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The number of elastic constants for a completely anisotropic elastic material which follows Hooke’s law is
  • a)
    2
  • b)
    4
  • c)
    21
  • d)
    25
Correct answer is option 'C'. Can you explain this answer?
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The number of elastic constants for a completely anisotropic elastic m...
's law is 21.

Hooke's law states that the stress applied to a solid is directly proportional to the strain produced. For an anisotropic material, the elastic behavior (i.e. the relationship between stress and strain) can vary depending on the direction in which the stress is applied. Therefore, to fully describe the elastic behavior of an anisotropic material, we need to specify the elastic constants for each direction.

There are 21 independent elastic constants for a completely anisotropic material, which can be arranged in a 6x6 matrix known as the stiffness matrix. These constants include the Young's moduli, shear moduli, and Poisson's ratios for each possible combination of stress and strain directions.
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