Question
Download Solution PDFThe number of independent elastic constant for a complete isotropic elastic material which follows Hooks law is _____.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Isotropic Material:
- Isotropic materials have identical material properties in all directions at every given point.
- When a specific load is applied at any point of isotropic materials, it will exhibit the same strength, stress, strain, young’s modulus, and hardness in the x, y, or z-axis direction.
Examples: metals, glasses.
- Almost every metal exhibits isotropic behaviour at the micro-level because all single-crystal systems are isotropic with respect to mechanical properties.
- There are a few exceptional cases where metals exhibit anisotropic behaviour at the micro-level.
- Random localized distribution of anisotropic behaviour at the micro-level, nullify each other and the net effect at the macro level is isotropic behaviour.
For an isotropic, homogeneous, and elastic material obeying Hook's law, the number of independent elastic constants is 2.
It means to fully define the elastic behaviour of isotropic material only 2 elastic constants are good enough.
E = 2G (1 + μ) = 3K(1 - 2μ)
As seen in the above equations there are a total of 4 elastic constants.
If we know two of them, then we can find other constants also.
∴ there are 2 independent elastic constants required to define the stress-strain relationship for isotropic material.
Additional Information
Orthotropic material
- A material is said to be orthotropic if it has three different properties in three mutually perpendicular directions.
- There are 9 independent elastic constants required to define the stress-strain relationship for orthotropic material.
Anisotropic material
- A material is said to be anisotropic if it has different properties in each direction.
- There are 21 independent elastic constants required to define the stress-strain relationship for an anisotropic material.
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