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Strain Energy due to Change in Volume given Principal Stresses Formula

GoStrain Energy due to Change in Volume given Volumetric Stress Formula

GoStrain Energy due to Change in Volume with No Distortion 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{(1 - 2 \cdot 𝛎)}{6 \cdot E} \cdot {(σ 1 + σ 2 + σ 3)}^{2}

U_v - Strain Energy for Volume Change?𝛎 - Poisson's Ratio?E - Young's Modulus of Specimen?σ₁ - First Principal Stress?σ₂ - Second Principal Stress?σ₃ - Third Principal Stress?

Strain Energy due to Change in Volume given Principal Stresses Example

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

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

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

7.6028 = \frac{(1 - 2 \cdot 0.3)}{6 \cdot 190} \cdot {(35.2 + 47 + 65)}^{2}

7.6028kJ/m³ = \frac{(1 - 2 \cdot 0.3)}{6 \cdot 190GPa} \cdot {(35.2N/mm² + 47N/mm² + 65N/mm²)}^{2}

7.6028 = \frac{(1 - 2 \cdot 0.3)}{6 \cdot 190} \cdot {(35.2 + 47 + 65)}^{2}

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Strain Energy due to Change in Volume given Principal Stresses Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

U v = \frac{(1 - 2 \cdot 0.3)}{6 \cdot 190GPa} \cdot {(35.2N/mm² + 47N/mm² + 65N/mm²)}^{2}

Next Step Convert Units

∴

U v = \frac{(1 - 2 \cdot 0.3)}{6 \cdot 1.9E+11Pa} \cdot {(3.5E+7Pa + 4.7E+7Pa + 6.5E+7Pa)}^{2}

Next Step Prepare to Evaluate

∴

U v = \frac{(1 - 2 \cdot 0.3)}{6 \cdot 1.9E+11} \cdot {(3.5E+7 + 4.7E+7 + 6.5E+7)}^{2}

Next Step Evaluate

∴

U v = 7602.75087719298J/m³

Next Step Convert to Output's Unit

∴

U v = 7.60275087719298kJ/m³

LAST Step Rounding Answer

∴

U v = 7.6028kJ/m³

Strain Energy due to Change in Volume given Principal Stresses 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

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

First Principal Stress

First Principal Stress is the first one among the two or three principal stresses acting on a biaxial or triaxial stressed component.

Symbol: σ₁

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find First Principal Stress

Second Principal Stress

Second Principal Stress is the second one among the two or three principal stresses acting on a biaxial or triaxial stressed component.

Symbol: σ₂

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Second Principal Stress

Third Principal Stress

Third Principal Stress is the third one among the two or three principal stresses acting on a biaxial or triaxial stressed component.

Symbol: σ₃

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Third Principal Stress

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 with No Distortion

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

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 Principal Stresses?

Strain Energy due to Change in Volume given Principal Stresses evaluator uses 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 to evaluate the Strain Energy for Volume Change, Strain Energy due to Change in Volume given Principal Stresses 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 given Principal Stresses using this online evaluator? To use this online evaluator for Strain Energy due to Change in Volume given Principal Stresses, enter Poisson's Ratio (𝛎), Young's Modulus of Specimen (E), First Principal Stress (σ₁), Second Principal Stress (σ₂) & Third Principal Stress (σ₃) and hit the calculate button.

FAQs on Strain Energy due to Change in Volume given Principal Stresses

What is the formula to find Strain Energy due to Change in Volume given Principal Stresses?

The formula of Strain Energy due to Change in Volume given Principal Stresses is expressed as 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. Here is an example- 0.007582 = ((1-2*0.3))/(6*190000000000)*(35200000+47000000+65000000)^2.

How to calculate Strain Energy due to Change in Volume given Principal Stresses?

With Poisson's Ratio (𝛎), Young's Modulus of Specimen (E), First Principal Stress (σ₁), Second Principal Stress (σ₂) & Third Principal Stress (σ₃) we can find Strain Energy due to Change in Volume given Principal Stresses using the formula - 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.

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=3/2*((1-2*Poisson's Ratio)*Stress for Volume Change^2)/Young's Modulus of Specimen

Can the Strain Energy due to Change in Volume given Principal Stresses be negative?

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

Which unit is used to measure Strain Energy due to Change in Volume given Principal Stresses?

Strain Energy due to Change in Volume given Principal Stresses 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 Principal Stresses can be measured.

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Strain Energy due to Change in Volume given Principal Stresses Formula

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

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

Strain Energy due to Change in Volume given Principal Stresses Example

Strain Energy due to Change in Volume given Principal Stresses Solution

Strain Energy due to Change in Volume given Principal Stresses 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 Principal Stresses?

FAQs on Strain Energy due to Change in Volume given Principal Stresses

Variable Name

GoStrain Energy due to Change in Volume given Volumetric Stress Formula

GoStrain Energy due to Change in Volume with No Distortion Formula