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**define young modulus 2 bulk modulus 3rigidity modulus state relation between them**

by chitu123 01.11.2014

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by chitu123 01.11.2014

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Youngs modulus of elasticity Y is defined for solids. It is the ratio of stress σ to strain ε. Stress is the Compressive or tensile force per unit area of cross section exerted on a solid object. The strain is the ratio of elongation or extension in the size of object (in the direction of force) to the original total length of the object.

Y = Stress / Strain = σ/ε = (F/A ) / (ΔL / L) = F L / (A ΔL) N/m²

Bulk modulus of elasticity is the change in the pressure ΔP in the substance to the ratio of volume strain. The change in pressure causes a change in the volume of fluid.

B = - ΔP / (ΔV / V) = - V ΔP / ΔV N/m²

Rigidity modulus G or (1/K ) of elasticity is the ratio of lateral (shearing) stress to the lateral (shearing) strain or the angle of bend in the substance. A tangential stress is applied on the substance which is fixed at one end, and the angle bent at the free end is measured.

G = shearing stress / shearing strain = (F / A) / θ

Poissons ratio = σ_P = (Δd/d) / (ΔL/L)

= lateral strain (in diameter d of cross section) / longitudinal strain (in length L along tensile force)

relations:

for most substances is Y = 3 G

Y = 2 G ( 1 + σ_P )

Y < 3 B

Y = 3 B ( 1 - σ_P)

1/Y = 1/(4G) + 1/(6B)

Y = Stress / Strain = σ/ε = (F/A ) / (ΔL / L) = F L / (A ΔL) N/m²

Bulk modulus of elasticity is the change in the pressure ΔP in the substance to the ratio of volume strain. The change in pressure causes a change in the volume of fluid.

B = - ΔP / (ΔV / V) = - V ΔP / ΔV N/m²

Rigidity modulus G or (1/K ) of elasticity is the ratio of lateral (shearing) stress to the lateral (shearing) strain or the angle of bend in the substance. A tangential stress is applied on the substance which is fixed at one end, and the angle bent at the free end is measured.

G = shearing stress / shearing strain = (F / A) / θ

Poissons ratio = σ_P = (Δd/d) / (ΔL/L)

= lateral strain (in diameter d of cross section) / longitudinal strain (in length L along tensile force)

relations:

for most substances is Y = 3 G

Y = 2 G ( 1 + σ_P )

Y < 3 B

Y = 3 B ( 1 - σ_P)

1/Y = 1/(4G) + 1/(6B)