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a) Justify briefly why, in the absence of long-range body forces, the stress tensor σij must be symmetric. b) In equilib
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a) Justify briefly why, in the absence of long-range body forces, the stress tensor σij must be symmetric. b) In equilib
a) Justify briefly why, in the absence of long-range body forces, the stress tensor σij must be symmetric. b) In equilibrium, the free energy density of a crystal may be expressed as F = 2 Cijkl Uij Ukl, where Ui j is the deformation tensor and Cijkl is the elastic constants tensor. Assum- ing Cijkl = Cklij, find the relationship between the σij and Ukl. = c) A general rank-4 tensor Aijkl in three dimensions has 81 components. Show, using the symmetries of uk and σij, and that Cijkl Cklij, that Cijkl has at most 21 independent components.
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