Imagine a 3D state of strain in amechanical part, measured perhaps by digital volume correlation or other means, given inCartesian coordinates by€rx = a(x² + y²),€yy = a(y² +2²), Exy=b(xyz), Exz = €yz = €zz = 0,where a and b are constants and x, y, z are coordinates in space. Determine whether thismeasured strain field is a possible state of strain for a continuum that remains intact andcontinuous after deformation.

Answered: Imagine a 3D state of strain in a…

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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Imagine a 3D state of strain in a
mechanical part, measured perhaps by digital volume correlation or other means, given in
Cartesian coordinates by
€rx = a(x² + y²),
€yy = a(y² +2²), Exy=b(xyz), Exz = €yz = €zz = 0,
where a and b are constants and x, y, z are coordinates in space. Determine whether this
measured strain field is a possible state of strain for a continuum that remains intact and
continuous after deformation.

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A mechanical part undergoing strain must satisfy the requirements of an isotropic and incompressible material, meaning that its volume must remain constant during deformation. The state of strain described in your question can be analyzed by checking whether it satisfies these requirements.

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