Talk:Orthotropic material

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The page has been cleaned up, even though it wasn't stupid or rubbish before. Glass is isotropic, not orthotropic. A silicon wafer is a single crystal of silicon, which is most definitely anistropic (with cubic symmetry) and neither isotropic nor orthotropic.--128.220.254.4 04:20, 12 February 2007 (UTC) --- this page is stupid and rubbish --- GLASS IS ISOTROPIC OR ORTHOTROPIC AND ALSO SILICON WAFER IS ISOTROPIC OR ORTHOTROPIC ---

Higher symmetry like cubic or fully isotropic like the glass implies that it also has orthotropic symmetry. But these materials are just not good examples any more. --Ulrich67 (talk) 00:47, 23 January 2011 (UTC)

Material Symmetry

Just a quick note regarding material symmetry: If a material has two mutually orthogonal planes of symmetry, then that material also has a third plane of symmetry (automatically). In other words there are no materials with just two orthogonal planes of symmetry. If two exist, then there are really three planes of symmetry. See Robert Jones, "Mechanics of Composite Materials", second edition, page 59. Gpayette 04:26, 10 October 2007 (UTC)

I am not sure whether or not this contradicts the statement in the article, which refers to axes of two-fold rotational symmetry - a rather limited kind of symmetry.

They key question for me is this - Can you give an example of a material which is NOT orthotropic by this definition? Any material whose properties are described by a tensor is surely orthotropic. A material which is not orthotropic would have different properties along oppositely-directed axes. This would make no sense for stress or strain, which are intrinsically bi-directional, but is at least conceivable (but not necessarily possible) for optical behaviour

Mkovari, 11:57, 1 March 2010 (UTC)

By the way, I am not sure you are right about silicon. I believe that if a property is described by a tensor then if it has cubic symmetry it is isotropic. (The only tensor with cubic symmetry is the unit tensor.) This means that all normal properties (mechanical, acoustic, optical etc) are isotropic.

One more point - I suppose one should really decide whther the term orthotropic includes the special case of isotropic. Mkovari (talk) 12:12, 1 March 2010 (UTC)

There is no question that a fully isotropic (or cubic) material is also othotropic.

For a material with cubic symmetry all properties described by a second order tensor (e.g. optical) are isotropic. But mechanical properties are not described by a second order tensor, but a 4th oder tensor - the Voigt notation is just a trick to write the 4th order tensor as a matrix.

For the properties that are described by a symmetric second order tensor its always possible to find a coordinate system to get the diagonal form. So from these properties its not possible to decide if a material is othotropic or not. --Ulrich67 (talk) 01:21, 23 January 2011 (UTC)

Merge proposal

{{Merge to |infinitesimal stress theory|stress|strain tensor|discuss=Talk:Orthotropic#Material Symmetry|date=January 2013}}

"Orthotropic" seems to be just a fancy name for "fully non-isotropic". Methinks that all the mathematical content of this article should be merged into the general articles on elastic theory (which apparently say much of what is said here, only deeper and better.) The article may remain for the benefit of readers who want to know what the word means, but reduced to a single-line definition and hopefully a list of important examples (such as wood) where the absence of any axis of circular symmetry is significant. --Jorge Stolfi (talk) 11:37, 25 January 2013 (UTC)

"Orthotropic" is NOT just a fancy name for "fully non-isotropic". Please read some of the primary literature before making changes to the article. Bbanerje (talk) 20:15, 28 January 2013 (UTC)

OK, sorry for my ignorance. I understand it now. --Jorge Stolfi (talk) 17:37, 5 February 2013 (UTC)

Symmetry

The article is not consistent with the type of symmetry: In the introduction it is a twofold rotation. In the section "Orthotropic material properties" it is symmetry planes (mirror). There is a slight difference between these two cases. The difference is a point inversion (factor -1 in matrix form). It does not change things for properties that are described by a tensor of even rank, like the ones described here. But it will change things for properties described by a 3rd rank tensor like piezo-electricity. So there is clarification needed.--91.3.118.227 (talk) 10:51, 23 January 2011 (UTC)

I agree. The introduction needs to be made consistent with the rest of the article. We should also add a bit on third-order material tensors. Can you help with that? Bbanerje (talk) 21:23, 23 January 2011 (UTC)

If I understand it correctly the definition on top is correct in the sense that rotational symmetry is needed, but not the mirror planes. For the rotation its also true that if there are 2 orthogonal axis of symmetry than there is always also a third - just doing the two rotations gives one rotation about this 3rd axis. For the mirror planes this is not correct: there can be two mirror-planes without a third. If there are 3 such orthogonal planes then there are axis of rotation as well - but not the other way around. So there is a problem in the math part as well. The problem is not bad with 2nd or 4th order Tensors - because here its possible to introduce a factor of -1 (or point inversion) and make a mirror from a 180 Deg. rotation. That is probably the origin of the sentence 'It can be shown that if the matrix for a material is invariant under reflection about two orthogonal planes then it is also invariant under reflection about the third orthogonal plane.' The tricky part is that this 3rd symmetry operation is only for even order tensors, but not for the material itself. --Ulrich67 (talk) 18:05, 24 January 2011 (UTC)

Searching the Web for definitions of orthotropic give many different answers. The most common I found was the definition via the properties, not the symmetry. So there should be a note on the different possible definitions. The ones I found: 1) different properties in 3 orthogonal directions, 2) at least 2 mirror planes and 3) At least 2 Axis of 2-fold rotation. As far as I understand it, versions 2 and 3 both lead to Version 1). In point symmetric materials versions 2 and 3 are come together. In not point symmetric materials the two Versions are exclusive. A probably good book on this topic is J.F. Nye, 1957, Physical Properties of Crystals: Their Representation by Tensors and Matrices. Oxford University Press. ISBN 9780198511656.--Ulrich67 (talk) 20:26, 24 January 2011 (UTC)

Norris's 1991 paper will help clarify why the symmetry plane approach is used in elasticity etc. Bbanerje (talk) 23:47, 24 January 2011 (UTC)

This paper is about nonlinear elasticity. This includes even higher order Tensors. One thing to learn from this, is that linearity is important for the symmetry arguments- so one should be careful with magnetic permeability which is often nonlinear in ferro-magnets. --Ulrich67 (talk) 20:14, 29 January 2011 (UTC)

Is this topic still active? From my point of view, it would be nicer, if the reflection-transformation matrices A1, A2 and A3 were replaced by 180-degrees-rotation transformation matrices. Using this replacement, the results will not change. But the symmetry-conditions become more realistic: An orienation-changing transformation (like a reflection) is unrealistic for solids. Whereas a 180-degrees-rotation makes perfect sense. The interpretation is also obvious: The material behaviour does not change, if you rotate your particle (and its neighborhood) by 180 degrees about any axis of orthotropy. Comments? --Kassbohm (talk) 06:47, 10 July 2014 (UTC)

Bounds on elastic constants

It seems that the conclusion that

$S_{11}>0~,~~S_{22}>0~,~~S_{33}>0~,~~S_{44}>0~,~~S_{55}>0~,~~S_{66}>0$

or

$E_{1}>0,E_{2}>0,E_{3}>0,G_{12}>0,G_{23}>0,G_{13}>0$

is not quite correct for orthotropic materials, in a way that the Poisson's ratios can impact the positive-definiteness of ${\underline {\underline {\mathsf {S}}}}$. --Kxiaocai (talk) 12:09, 30 December 2014 (UTC)