Solid Mechanics Homework 11-15
This set of homework relies on a few elementary facts of the algebra of vectors and tensors. If you are vague about these facts, see some old notes I wrote when I taught ES 240 in 2006: http://www.imechanica.org/node/205/revisions/1385/view
11. Positive-definite elastic energy density
12. The coefficient of thermal expansion (CTE) is a second-rank tensor.
13. Hooke's law for anisotropic, linearly elastic solids
14. Invariants of a tensor
15. A "derivation" of the Mises (1913) yield criterion
Return to the outline of the course.
| Attachment | Size |
|---|---|
| Homework 11-15.doc | 84 KB |
| Homework 11-15.pdf | 35.29 KB |
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possible error?
is the range for ν correct in #11? which would then allow λ to be negative?
thanks,
will
No problem with the given range of v
λ is only an parameter for convinience and can readily vary with reasonable v.
Copied from Wiki
Poisson's ratio is the ratio of the relative contraction strain, or transverse strain (normal to the applied load), divided by the relative extension strain (in the direction of the applied load). For a perfectly incompressible material, the Poisson's ratio would be exactly 0.5. Most practical engineering materials have ν between 0.0 and 0.5. Cork is close to 0.0, most steels are around 0.3, and rubber is almost 0.5. Some materials, mostly polymer foams, have a negative Poisson's ratio; if these auxetic materials are stretched in one direction, they become thicker in perpendicular directions.
It is right
Of course the λ can be negative.You can prove it from math or there indeed some materials'λ is negative.
pdf file?
Prof. Suo, would you mind posting the .pdf file for the hw assignments? I don't have word on my computer, and google docs doesn't read some of the symbols used in the assigments.
OOo
You might try installing OpeOoffice, a free/open-source office suite. It seems to dislay all the math and such properly for me and could make it easier for you to read Word documents people paste in the future.
http://www.openoffice.org/
pdf file of homework is attached
John: The pdf file is attched. I'll remeber to do so in future.