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Infinitesimal strain theory
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===Octahedral strains=== Let (<math>\mathbf{n}_1, \mathbf{n}_2, \mathbf{n}_3</math>) be the directions of the three principal strains. An '''octahedral plane''' is one whose normal makes equal angles with the three principal directions. The engineering [[shear strain]] on an octahedral plane is called the '''octahedral shear strain''' and is given by <math display="block"> \gamma_{\mathrm{oct}} = \tfrac{2}{3}\sqrt{(\varepsilon_1-\varepsilon_2)^2 + (\varepsilon_2-\varepsilon_3)^2 + (\varepsilon_3-\varepsilon_1)^2} </math> where <math>\varepsilon_1, \varepsilon_2, \varepsilon_3</math> are the principal strains.{{citation needed|date=January 2012}} The [[normal strain]] on an octahedral plane is given by <math display="block"> \varepsilon_{\mathrm{oct}} = \tfrac{1}{3}(\varepsilon_1 + \varepsilon_2 + \varepsilon_3) </math> {{citation needed|date=January 2012}}
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