Continuum Mechanics by A. J. M. Spencer

Author:A. J. M. Spencer
Language: eng
Format: epub
ISBN: 9780486139470
Publisher: Dover Publications
Published: 2012-07-18T04:00:00+00:00

3. Find the components of the tensors F, C, B, F—1, C—1, B—1, γ and η for the deformation

x1 = a1(X1 + αX2),

x2 = a2X2,

x3 = a3X3

where a1, a2, a3 and α are constants. Find the conditions on these constants for the deformation to be possible in an incompressible material. A body which in the reference configuration is a unit cube with its edges parallel to the coordinate axes undergoes this deformation. Determine the lengths of its edges, and the angles between the edges, after the deformation. Sketch the deformed body.

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