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According to Von-Mises’ distortion energy theory, the distortion energy under three dimensional stress state is represented by

Answer (Detailed Solution Below)

Option 3 :
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Detailed Solution

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Explanation:

Total strain energy in the three-dimensional system is:

Total strain energy per unit volume:

U = 

Total strain energy can be split into two strain energy:

  • The strain energy of distortion
  • The strain energy of uniform compression, tension or energy of dilation.

The energy of dilation:

Uv = 

Strain energy of distortion:

Distortion energy = (total Strain energy) - (energy of dilation)

Ud = 

on simplifying above expression we get

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