Answered: If n1 is an eigenvector for a strain…

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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If n₁is an eigenvector for a strain tensor, show it is also a principal direction for the stress tensor

Expert Solution

Step 1: show that the eigenvector for a strain tensor is also the principal direction for the stress tensor

Given:

The eigenvector for a strain tensor is $n subscript 1$ .

Concept used:

The relative change in the position of points within a body that has experienced deformation is known as strain. In two dimensions, the typical example is a square that has been twisted into a parallelepiped.

The definition of stress is force per unit area. Quantify the stress on a cube of material in multiple directions if an arbitrary load provided. These data will be combined to generate the stress tensor, which is the second rank tensor.

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