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The number of independent elastic constants required to express the stress-strain relationship for linearly elastic isotropic materia! is
- a)One
- b)Two
- c)Three
- d)Four
Correct answer is option 'B'. Can you explain this answer?
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The number of independent elastic constants required to express the st...
There are two independent elastic constants E and G for an isotropic linear elastic material.
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The number of independent elastic constants required to express the st...
Explanation:
In linearly elastic isotropic materials, the stress-strain relationship can be expressed using two independent elastic constants. These elastic constants are known as Young's modulus (E) and Poisson's ratio (ν).
Young's Modulus:
Young's modulus is a measure of the stiffness of a material. It relates the stress applied to a material to the resulting strain. Mathematically, it is defined as the ratio of the stress (σ) to the strain (ε) in the elastic region:
E = σ / ε
Young's modulus represents the ratio of the axial stress to the axial strain.
Poisson's Ratio:
Poisson's ratio is a measure of the lateral strain that occurs when a material is stretched or compressed in one direction. It is defined as the negative ratio of the lateral strain (ε_lateral) to the axial strain (ε_axial):
ν = -ε_lateral / ε_axial
Poisson's ratio indicates the ratio of the transverse strain to the axial strain.
Independent Elastic Constants:
For linearly elastic isotropic materials, the stress-strain relationship can be expressed using two independent elastic constants: Young's modulus (E) and Poisson's ratio (ν).
These two constants are independent because they can be measured independently and are not dependent on each other.
Young's modulus represents the stiffness of the material, while Poisson's ratio represents the lateral strain. Together, they provide a complete description of the stress-strain relationship for linearly elastic isotropic materials.
Conclusion:
Therefore, the correct answer is option B - Two. Two independent elastic constants (Young's modulus and Poisson's ratio) are required to express the stress-strain relationship for linearly elastic isotropic materials.
In linearly elastic isotropic materials, the stress-strain relationship can be expressed using two independent elastic constants. These elastic constants are known as Young's modulus (E) and Poisson's ratio (ν).
Young's Modulus:
Young's modulus is a measure of the stiffness of a material. It relates the stress applied to a material to the resulting strain. Mathematically, it is defined as the ratio of the stress (σ) to the strain (ε) in the elastic region:
E = σ / ε
Young's modulus represents the ratio of the axial stress to the axial strain.
Poisson's Ratio:
Poisson's ratio is a measure of the lateral strain that occurs when a material is stretched or compressed in one direction. It is defined as the negative ratio of the lateral strain (ε_lateral) to the axial strain (ε_axial):
ν = -ε_lateral / ε_axial
Poisson's ratio indicates the ratio of the transverse strain to the axial strain.
Independent Elastic Constants:
For linearly elastic isotropic materials, the stress-strain relationship can be expressed using two independent elastic constants: Young's modulus (E) and Poisson's ratio (ν).
These two constants are independent because they can be measured independently and are not dependent on each other.
Young's modulus represents the stiffness of the material, while Poisson's ratio represents the lateral strain. Together, they provide a complete description of the stress-strain relationship for linearly elastic isotropic materials.
Conclusion:
Therefore, the correct answer is option B - Two. Two independent elastic constants (Young's modulus and Poisson's ratio) are required to express the stress-strain relationship for linearly elastic isotropic materials.
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