Closed Form Equations for Elasticity Properties for Anisotropic Materials

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SUMMARY

The discussion focuses on obtaining closed form equations for elasticity properties (Ex, Ey, Ez, Gxy, Gxz, Gyz, vxy, vxz, vyz) from a 6x6 anisotropic stiffness or compliance matrix. Participants express uncertainty about the existence of such solutions, with references to related threads and an example for orthotropic materials provided. The need for a definitive closed form solution remains unresolved, indicating a gap in available resources for this specific topic.

PREREQUISITES
  • Understanding of elasticity properties in materials science
  • Familiarity with anisotropic stiffness and compliance matrices
  • Knowledge of orthotropic material behavior
  • Basic principles of solid mechanics
NEXT STEPS
  • Research closed form solutions for elasticity properties of anisotropic materials
  • Study the derivation of stiffness and compliance matrices in materials science
  • Explore the application of Hooke's law to orthotropic materials
  • Investigate numerical methods for solving elasticity problems in anisotropic materials
USEFUL FOR

Materials scientists, mechanical engineers, and researchers focused on the mechanical properties of anisotropic materials will benefit from this discussion.

jester117
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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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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?
 
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
 

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