Suppose the motion of a continuous body is given by x(X) = (3X1+ X2)e1 + (X2+ 2X1)e2+ X3e3 Determine the following deformation and strain measures a) Left and Right Cauchy-Green deformation tensors. b) Piola deformation tensor. c) Cauchy deformation tensor. d) Lagrange strain tensor and Green Euler strain tensor. e) Principal stretches.

Suppose the motion of a continuous body is given by x(X) = (3X1+ X2)e1 + (X2+ 2X1)e2+ X3e3 Determine the following deformation and strain measures a) Left and Right Cauchy-Green deformation tensors. b) Piola deformation tensor. c) Cauchy deformation tensor. d) Lagrange strain tensor and Green Euler strain tensor. e) Principal stretches.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Exercise 4
Suppose the motion of a continuous body is given by
x(X) = (3X1+ X2)e1 + (X2+ 2X1)e2+ X3e3
Determine the following deformation and strain measures
a) Left and Right Cauchy-Green deformation tensors.
b) Piola deformation tensor.
c) Cauchy deformation tensor.
d) Lagrange strain tensor and Green Euler strain tensor.
e) Principal stretches.
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