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GATE 2016 CE (CE2) – Question 41

Solid Mechanics · Simple stress and strain relationships · 2 marks · Multiple choice

An elastic isotropic body is in a hydrostatic state of stress as shown in the figure. For no change in the volume to occur, what should be its Poisson's ratio?

Diagram for GATE 2016 CE (CE2) question 41
  1. 0.00
  2. 0.25
  3. 0.50
  4. 1.00

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Correct answer: (C) 0.50

Explanation

For isotropic linear elasticity, volumetric strain is(1−2ν)(σx+σy+σz)/E. A nonzero hydrostatic stress has a nonzero stress sum, so zero volumetric strain requires1−2ν=0. Therefore **ν=0.50, C**, the incompressible limiting value.