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I'm looking for physical and mathematical explanations for a phenomenon I've noticed when working with rotated material properties relative to an XYZ coordinate system. For certain rotations (~40 to ~50 degrees) about a single axis the S12, S13, or S23 components of the compliance matrix become positive, which implies that the corresponding Poisson's ratios are negative. The material I'm trying to simulate is a single crystal metal, so I wouldn't expect a negative Poisson's ratio.

I'm able to simulate this result across multiple methods for basis transformation, so I doubt there's an error there. I've also been able to confirm that the stiffness-compliance matrix inversion is correct.

If you'd like to simulate the problem, you can use this site: <http://www.efunda.com/formulae/solid_mechanics/composites/calc_ufrp_cs_arbitrary.cfm>. I used Msi units, both Young's moduli = 18, shear modulus = 18, Poisson's ratio = 0.38, and theta = 45.

Of relevance:

The form of the compliance matrix used, http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/hooke_orthotropic.cfm

Relevant articles,

http://arc.aiaa.org/doi/abs/10.2514/3.4974

http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=1415488

Thanks for looking into this,

jester117

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# Negative Poisson's Ratio in Rotated Orthotropic Material

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