Identifying symmetry classes of elasticity tensors using monoclinic distance function
Journal of Elasticity, cilt.102, sa.2, ss.175-190, 2011 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 102 Sayı: 2
- Basım Tarihi: 2011
- Doi Numarası: 10.1007/s10659-010-9272-7
- Dergi Adı: Journal of Elasticity
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.175-190
- Anahtar Kelimeler: Anisotropy, Elasticity tensor, Frobenius distance, Symmetry class
- Boğaziçi Üniversitesi Adresli: Evet
Özet
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 ℝ3 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. © 2010 Springer Science+Business Media B.V.