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The independent elastic constants for homogeneous and isotropic material are
- a)E, G, K, V
- b)E, G, K
- c)E, G, V
- d)E, G
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The independent elastic constants for homogeneous and isotropic materi...
Only two independent elastic constant are required to express the stress-strain relation for a linearly elastic, isotropic material. We can find third elastic constant and Poisson’s ratio for the material.
This question is part of UPSC exam. View all Mechanical Engineering courses
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The independent elastic constants for homogeneous and isotropic materi...
**Explanation:**
In mechanics, elastic constants are the measures of stiffness of a material. Homogeneous and isotropic materials have the same properties in all directions and at all points within the material. The independent elastic constants for such materials are:
**a) E, G, K, V**
**E**: Young's modulus (also known as the modulus of elasticity) is a measure of the stiffness of a material. It relates the stress applied to a material to the resulting strain within the elastic limit. Young's modulus is a measure of the material's resistance to elastic deformation when a force is applied.
**G**: Shear modulus (also known as the modulus of rigidity) is a measure of the material's resistance to shear deformation. It relates the shear stress applied to a material to the resulting shear strain within the elastic limit. Shear modulus measures the material's ability to withstand shear forces.
**K**: Bulk modulus is a measure of the material's resistance to uniform compression. It relates the hydrostatic stress applied to a material to the resulting volumetric strain within the elastic limit. Bulk modulus measures the material's ability to withstand changes in volume under pressure.
**V**: Poisson's ratio is a measure of the ratio of lateral strain to axial strain when a material is subjected to tensile or compressive stress. It describes the material's tendency to expand or contract in response to stress.
However, the correct answer is:
**b) E, G, K**
This is because Poisson's ratio (V) can be expressed in terms of the other three elastic constants (E, G, K). Poisson's ratio is given by the equation:
V = (3K - 2G) / (2(3K + G))
Therefore, Poisson's ratio can be determined if the values of E, G, and K are known. As a result, Poisson's ratio is not considered an independent elastic constant for homogeneous and isotropic materials.
Hence, the correct answer is option 'b) E, G, K'.
In mechanics, elastic constants are the measures of stiffness of a material. Homogeneous and isotropic materials have the same properties in all directions and at all points within the material. The independent elastic constants for such materials are:
**a) E, G, K, V**
**E**: Young's modulus (also known as the modulus of elasticity) is a measure of the stiffness of a material. It relates the stress applied to a material to the resulting strain within the elastic limit. Young's modulus is a measure of the material's resistance to elastic deformation when a force is applied.
**G**: Shear modulus (also known as the modulus of rigidity) is a measure of the material's resistance to shear deformation. It relates the shear stress applied to a material to the resulting shear strain within the elastic limit. Shear modulus measures the material's ability to withstand shear forces.
**K**: Bulk modulus is a measure of the material's resistance to uniform compression. It relates the hydrostatic stress applied to a material to the resulting volumetric strain within the elastic limit. Bulk modulus measures the material's ability to withstand changes in volume under pressure.
**V**: Poisson's ratio is a measure of the ratio of lateral strain to axial strain when a material is subjected to tensile or compressive stress. It describes the material's tendency to expand or contract in response to stress.
However, the correct answer is:
**b) E, G, K**
This is because Poisson's ratio (V) can be expressed in terms of the other three elastic constants (E, G, K). Poisson's ratio is given by the equation:
V = (3K - 2G) / (2(3K + G))
Therefore, Poisson's ratio can be determined if the values of E, G, and K are known. As a result, Poisson's ratio is not considered an independent elastic constant for homogeneous and isotropic materials.
Hence, the correct answer is option 'b) E, G, K'.
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The independent elastic constants for homogeneous and isotropic material area)E, G, K, Vb)E, G, Kc)E, G, Vd)E, GCorrect answer is option 'D'. Can you explain this answer?
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