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Volumetric Strain using Young's Modulus and Poisson's Ratio Formula

GoVolumetric Strain given Bulk Modulus Formula

GoVolumetric Strain given Change in Length Formula

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

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

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

Volumetric Strain using Young's Modulus and Poisson's Ratio Example

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

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

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

0.004 = \frac{3 \cdot 16.6 \cdot (1 - 2 \cdot -0.3)}{20000}

0.004 = \frac{3 \cdot 16.6MPa \cdot (1 - 2 \cdot -0.3)}{20000MPa}

0.004 = \frac{3 \cdot 16.6 \cdot (1 - 2 \cdot -0.3)}{20000}

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Volumetric Strain using Young's Modulus and Poisson's Ratio Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ε v = \frac{3 \cdot 16.6MPa \cdot (1 - 2 \cdot -0.3)}{20000MPa}

Next Step Convert Units

∴

ε v = \frac{3 \cdot 1.7E+7Pa \cdot (1 - 2 \cdot -0.3)}{2E+10Pa}

Next Step Prepare to Evaluate

∴

ε v = \frac{3 \cdot 1.7E+7 \cdot (1 - 2 \cdot -0.3)}{2E+10}

Next Step Evaluate

∴

ε v = 0.003984

LAST Step Rounding Answer

∴

ε v = 0.004

Volumetric Strain using Young's Modulus and Poisson's Ratio Formula Elements

Variables

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

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

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

Other Formulas to find Volumetric Strain

Go Volumetric Strain given Bulk Modulus

ε v = \frac{σ}{K}

Go Volumetric Strain given Change in Length

ε v = (\frac{Δl}{l}) \cdot (1 - 2 \cdot 𝛎)

Go Volumetric Strain given Change in Length, Breadth and Width

ε v = \frac{Δl}{l} + \frac{Δb}{b} + \frac{Δd}{d}

Go Volumetric Strain given Longitudinal and Lateral Strain

ε v = ε ln + 2 \cdot ε L

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 Volumetric Strain using Young's Modulus and Poisson's Ratio?

Volumetric Strain using Young's Modulus and Poisson's Ratio evaluator uses Volumetric Strain = (3*Tensile Stress*(1-2*Poisson's Ratio))/Young's Modulus to evaluate the Volumetric Strain, Volumetric Strain using Young's Modulus and Poisson's Ratio formula is defined as a relationship that describes how a material deforms in volume under applied stress, taking into account its elastic properties and the interplay between longitudinal and lateral strains. It is essential in understanding material behavior under load. Volumetric Strain is denoted by ε_v symbol.

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

FAQs on Volumetric Strain using Young's Modulus and Poisson's Ratio

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

The formula of Volumetric Strain using Young's Modulus and Poisson's Ratio is expressed as Volumetric Strain = (3*Tensile Stress*(1-2*Poisson's Ratio))/Young's Modulus. Here is an example- 0.003984 = (3*16600000*(1-2*(-0.3)))/20000000000.

How to calculate Volumetric Strain using Young's Modulus and Poisson's Ratio?

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

What are the other ways to Calculate Volumetric Strain?

Here are the different ways to Calculate Volumetric Strain-

Volumetric Strain=Direct Stress/Bulk Modulus
Volumetric Strain=(Change in Length/Length of Section)*(1-2*Poisson's Ratio)
Volumetric Strain=Change in Length/Length of Section+Change in Breadth/Breadth of Bar+Change in Depth/Depth of Bar

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Volumetric Strain using Young's Modulus and Poisson's Ratio Formula

​GoVolumetric Strain given Bulk Modulus Formula

​GoVolumetric Strain given Change in Length Formula

Volumetric Strain using Young's Modulus and Poisson's Ratio Example

Volumetric Strain using Young's Modulus and Poisson's Ratio Solution

Volumetric Strain using Young's Modulus and Poisson's Ratio Formula Elements

Other Formulas to find Volumetric Strain

Other formulas in Volumetric Strain category

How to Evaluate Volumetric Strain using Young's Modulus and Poisson's Ratio?

FAQs on Volumetric Strain using Young's Modulus and Poisson's Ratio

Variable Name

GoVolumetric Strain given Bulk Modulus Formula

GoVolumetric Strain given Change in Length Formula