Let F = Vay, C = FTF and SR the Piola-Kirchhoff stress tensor. Define E = F-¹SR. This is known as the second Piola-Kirchhoff stress tensor. (b) Show that SR: F = x:C₁ where denotes time derivative. Hint. When A is symmetric, A: B = AT : BT = A : BT for any tensor B.

Let F = Vay, C = FTF and SR the Piola-Kirchhoff stress tensor. Define E = F-¹SR. This is known as the second Piola-Kirchhoff stress tensor. (b) Show that SR: F = x:C₁ where denotes time derivative. Hint. When A is symmetric, A: B = AT : BT = A : BT for any tensor B.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.59P

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Question

Let F = Vay, C = FTF and SR the Piola-Kirchhoff stress tensor. Define
E = F-'SR. This is known as the second Piola-Kirchhoff stress tensor.
(b) Show that
SR:
where
denotes time derivative.
Hint. When A is symmetric, A : B = AT : B™ = A : BT for any tensor B.

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