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The independent elastic constants for a 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?
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The independent elastic constants for a homogeneous and isotropic mate...
The independent elastic constants for a homogeneous and isotropic material are E, G, and ν (Poisson's ratio).
Elastic Constants:
- Elastic constants are the physical properties of materials that describe their response to applied stress or strain.
- Elastic constants are used to calculate the deformation of materials under stress or strain.
- The three independent elastic constants for a homogeneous and isotropic material are Young's modulus (E), shear modulus (G), and Poisson's ratio (ν).
Young's Modulus (E):
- Young's modulus is a measure of the stiffness of a material.
- It quantifies the relationship between stress (force per unit area) and strain (deformation) in the linear region of the stress-strain curve.
- Young's modulus is defined as the ratio of stress to strain in the linear region of the curve.
- It has units of Pascals (Pa) or Newtons per square meter (N/m²).
Shear Modulus (G):
- Shear modulus is a measure of the resistance of a material to shear deformation.
- It quantifies the relationship between shear stress (force per unit area parallel to the surface) and shear strain (angular deformation) in the linear region of the stress-strain curve.
- Shear modulus is defined as the ratio of shear stress to shear strain in the linear region of the curve.
- It has units of Pascals (Pa) or Newtons per square meter (N/m²).
Poisson's Ratio (ν):
- Poisson's ratio is a measure of the lateral strain (transverse strain) that occurs when a material is subjected to axial strain (longitudinal strain).
- It quantifies the relationship between the transverse strain and the longitudinal strain.
- Poisson's ratio is defined as the negative ratio of transverse strain to longitudinal strain.
- It is dimensionless and typically ranges from 0 to 0.5 for most materials.
Conclusion:
- The independent elastic constants for a homogeneous and isotropic material are E, G, and ν.
- These elastic constants are used to calculate the deformation of materials under stress or strain.
- Young's modulus (E) is a measure of stiffness, shear modulus (G) is a measure of resistance to shear deformation, and Poisson's ratio (ν) is a measure of lateral strain.
Elastic Constants:
- Elastic constants are the physical properties of materials that describe their response to applied stress or strain.
- Elastic constants are used to calculate the deformation of materials under stress or strain.
- The three independent elastic constants for a homogeneous and isotropic material are Young's modulus (E), shear modulus (G), and Poisson's ratio (ν).
Young's Modulus (E):
- Young's modulus is a measure of the stiffness of a material.
- It quantifies the relationship between stress (force per unit area) and strain (deformation) in the linear region of the stress-strain curve.
- Young's modulus is defined as the ratio of stress to strain in the linear region of the curve.
- It has units of Pascals (Pa) or Newtons per square meter (N/m²).
Shear Modulus (G):
- Shear modulus is a measure of the resistance of a material to shear deformation.
- It quantifies the relationship between shear stress (force per unit area parallel to the surface) and shear strain (angular deformation) in the linear region of the stress-strain curve.
- Shear modulus is defined as the ratio of shear stress to shear strain in the linear region of the curve.
- It has units of Pascals (Pa) or Newtons per square meter (N/m²).
Poisson's Ratio (ν):
- Poisson's ratio is a measure of the lateral strain (transverse strain) that occurs when a material is subjected to axial strain (longitudinal strain).
- It quantifies the relationship between the transverse strain and the longitudinal strain.
- Poisson's ratio is defined as the negative ratio of transverse strain to longitudinal strain.
- It is dimensionless and typically ranges from 0 to 0.5 for most materials.
Conclusion:
- The independent elastic constants for a homogeneous and isotropic material are E, G, and ν.
- These elastic constants are used to calculate the deformation of materials under stress or strain.
- Young's modulus (E) is a measure of stiffness, shear modulus (G) is a measure of resistance to shear deformation, and Poisson's ratio (ν) is a measure of lateral strain.
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The independent elastic constants for a homogeneous and isotropic mate...
Homogeneous and isotropic material have two independent elastic constant E, u E=2G(1+u) so we can say that two independent constant E & G
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The independent elastic constants for a 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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