In armchair graphene sheets, crack propagates perpendicular to the applied strain, whereas crack propagation in zigzag sheets occurs at an angle to the straining direction. This occurs due to different bond structure along armchair and zigzag directions as shown in Fig. 1. Videos 1 and 2 show the fracture of armchair and zigzag sheets, respectively.
Fig. 1: Armchair and zigzag directions of graohene
I attach some class notes developed by the late Professor Donald Carlson from which many generations of students at the University of Illinois learnt Continuum Mechanics.
Linear algebra is significant to many aspects of mechanics. For some years I have been using the book by Shilov. But this book may or may not be a good one to recommend to a student, depending on his or her prior experience. On StackExchange Mathematics, there are several excellent threads discussing textbooks of linear algebra. A particular recommendation was made for
Amit Acharya Claude Fressengeas
Springer Proceedings in Mathematics and Statistics on Differential Geometry and Continuum Mechanics, Vol. 137, pages 123-165. Ed: G. Q Chen, M. Grinfeld, R.J. Knops (Proceedings of Workshop held at the Intl. Centre for Mathematical Sciences in Edinburgh, 2013.)
I recent read the book of Prof. J. Tinsley Oden "A short course on nonlinear continuum mechanics"
http://users.ices.utexas.edu/~arbogast/cam397/oden0908.pdf
which declares that reference configuration is an open, bounded, connected subset of R3 with a smooth boundary (in Page 1).
It is strange to me beacause that means we cannot consider the boundary of the deformable bodies in its following discussion.
I recent read the book of Prof. J. Tinsley Oden "A short course on nonlinear continuum mechanics"
http://users.ices.utexas.edu/~arbogast/cam397/oden0908.pdf
which declares that reference configuration is an open, bounded, connected subset of R3 with a smooth boundary (in Page 1).
It is strange to me beacause that means we cannot consider the boundary of the deformable bodies in its following discussion.
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