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Solid Mechanics Homework 11-15

Submitted by Zhigang Suo on
ES 240
Fall 2006
solid mechanics
homework
Fall 2008

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:  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
Nanshu Lu

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.

Wed, 10/11/2006 - 01:42 Permalink
John M. Kolinski

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.

Sun, 10/05/2008 - 22:50 Permalink