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Young's Modulus from shear modulus Formula

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Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain. Check FAQs

E = 2 \cdot G \cdot (1 + 𝛎)

E - Young's Modulus?G - Shear Modulus?𝛎 - Poisson's Ratio?

Young's Modulus from shear modulus Example

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Here is how the Young's Modulus from shear modulus equation looks like with Values.

Here is how the Young's Modulus from shear modulus equation looks like with Units.

Here is how the Young's Modulus from shear modulus equation looks like.

6.5E+10 = 2 \cdot 25 \cdot (1 + 0.3)

6.5E+10N/m = 2 \cdot 25GPa \cdot (1 + 0.3)

6.5E+10 = 2 \cdot 25 \cdot (1 + 0.3)

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Young's Modulus from shear modulus Solution

Follow our step by step solution on how to calculate Young's Modulus from shear modulus?

FIRST Step Consider the formula

E = 2 \cdot G \cdot (1 + 𝛎)

Next Step Substitute values of Variables

∴

E = 2 \cdot 25GPa \cdot (1 + 0.3)

Next Step Convert Units

∴

E = 2 \cdot 2.5E+10Pa \cdot (1 + 0.3)

Next Step Prepare to Evaluate

∴

E = 2 \cdot 2.5E+10 \cdot (1 + 0.3)

Next Step Evaluate

∴

E = 65000000000N/m

LAST Step Rounding Answer

∴

E = 6.5E+10N/m

Young's Modulus from shear modulus Formula Elements

Variables

Young's Modulus

Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

Symbol: E

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Young's Modulus

Shear Modulus

Shear modulus is the slope of the linear elastic region of the shear stress–strain curve.

Symbol: G

Measurement: PressureUnit: GPa

Note: Value should be greater than 0.

Formulas to find Shear Modulus

Poisson's Ratio

Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value should be between -1 to 0.5.

Formulas to find Poisson's Ratio

Other formulas in Ceramics and Composites category

Go Critical Fiber Length

l c = σ f \cdot \frac{d}{2 \cdot τ c}

Go Young's Modulus of porous material

E = E 0 \cdot (1 - (0.019 \cdot η v) + (0.00009 \cdot η v \cdot η v))

Go Schottky Defect Concentration

N S = N \cdot \exp (- \frac{Q s}{2 \cdot R \cdot T})

Go Young's Modulus of composite in longitudinal direction

E cl = E m \cdot (1 - V f) + E f \cdot V f

How to Evaluate Young's Modulus from shear modulus?

Young's Modulus from shear modulus evaluator uses Young's Modulus = 2*Shear Modulus*(1+Poisson's Ratio) to evaluate the Young's Modulus, Young's Modulus from shear modulus can be obtained via Poisson's ratio. Young's Modulus is denoted by E symbol.

How to evaluate Young's Modulus from shear modulus using this online evaluator? To use this online evaluator for Young's Modulus from shear modulus, enter Shear Modulus (G) & Poisson's Ratio (𝛎) and hit the calculate button.

FAQs on Young's Modulus from shear modulus

What is the formula to find Young's Modulus from shear modulus?

The formula of Young's Modulus from shear modulus is expressed as Young's Modulus = 2*Shear Modulus*(1+Poisson's Ratio). Here is an example- 6.5E+10 = 2*25000000000*(1+0.3).

How to calculate Young's Modulus from shear modulus?

With Shear Modulus (G) & Poisson's Ratio (𝛎) we can find Young's Modulus from shear modulus using the formula - Young's Modulus = 2*Shear Modulus*(1+Poisson's Ratio).

Can the Young's Modulus from shear modulus be negative?

No, the Young's Modulus from shear modulus, measured in Stiffness Constant cannot be negative.

Which unit is used to measure Young's Modulus from shear modulus?

Young's Modulus from shear modulus is usually measured using the Newton per Meter[N/m] for Stiffness Constant. Newton per Millimeter[N/m], Kilonewton per Millimeter[N/m] are the few other units in which Young's Modulus from shear modulus can be measured.

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