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For a linearly elastic, isotropic and homogeneous material, the number of elastic constants required to relate stress and strain is:
- a)Two
- b)Three
- c)Four
- d)Six
Correct answer is option 'A'. Can you explain this answer?
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For a linearly elastic, isotropic and homogeneous material, the number...
Elastic Constants for Linearly Elastic, Isotropic and Homogeneous Material
Linearly elastic, isotropic and homogeneous materials are those materials that behave similarly in any direction, have uniform properties throughout and demonstrate elasticity that is linear as long as the stress is below the yield point.
Number of Elastic Constants
The elastic constants relate stress and strain in a linearly elastic, isotropic and homogeneous material. The number of elastic constants required to relate stress and strain is two.
Explanation
In a linearly elastic, isotropic and homogeneous material, the stress and strain are related by two elastic constants, namely Young’s modulus and Poisson’s ratio. Young's modulus is defined as the ratio of stress to strain along the longitudinal axis of the material, whereas Poisson's ratio is the ratio of lateral strain to longitudinal strain.
Thus, the combination of these two elastic constants is enough to fully describe the material behavior for small deformations. Therefore, the number of elastic constants required to relate stress and strain is two in a linearly elastic, isotropic and homogeneous material.
Conclusion
In conclusion, the elastic constants required to relate stress and strain in a linearly elastic, isotropic and homogeneous material are Young’s modulus and Poisson’s ratio. The combination of these two elastic constants is enough to fully describe the material behavior for small deformations, and therefore, the number of elastic constants required is two.
Linearly elastic, isotropic and homogeneous materials are those materials that behave similarly in any direction, have uniform properties throughout and demonstrate elasticity that is linear as long as the stress is below the yield point.
Number of Elastic Constants
The elastic constants relate stress and strain in a linearly elastic, isotropic and homogeneous material. The number of elastic constants required to relate stress and strain is two.
Explanation
In a linearly elastic, isotropic and homogeneous material, the stress and strain are related by two elastic constants, namely Young’s modulus and Poisson’s ratio. Young's modulus is defined as the ratio of stress to strain along the longitudinal axis of the material, whereas Poisson's ratio is the ratio of lateral strain to longitudinal strain.
Thus, the combination of these two elastic constants is enough to fully describe the material behavior for small deformations. Therefore, the number of elastic constants required to relate stress and strain is two in a linearly elastic, isotropic and homogeneous material.
Conclusion
In conclusion, the elastic constants required to relate stress and strain in a linearly elastic, isotropic and homogeneous material are Young’s modulus and Poisson’s ratio. The combination of these two elastic constants is enough to fully describe the material behavior for small deformations, and therefore, the number of elastic constants required is two.
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For a linearly elastic, isotropic and homogeneous material, the number...
In all the formulas of elastic constants we need atmost 2 elastic constants..like E=2G(1+poisson ratio) E=3K(1-2*Poisson's ratio) Nw observe in each equ we have 2 elastic constants n Poisson's ratio..so 2 elastic constants are enough to corelate stress strain value. Cause using any of the 3 pairs like E&G,G&K,K&E..u can get stress value n corresponding strain also.
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For a linearly elastic, isotropic and homogeneous material, the number of elastic constants required to relate stress and strain is:a)Twob)Threec)Fourd)SixCorrect answer is option 'A'. Can you explain this answer?
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