Show that the principal directions of stress and strain are the same for isotropic linear elastic materials. Note: this means that if you know the direction of largest principal stress at a point, you also know the direction of largest stretch/strain at that point. Also note: this is not the case for anisotropic solids.How are the principal stresses and strains related? Write the principal stresses in terms of principal strains and invariants of the strain tensor.

Answered: Show that the principal directions of…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Show that the principal directions of stress and strain are the same for isotropic linear elastic materials. Note: this means that if you know the direction of largest principal stress at a point, you also know the direction of largest stretch/strain at that point. Also note: this is not the case for anisotropic solids.
How are the principal stresses and strains related? Write the principal stresses in terms of principal strains and invariants of the strain tensor.

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