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Young's Modulus using Poisson's Ratio Formula

GoYoung's Modulus using Bulk 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 = \frac{3 \cdot σ t \cdot (1 - 2 \cdot 𝛎)}{ε v}

E - Young's Modulus?σ_t - Tensile Stress?𝛎 - Poisson's Ratio?ε_v - Volumetric Strain?

Young's Modulus using Poisson's Ratio Example

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Here is how the Young's Modulus using Poisson's Ratio equation looks like with Values.

Here is how the Young's Modulus using Poisson's Ratio equation looks like with Units.

Here is how the Young's Modulus using Poisson's Ratio equation looks like.

796800 = \frac{3 \cdot 16.6 \cdot (1 - 2 \cdot -0.3)}{0.0001}

796800MPa = \frac{3 \cdot 16.6MPa \cdot (1 - 2 \cdot -0.3)}{0.0001}

796800 = \frac{3 \cdot 16.6 \cdot (1 - 2 \cdot -0.3)}{0.0001}

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Young's Modulus using Poisson's Ratio Solution

Follow our step by step solution on how to calculate Young's Modulus using Poisson's Ratio?

FIRST Step Consider the formula

E = \frac{3 \cdot σ t \cdot (1 - 2 \cdot 𝛎)}{ε v}

Next Step Substitute values of Variables

∴

E = \frac{3 \cdot 16.6MPa \cdot (1 - 2 \cdot -0.3)}{0.0001}

Next Step Convert Units

∴

E = \frac{3 \cdot 1.7E+7Pa \cdot (1 - 2 \cdot -0.3)}{0.0001}

Next Step Prepare to Evaluate

∴

E = \frac{3 \cdot 1.7E+7 \cdot (1 - 2 \cdot -0.3)}{0.0001}

Next Step Evaluate

∴

E = 796800000000Pa

LAST Step Convert to Output's Unit

∴

E = 796800MPa

Young's Modulus using Poisson's Ratio 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: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Young's Modulus

Tensile Stress

The Tensile Stress is the external force per unit area of the material resulting in the stretch of the material.

Symbol: σ_t

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Tensile Stress

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

Volumetric Strain

The Volumetric Strain is the ratio of change in volume to original volume.

Symbol: ε_v

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Volumetric Strain

Other Formulas to find Young's Modulus

Go Young's Modulus using Bulk Modulus

E = 3 \cdot K \cdot (1 - 2 \cdot 𝛎)

Other formulas in Volumetric Strain category

Go Bulk Modulus given Direct Stress

K = \frac{σ}{ε v}

Go Bulk Modulus using Young's Modulus

K = \frac{E}{3 \cdot (1 - 2 \cdot 𝛎)}

Go Direct Stress for given Bulk Modulus and Volumetric Strain

σ = K \cdot ε v

Go Lateral Strain given Volumetric and Longitudinal Strain

ε L = - \frac{ε ln - ε v}{2}

How to Evaluate Young's Modulus using Poisson's Ratio?

Young's Modulus using Poisson's Ratio evaluator uses Young's Modulus = (3*Tensile Stress*(1-2*Poisson's Ratio))/Volumetric Strain to evaluate the Young's Modulus, Young's Modulus using Poisson's Ratio formula is defined as a relationship that describes the elasticity of materials by relating tensile stress to volumetric strain, incorporating Poisson's ratio. It provides insight into how materials deform under stress, which is crucial for engineering and material science applications. Young's Modulus is denoted by E symbol.

How to evaluate Young's Modulus using Poisson's Ratio using this online evaluator? To use this online evaluator for Young's Modulus using Poisson's Ratio, enter Tensile Stress (σ_t), Poisson's Ratio (𝛎) & Volumetric Strain (ε_v) and hit the calculate button.

FAQs on Young's Modulus using Poisson's Ratio

What is the formula to find Young's Modulus using Poisson's Ratio?

The formula of Young's Modulus using Poisson's Ratio is expressed as Young's Modulus = (3*Tensile Stress*(1-2*Poisson's Ratio))/Volumetric Strain. Here is an example- 0.7968 = (3*16600000*(1-2*(-0.3)))/0.0001.

How to calculate Young's Modulus using Poisson's Ratio?

With Tensile Stress (σ_t), Poisson's Ratio (𝛎) & Volumetric Strain (ε_v) we can find Young's Modulus using Poisson's Ratio using the formula - Young's Modulus = (3*Tensile Stress*(1-2*Poisson's Ratio))/Volumetric Strain.

What are the other ways to Calculate Young's Modulus?

Here are the different ways to Calculate Young's Modulus-

Young's Modulus=3*Bulk Modulus*(1-2*Poisson's Ratio)

Can the Young's Modulus using Poisson's Ratio be negative?

Yes, the Young's Modulus using Poisson's Ratio, measured in Stress can be negative.

Which unit is used to measure Young's Modulus using Poisson's Ratio?

Young's Modulus using Poisson's Ratio is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Young's Modulus using Poisson's Ratio can be measured.

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Young's Modulus using Poisson's Ratio Formula

​GoYoung's Modulus using Bulk Modulus Formula

Young's Modulus using Poisson's Ratio Example

Young's Modulus using Poisson's Ratio Solution

Young's Modulus using Poisson's Ratio Formula Elements

Other Formulas to find Young's Modulus

Other formulas in Volumetric Strain category

How to Evaluate Young's Modulus using Poisson's Ratio?

FAQs on Young's Modulus using Poisson's Ratio

Variable Name

GoYoung's Modulus using Bulk Modulus Formula