QUESTION: ANISOTROPY AND POISSON'S RATIO
Robert Dillworth
orthotropic material modeling, there's a distinction made between minor
and major Poisson's ratios. I understand that there will be 3 different
values of the ratio, but beyond that, the documentation implies that
there is are 3 majors and 3 minors.
Can someone explain this concept to me and direct me to appropriate
reading on the subject?
Thank you.
Richard L. Citerley
The analysis of orthotropic or anisotropic materials requires some
understanding of Hooke's Law, equilibrium, least work and
strain-displacement relations. Most materials require planes of
symmetry in their layup. If you are within the elastic range of the
materials, the equations of symmetry boil down to three identities:
E2 v21 = E1 v12 ; E3 v32 = E2 v23 ; E1 v13 = E3 v31.
where E is the elastic modulus and v is the Poisson's ratio, noted to
the three orthogonal directions. Little development has been made for
inelastic behavior for anisotropic materials, but there have been a
number of studies for orthotropic.
To get a feel for how these Poisson's ratios are used, I might suggest
that you review S.A. Ambartsumyan, Theory of Anisotropic Shells, NASA TT
F-118, May 1964.
There are some ASTM standards that describe functional tests for
determining Poisson's ratio. I do not have these references at my
fingertips.
Remember, a body of revolution whose principal curvatures do not
coincide with the material's principle direction is an anisotropic body,
even though the material may have ortotropic properties.
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Richard L. Citerley Tele: (209)-295-8655
E-mail: cite...@volcano.net Fax: (209)-295-8657
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Robert Dillworth
Thank you for responding.
I understand the relationship between the products of elastic moduli and
Poisson's ratios that you point out, but the ANSYS documentation I
referred to gave me the impression that, given three different Poisson's
ratios for an orthotropic material, one must know if they have the three
MAJOR ratios, or the three MINOR ratios -- as if there were actually SIX
distinct values. Specifically, the distinction between the group of
three major of three minor is the point that I do not understand.
Material Fellow
v32 NOT EQUAL v23......
E2 v21 = E1 v12 ; E3 v32 = E2 v23 ; E1 v13 = E3 v31.
There are SIX v(ij) terms in the above....
Suggest that you read one of the real books on anisotropic elasticity.
Not the ANSYS manual.
jim buch
When you use stuff you don't understand, you don't know when you made an
input mistake.