Journal
JOURNAL OF ELASTICITY
Volume 102, Issue 2, Pages 175-190Publisher
SPRINGER
DOI: 10.1007/s10659-010-9272-7
Keywords
Anisotropy; Symmetry class; Elasticity tensor; Frobenius distance
Funding
- Memorial University of Newfoundland
- M.A. Slawinski's research grant
- Natural Sciences and Engineering Research Council of Canada
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We present a method to identify the symmetry class of an elasticity tensor whose components are given with respect to an arbitrarily oriented coordinate system. The method is based on the concept of distance in the space of tensors, and relies on the monoclinic or transversely isotropic distance function. Since the orientation of a monoclinic or transversely isotropic tensor depends on two Euler angles only, we can plot the corresponding distance functions on the unit sphere in R-3 and observe the symmetry pattern of the plot. In particular, the monoclinic distance function vanishes in the directions of the normals of the mirror planes, so the number and location of the zeros allows us to identify the symmetry class and the orientation of the natural coordinate system. Observing the approximate locations of the zeros on the plot, we can constrain a numerical algorithm for finding the exact orientation of the natural coordinate system.
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