Anisotropic Modulus of elasticity and Poisson's ratio

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SUMMARY

The discussion focuses on calculating the anisotropic modulus of elasticity and Poisson's ratio using experimental data for a material exhibiting anisotropic behavior. The user, Syed, has stress and strain data in three directions (sigma_x, sigma_y, sigma_z, epsilon_x, epsilon_y, epsilon_z) and seeks to determine six unknowns: Ex, Ey, Ez, Vxy, Vyx, and Vxz. The challenge lies in the limited equations available when shear stress is ignored, as referenced from a rock mechanics textbook. The need for additional insights or alternative approaches is emphasized to resolve the equations effectively.

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  • Familiarity with Young's modulus and Poisson's ratio
  • Knowledge of stress-strain relationships in three dimensions
  • Basic principles of rock mechanics
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rabbahs
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Hi,
I have some experimental data and I am interested to use this data to calculated modulus of elasticiy (young's modulus) and Poisson's ratio. The material for which the data is given in an anisotropic material, therefore I need to calculate modulus of elasticity and poisson's ration is x,y and z direction.
the data which I have is the stress in three direction and corresponding strain in three direction.

So , my problem is simple.
Knows: sigma_x, sigma_y, sigma_z, epsilon_x, epsilon_y, epsilon_y (6 knows)
Unknows: Ex, Ey, Ez, Vxy, Vyx, Vxz (6 unknows).

I have seen a formula in rock mechanics book (see the following image), but it will resolve into only three equation if the shear stress is ignored.

Please help me out.
Thanks
Syed

upload_2014-11-4_14-29-14-png.75095.png
 
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