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Strain Energy due to Change in Volume given Volumetric Stress Formula

GoStrain Energy due to Change in Volume with No Distortion Formula

GoStrain Energy due to Change in Volume given Principal Stresses Formula

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Strain Energy for Volume Change with no distortion is defined as the energy stored in the body per unit volume due to deformation. Check FAQs

U v = \frac{3}{2} \cdot σ v \cdot ε v

U_v - Strain Energy for Volume Change?σ_v - Stress for Volume Change?ε_v - Strain for Volume Change?

Strain Energy due to Change in Volume given Volumetric Stress Example

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Here is how the Strain Energy due to Change in Volume given Volumetric Stress equation looks like with Values.

Here is how the Strain Energy due to Change in Volume given Volumetric Stress equation looks like with Units.

Here is how the Strain Energy due to Change in Volume given Volumetric Stress equation looks like.

101.4 = \frac{3}{2} \cdot 52 \cdot 0.0013

101.4kJ/m³ = \frac{3}{2} \cdot 52N/mm² \cdot 0.0013

101.4 = \frac{3}{2} \cdot 52 \cdot 0.0013

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Strain Energy due to Change in Volume given Volumetric Stress Solution

Follow our step by step solution on how to calculate Strain Energy due to Change in Volume given Volumetric Stress?

FIRST Step Consider the formula

U v = \frac{3}{2} \cdot σ v \cdot ε v

Next Step Substitute values of Variables

∴

U v = \frac{3}{2} \cdot 52N/mm² \cdot 0.0013

Next Step Convert Units

∴

U v = \frac{3}{2} \cdot 5.2E+7Pa \cdot 0.0013

Next Step Prepare to Evaluate

∴

U v = \frac{3}{2} \cdot 5.2E+7 \cdot 0.0013

Next Step Evaluate

∴

U v = 101400J/m³

LAST Step Convert to Output's Unit

∴

U v = 101.4kJ/m³

Strain Energy due to Change in Volume given Volumetric Stress Formula Elements

Variables

Strain Energy for Volume Change

Strain Energy for Volume Change with no distortion is defined as the energy stored in the body per unit volume due to deformation.

Symbol: U_v

Measurement: Energy DensityUnit: kJ/m³

Note: Value should be greater than 0.

Formulas to find Strain Energy for Volume Change

Stress for Volume Change

Stress for Volume Change is defined as the stress in the specimen for a given volume change.

Symbol: σ_v

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Stress for Volume Change

Strain for Volume Change

Strain for Volume Change is defined as the strain in the specimen for a given volume change.

Symbol: ε_v

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Strain for Volume Change

Other Formulas to find Strain Energy for Volume Change

Go Strain Energy due to Change in Volume with No Distortion

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

Go Strain Energy due to Change in Volume given Principal Stresses

U v = \frac{(1 - 2 \cdot 𝛎)}{6 \cdot E} \cdot {(σ 1 + σ 2 + σ 3)}^{2}

Other formulas in Distortion Energy Theory category

Go Shear Yield Strength by Maximum Distortion Energy Theory

S sy = 0.577 \cdot σ y

Go Total Strain Energy per Unit Volume

U Total = U d + U v

Go Stress due to Change in Volume with No Distortion

σ v = \frac{σ 1 + σ 2 + σ 3}{3}

Go Volumetric Strain with No Distortion

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

How to Evaluate Strain Energy due to Change in Volume given Volumetric Stress?

Strain Energy due to Change in Volume given Volumetric Stress evaluator uses Strain Energy for Volume Change = 3/2*Stress for Volume Change*Strain for Volume Change to evaluate the Strain Energy for Volume Change, Strain Energy due to Change in Volume given Volumetric Stress is defined as the energy stored in a body due to deformation. This energy is the energy stored when volume changes with zero distortion. Strain Energy for Volume Change is denoted by U_v symbol.

How to evaluate Strain Energy due to Change in Volume given Volumetric Stress using this online evaluator? To use this online evaluator for Strain Energy due to Change in Volume given Volumetric Stress, enter Stress for Volume Change (σ_v) & Strain for Volume Change (ε_v) and hit the calculate button.

FAQs on Strain Energy due to Change in Volume given Volumetric Stress

What is the formula to find Strain Energy due to Change in Volume given Volumetric Stress?

The formula of Strain Energy due to Change in Volume given Volumetric Stress is expressed as Strain Energy for Volume Change = 3/2*Stress for Volume Change*Strain for Volume Change. Here is an example- 1E-7 = 3/2*52000000*0.0013.

How to calculate Strain Energy due to Change in Volume given Volumetric Stress?

With Stress for Volume Change (σ_v) & Strain for Volume Change (ε_v) we can find Strain Energy due to Change in Volume given Volumetric Stress using the formula - Strain Energy for Volume Change = 3/2*Stress for Volume Change*Strain for Volume Change.

What are the other ways to Calculate Strain Energy for Volume Change?

Here are the different ways to Calculate Strain Energy for Volume Change-

Strain Energy for Volume Change=3/2*((1-2*Poisson's Ratio)*Stress for Volume Change^2)/Young's Modulus of Specimen
Strain Energy for Volume Change=((1-2*Poisson's Ratio))/(6*Young's Modulus of Specimen)*(First Principal Stress+Second Principal Stress+Third Principal Stress)^2

Can the Strain Energy due to Change in Volume given Volumetric Stress be negative?

No, the Strain Energy due to Change in Volume given Volumetric Stress, measured in Energy Density cannot be negative.

Which unit is used to measure Strain Energy due to Change in Volume given Volumetric Stress?

Strain Energy due to Change in Volume given Volumetric Stress is usually measured using the Kilojoule per Cubic Meter[kJ/m³] for Energy Density. Joule per Cubic Meter[kJ/m³], Megajoule per Cubic Meter[kJ/m³] are the few other units in which Strain Energy due to Change in Volume given Volumetric Stress can be measured.

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Strain Energy due to Change in Volume given Volumetric Stress Formula

​GoStrain Energy due to Change in Volume with No Distortion Formula

​GoStrain Energy due to Change in Volume given Principal Stresses Formula

Strain Energy due to Change in Volume given Volumetric Stress Example

Strain Energy due to Change in Volume given Volumetric Stress Solution

Strain Energy due to Change in Volume given Volumetric Stress Formula Elements

Other Formulas to find Strain Energy for Volume Change

Other formulas in Distortion Energy Theory category

How to Evaluate Strain Energy due to Change in Volume given Volumetric Stress?

FAQs on Strain Energy due to Change in Volume given Volumetric Stress

Variable Name

GoStrain Energy due to Change in Volume with No Distortion Formula

GoStrain Energy due to Change in Volume given Principal Stresses Formula