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An isotropic elastic material is characterized by
- a)two independent modulus of elasticity along two mutually perpendicular directions
- b)two independent modulus of elasticity along two mutually perpendicular directions and Poisson’s ratio
- c)a modulus of elasticity, a modulus of rigidity and Poisson’s ratio
- d)any two out of modulus of elasticity, a modulus of rigidity and Poisson’s ratio
Correct answer is option 'D'. Can you explain this answer?
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An isotropic elastic material is characterized bya) two independent m...
The independent elastic constant will be any two of E, G and μ.
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An isotropic elastic material is characterized bya) two independent m...
Isotropic Elastic Material Characteristics
An isotropic elastic material is a material which has the same elastic properties in all directions. This means that when a force is applied to the material, it will deform uniformly in all directions. The characteristics of an isotropic elastic material are:
Modulus of Elasticity (Young's Modulus)
Young's modulus is the measure of the stiffness of a material. It is the ratio of stress to strain in the elastic range. For isotropic materials, there is only one modulus of elasticity.
Modulus of Rigidity (Shear Modulus)
Modulus of rigidity is the measure of a material's resistance to shear deformation. It is the ratio of shear stress to shear strain in the elastic range. For isotropic materials, there is only one modulus of rigidity.
Poisson's Ratio
Poisson's ratio is the ratio of the transverse strain to the axial strain in a material. It is a measure of the lateral deformation of a material when it is subjected to an axial load. For isotropic materials, there is only one Poisson's ratio.
Conclusion
Therefore, an isotropic elastic material is characterized by any two out of modulus of elasticity, a modulus of rigidity and Poisson’s ratio. Since isotropic materials have the same elastic properties in all directions, there is no need for two independent modulus of elasticity along two mutually perpendicular directions.
An isotropic elastic material is a material which has the same elastic properties in all directions. This means that when a force is applied to the material, it will deform uniformly in all directions. The characteristics of an isotropic elastic material are:
Modulus of Elasticity (Young's Modulus)
Young's modulus is the measure of the stiffness of a material. It is the ratio of stress to strain in the elastic range. For isotropic materials, there is only one modulus of elasticity.
Modulus of Rigidity (Shear Modulus)
Modulus of rigidity is the measure of a material's resistance to shear deformation. It is the ratio of shear stress to shear strain in the elastic range. For isotropic materials, there is only one modulus of rigidity.
Poisson's Ratio
Poisson's ratio is the ratio of the transverse strain to the axial strain in a material. It is a measure of the lateral deformation of a material when it is subjected to an axial load. For isotropic materials, there is only one Poisson's ratio.
Conclusion
Therefore, an isotropic elastic material is characterized by any two out of modulus of elasticity, a modulus of rigidity and Poisson’s ratio. Since isotropic materials have the same elastic properties in all directions, there is no need for two independent modulus of elasticity along two mutually perpendicular directions.
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An isotropic elastic material is characterized bya) two independent modulus of elasticity along two mutually perpendicular directionsb) two independent modulus of elasticity along two mutually perpendicular directions and Poisson’s ratioc) a modulus of elasticity, a modulus of rigidity and Poisson’s ratiod) any two out of modulus of elasticity, a modulus of rigidity and Poisson’s ratioCorrect answer is option 'D'. Can you explain this answer?
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