Abstract
Given an arbitrary tensor in an n-dimensional Euclidean space, it is required to find its 'nearest' tensor of some preassigned symmetry, i.e. the tensor of this symmetry which has the minimum invariant 'distance' from the given tensor. General theorems are given concerning the construction and properties of these nearest tensors. The theorems are applied, in the case of elastic tensors, for the construction of the nearest isotropic and cubic tehsors to a given anisotropic elastic tensor, and the nearest hexagonal polar tensor to a cubic elastic tensor.
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