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elastic constants: definition

How a crystalline material responds to applied stress, is an important engineering property. You will learn (or refresh) the formalism to describe stress-strain relationships, which is useful in experimental as well as in computational research. You will learn how to determine the strain tensor for a given deformation of a unit cell.

Warning: in this video, a few of the equations that are shown are inconsistent with the rest of the course. All spoken explanations are correct. The downloadable slides have been corrected. These are the time stamps in the video to which these changes apply: 10m20s: in the stress-strain relations there should be an extra factor 2 in front of εyz, εxz and εxy. 11m48s: same factor 2 missing, in the 1×6 matrix as well as in the 6×1 matrix. 12m21s: same factor 2 missing. 13m18s: same as at 11m48s, with consequences in the worked out version of the matrix product.

If after this video you feel you want to learn more about continuum mechanics, then www.continuummechanics.org is an excellent source.

After the video, digest your new knowledge by this task:

Use the strain tool of the Bilbao Crystallographic Server to determine the strain tensor that corresponds to a volume-conserving increase by 2% of the c/a-ratio of hcp-Scandium. Upload a pdf file in which you describe in a few lines how you proceed, and put your result in there. At the end of the quiz, the correct procedure will be reviewed.

elastic constants definition

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expected time: 40m
report time spent (page code AW08A)

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