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Full-Text Articles in Physical Sciences and Mathematics
A Representation Theorem For Material Tensors Of Textured Thin Sheets With Weak Planar Anisotropy, Yucong Sang
A Representation Theorem For Material Tensors Of Textured Thin Sheets With Weak Planar Anisotropy, Yucong Sang
Theses and Dissertations--Mathematics
Herein we consider material tensors that pertain to thin sheets or thin films, which we model as two-dimensional objects. We assume that the thin sheet in question carries a crystallographic texture characterized by an orientation distribution function defined on the rotation group SO(3), which is almost transversely-isotropic about the sheet normal so that mechanical and physical properties of the thin sheet have weak planar-anisotropy. We present a procedure by which a special orthonormal basis can be determined in each tensor subspace invariant under the action of the orthogonal group O(2). We call members of such special bases irreducible basis tensors …
Material Tensors And Pseudotensors Of Weakly-Textured Polycrystals With Orientation Measure Defined On The Orthogonal Group, Wenwen Du
Theses and Dissertations--Mathematics
Material properties of polycrystalline aggregates should manifest the influence of crystallographic texture as defined by the orientation distribution function (ODF). A representation theorem on material tensors of weakly-textured polycrystals was established by Man and Huang (2012), by which a given material tensor can be expressed as a linear combination of an orthonormal set of irreducible basis tensors, with the components given explicitly in terms of texture coefficients and a number of undetermined material parameters. Man and Huang's theorem is based on the classical assumption in texture analysis that ODFs are defined on the rotation group SO(3), which strictly speaking makes …