“A study of the symmetry of three-dimensional spaces is of great theoretical and practical significance, because symmetrical spaces include crystals (from which, of course, the majority of solids are formed), and all homogeneous fields without exception: electric, magnetic, gravitational, etc. A study of the structures of crystals is unthinkable without a knowledge of the laws governing symmetry of three-dimensional spaces” (from Shubnikov and Koptsik, 1974).
KeywordsMaterial Symmetry Representative Volume Element Elastic Symmetry Reflective Symmetry Tissue Mechanic
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- Cowin SC. 1995. On the number of distinct elastic constants associated with certain anisotropic elastic symmetries. In Theoretical, experimental, and numerical contributions to the mechanics of fluids and solids — a collection of papers in honor of Paul M. Naghdi, ed. J Casey, MJ Crochet, Z Ang Math Phys [Special Issue] 46:S210–S214.Google Scholar
- Cowin SC. 2002. Elastic symmetry restrictions from structural gradients. In rational continua, classical and new — a collection of papers dedicated to Gianfranco Capriz on the occasion of his 75th birthday, pp. 51–66, ed. P Podio-Guidugli, M Brocato. New York: Springer-Verlag.Google Scholar
- Cowin SC. 2003. Symmetry plane classification criteria and the symmetry group classification criteria are not equivalent in the case of asymmetric second order tensors. Chinese J Mech 19:9–14.Google Scholar
- Fedorov FI. 1968. Theory of elastic waves in crystals. New York: Plenum Press.Google Scholar
- Hull D. 1981. An introduction to composite materials. Cambridge: Cambridge UP.Google Scholar
- Neville C. 1993. Biology of fibrous composites. Cambridge: Cambridge UP.Google Scholar
- Shubnikov AV, Koptsik VA. 1974. Symmetry in science and art. New York: Plenum.Google Scholar
- Thompson W(Lord Kelvin). 1904. Baltimore lectures on molecular dynamics and the wave theory of light. London: CJ Clay & Sons.Google Scholar
- Wainwight SA, Biggs WD, Currey JD, Gosline JM. 1976. Mechanical design in organisms. London: Arnold.Google Scholar