Starting with relations (6.1.16) and (6.1.17), show that the volumetric and distortional strain energies can be expressed in terms of the invariants of the stress matrix as:

Equation 6.1 .16

Equation 6.1 .17

Results from Exercise 6.10 may be helpful.

Data from exercise 6.10 

Verify the decomposition of the strain energy into volumetric and deviatoric parts as given by equations (6.1.16) and (6.1.17).

Equation 6.1 .16

Equation 6.1 .17

Transcribed Image Text:

1 U = 2 Gijeij = 1 jjekk 1-2v 6E -jjkk 1 - 2v 6E (0x + ay +0)