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Understanding the Nature of Shear-Shear and Shear-Extension Coupling

Understanding the Nature of Shear-Shear and Shear-Extension Coupling

Understanding the Nature of Shear-Shear and Shear-Extension Coupling

(OP)
Hi Everyone,

While checking on a thread about Orthotropic and Monoclinic materials ( http://www.eng-tips.com/viewthread.cfm?qid=347566 ) to see if I had gotten a response, it dawned on me: in anisotropic materials, just what are the physical interpretations of shear-shear and shear-extension coupling? How do these truly work in a full understanding of the bridge from traditional mechanics to continuum mechanics?

Extension-Extension coupling is easy enough to understand in terms of Poisson's ratio, especially in materials up to the orthotropic level. In non-isotropic materials, there is not a direct coupling of strain and stress equally in each direction. However, when one considers a material such as wood, where there is effect shear-coupling, the nature of this often seems to become extremely vague and ambiguous. I can visualize a perfect cube (with no dislocations) and pinching two different planes for shear-shear, or an extension and a shear pinch, and the resulting motions. However, mathematically and in the scheme of finite element modeling, this is still rather confusing.

Would you all please be so kind as to help me understand this more? Perhaps part of my confusion may be that I'm trying to understand in terms of a material's stiffness matrix, rather than the easier compliance matrix. I have a copy of Robert Jone's "Mechanics of Composite Materials", Timoshenko's "Theory of Plates and Shells", and several writings of Dr. David Roylance at MIT, which have helped me a good bit so far in understanding the theory's mechanics and limitations up through orthotropic materials. I am now at the point that getting past the conceptual ideas and truly understanding less friendly materials is still a challenge.

Particularly, when trying to understand it from general measurement test that one may be able to easily get general data from, as if you were going to order from a manufacturer. Are offset dog-bone style tests, strain gauges, or micro-scaled surface images and cut-aways the only ways to really measure this type coupling?

Any advice or insight shared will be greatly appreciated!

Thank you,

Kherszal

RE: Understanding the Nature of Shear-Shear and Shear-Extension Coupling

Jones book should be enough to get you there if you look at it a few times. Another good one is by Daniel and Ishai.

It is sort of hard to explain without figures, but imagine a unidirectional ply, rotated by 45 from the loaded direction (uniaxial load). Under uniaxial loading, there would be shear deformation of the ply (this is called shear-extension coupling).

Think about it this way. If that same uniaxial load was broken into an equivalent set (2 loads - one aligned with the fibers and one aligned normal to the fibers), you would expect one direction to stretch more than the other (since the fibers resist deformation than the the direction normal to it). The result is shearing deformation.

Shear-extension coupling only exists when the fibers are not aligned with either the 0 degree or 90 degree directions w.r.t. the load.

Brian
www.espcomposites.com

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