origin (0, 0, 0). Use the Right Cauchy Green strain tensor to determine whether these elements in the current configuration (dx(¹), dx(²)) are perpendicular. Use the Right Cauchy-Green strain tensor to evaluate the stretch of the line ele- ment dX = ₁ + e2, and hence determine whether the element contract, stretches, or stays the same lenght after deformation. Determine the Green-Lagrangian and Eulerian strain tensors. Decompose the deformation into a stretching and rotation tensors. Describe what kind of deformation the body is undergoing by including what the prin- cipal stretches are and the type of rotation the body is undergoing.

origin (0, 0, 0). Use the Right Cauchy Green strain tensor to determine whether these elements in the current configuration (dx(¹), dx(²)) are perpendicular. Use the Right Cauchy-Green strain tensor to evaluate the stretch of the line ele- ment dX = ₁ + e2, and hence determine whether the element contract, stretches, or stays the same lenght after deformation. Determine the Green-Lagrangian and Eulerian strain tensors. Decompose the deformation into a stretching and rotation tensors. Describe what kind of deformation the body is undergoing by including what the prin- cipal stretches are and the type of rotation the body is undergoing.

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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Question

X₁ = X₁ + 2X3,
x2 = X₂ - 2X3, X3 = −2X₁ + 2X2 + X3
Consider the two line elements dX(¹) = ₁, dX(²) = ₂ emanating from the the
origin (0, 0,0). Use the Right Cauchy Green strain tensor to determine whether
these elements in the current configuration (dr(¹), dx(²)) are perpendicular.
Use the Right Cauchy-Green strain tensor to evaluate the stretch of the line ele-
ment dX = ₁ +ē2, and hence determine whether the element contract, stretches,
or stays the same lenght after deformation.
Determine the Green-Lagrangian and Eulerian strain tensors.
Decompose the deformation into a stretching and rotation tensors. Describe
what kind of deformation the body is undergoing by including what the prin-
cipal stretches are and the type of rotation the body is undergoing.

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