Question

The number of independent elastic constants for a 3D anisotropic material are

• A. 9
• B. 2
• C. 21
• D. 5

Hint:

Isotropic: 2 constants; Orthotropic: 9; Anisotropic: 21.

Answer 1

The Correct Option is C

In the study of anisotropic materials within the field of aerospace engineering, understanding the number of independent elastic constants is essential. For a general 3D anisotropic material, the elasticity tensor is characterized by a fourth-order tensor comprising 81 components. However, due to the principles of material symmetry and thermodynamics (such as the symmetry in the stiffness tensor and the energy potential), these components are not all independent.

The major symmetry due to the stress-strain relationship, specifically the symmetry of the stress and strain tensors, reduces the number of independent constants from 81 to 21. This is due to the symmetric nature of the constitutive matrix, often referred to as the stiffness matrix in engineering mechanics.

Conclusion: For a 3D anisotropic material, the number of independent elastic constants is 21.