and analysis of structures made from them.

2. How are closed form equations derived for anisotropic materials?

Closed form equations are derived using principles of solid mechanics and material properties such as Young's modulus, Poisson's ratio, and shear modulus. These equations take into account the anisotropic nature of the material, meaning that its properties vary based on direction.

3. Can closed form equations be applied to all anisotropic materials?

No, closed form equations are specific to a certain type of anisotropic material and cannot be generalized to all anisotropic materials. Each material has its own unique set of properties and therefore requires its own set of closed form equations.

4. How accurate are closed form equations for predicting the behavior of anisotropic materials?

Closed form equations can provide a good estimate of the mechanical behavior of anisotropic materials, but they may not be completely accurate due to the complex nature of these materials. Factors such as microstructure and environmental conditions can also affect the accuracy of these equations.

5. Are closed form equations the only way to model the behavior of anisotropic materials?

No, there are other methods such as finite element analysis and experimental testing that can also be used to model the behavior of anisotropic materials. However, closed form equations are a useful tool for quick calculations and initial design considerations.

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