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Strain Energy due to Change in Volume with No Distortion Formula

GoStrain Energy due to Change in Volume given Volumetric Stress 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 \frac{(1 - 2 \cdot 𝛎) \cdot {σ v}^{2}}{E}

U_v - Strain Energy for Volume Change?𝛎 - Poisson's Ratio?σ_v - Stress for Volume Change?E - Young's Modulus of Specimen?

Strain Energy due to Change in Volume with No Distortion Example

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Here is how the Strain Energy due to Change in Volume with No Distortion equation looks like with Values.

Here is how the Strain Energy due to Change in Volume with No Distortion equation looks like with Units.

Here is how the Strain Energy due to Change in Volume with No Distortion equation looks like.

8.5389 = \frac{3}{2} \cdot \frac{(1 - 2 \cdot 0.3) \cdot 52^{2}}{190}

8.5389kJ/m³ = \frac{3}{2} \cdot \frac{(1 - 2 \cdot 0.3) \cdot {52N/mm²}^{2}}{190GPa}

8.5389 = \frac{3}{2} \cdot \frac{(1 - 2 \cdot 0.3) \cdot 52^{2}}{190}

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Strain Energy due to Change in Volume with No Distortion Solution

Follow our step by step solution on how to calculate Strain Energy due to Change in Volume with No Distortion?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

U v = \frac{3}{2} \cdot \frac{(1 - 2 \cdot 0.3) \cdot {52N/mm²}^{2}}{190GPa}

Next Step Convert Units

∴

U v = \frac{3}{2} \cdot \frac{(1 - 2 \cdot 0.3) \cdot {5.2E+7Pa}^{2}}{1.9E+11Pa}

Next Step Prepare to Evaluate

∴

U v = \frac{3}{2} \cdot \frac{(1 - 2 \cdot 0.3) \cdot {5.2E+7}^{2}}{1.9E+11}

Next Step Evaluate

∴

U v = 8538.94736842105J/m³

Next Step Convert to Output's Unit

∴

U v = 8.53894736842105kJ/m³

LAST Step Rounding Answer

∴

U v = 8.5389kJ/m³

Strain Energy due to Change in Volume with No Distortion 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

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

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

Young's Modulus of Specimen

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

Symbol: E

Measurement: PressureUnit: GPa

Note: Value should be greater than 0.

Formulas to find Young's Modulus of Specimen

Other Formulas to find Strain Energy for Volume Change

Go Strain Energy due to Change in Volume given Volumetric Stress

U v = \frac{3}{2} \cdot σ v \cdot ε v

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 with No Distortion?

Strain Energy due to Change in Volume with No Distortion evaluator uses Strain Energy for Volume Change = 3/2*((1-2*Poisson's Ratio)*Stress for Volume Change^2)/Young's Modulus of Specimen to evaluate the Strain Energy for Volume Change, Strain Energy due to Change in Volume with No Distortion formula 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 with No Distortion using this online evaluator? To use this online evaluator for Strain Energy due to Change in Volume with No Distortion, enter Poisson's Ratio (𝛎), Stress for Volume Change (σ_v) & Young's Modulus of Specimen (E) and hit the calculate button.

FAQs on Strain Energy due to Change in Volume with No Distortion

What is the formula to find Strain Energy due to Change in Volume with No Distortion?

The formula of Strain Energy due to Change in Volume with No Distortion is expressed as Strain Energy for Volume Change = 3/2*((1-2*Poisson's Ratio)*Stress for Volume Change^2)/Young's Modulus of Specimen. Here is an example- 8.5E-9 = 3/2*((1-2*0.3)*52000000^2)/190000000000.

How to calculate Strain Energy due to Change in Volume with No Distortion?

With Poisson's Ratio (𝛎), Stress for Volume Change (σ_v) & Young's Modulus of Specimen (E) we can find Strain Energy due to Change in Volume with No Distortion using the formula - Strain Energy for Volume Change = 3/2*((1-2*Poisson's Ratio)*Stress for Volume Change^2)/Young's Modulus of Specimen.

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*Stress for Volume Change*Strain for Volume Change
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 with No Distortion be negative?

No, the Strain Energy due to Change in Volume with No Distortion, measured in Energy Density cannot be negative.

Which unit is used to measure Strain Energy due to Change in Volume with No Distortion?

Strain Energy due to Change in Volume with No Distortion 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 with No Distortion can be measured.

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Strain Energy due to Change in Volume with No Distortion Formula

​GoStrain Energy due to Change in Volume given Volumetric Stress Formula

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

Strain Energy due to Change in Volume with No Distortion Example

Strain Energy due to Change in Volume with No Distortion Solution

Strain Energy due to Change in Volume with No Distortion 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 with No Distortion?

FAQs on Strain Energy due to Change in Volume with No Distortion

Variable Name

GoStrain Energy due to Change in Volume given Volumetric Stress Formula

GoStrain Energy due to Change in Volume given Principal Stresses Formula