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E
where K  – volumetric modulus of deformation.
3 1 2  
Analyzing the expression (3.29) we see that the Poisson's ratio
  5 , 0 . For the material with Poisson   5 , 0 (paraffin, rubber)
with an uniform all-round tensile the volume does not change.

3.9 Potential energy in a volume stress state

Consider the elementary parallelepiped that is under the
principal stresses  ,  and  . In the central tension or
1 2 3
compression (linear stress state, see. p.2.9) we have
1
u   .
n
2
Generalizing this formula for the case of simultaneous action of
three stresses, we obtain
1
u          . (3.30)
n 1 1 2 2 3 3
2
Substituting in the formula (3.30) the expression (3.25), we
obtain:
1
2
2
2
u        2         . (3.31)
n 1 2 3 1 2 1 3 2 3
2E

3.10 Strength theories

Strength theory is called the assumption of equal strength of
different types of stress states.
The objective of strength theories is the ability to express
conditions of appearance of plastic deformation or destruction of
the material in any complex stress state, when known only the
mechanical characteristics of the material obtained in its testing in
conditions of linear stress state.

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