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Distortion Strain Energy Formula

GoDistortion Strain Energy for Yielding Formula

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

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

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

Distortion Strain Energy Example

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Here is how the Distortion Strain Energy equation looks like with Values.

Here is how the Distortion Strain Energy equation looks like with Units.

Here is how the Distortion Strain Energy equation looks like.

1.5409 = \frac{(1 + 0.3)}{6 \cdot 190} \cdot ({(35.2 - 47)}^{2} + {(47 - 65)}^{2} + {(65 - 35.2)}^{2})

1.5409kJ/m³ = \frac{(1 + 0.3)}{6 \cdot 190GPa} \cdot ({(35.2N/mm² - 47N/mm²)}^{2} + {(47N/mm² - 65N/mm²)}^{2} + {(65N/mm² - 35.2N/mm²)}^{2})

1.5409 = \frac{(1 + 0.3)}{6 \cdot 190} \cdot ({(35.2 - 47)}^{2} + {(47 - 65)}^{2} + {(65 - 35.2)}^{2})

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Distortion Strain Energy Solution

Follow our step by step solution on how to calculate Distortion Strain Energy?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

U d = 1540.93333333333J/m³

Next Step Convert to Output's Unit

∴

U d = 1.54093333333333kJ/m³

LAST Step Rounding Answer

∴

U d = 1.5409kJ/m³

Distortion Strain Energy Formula Elements

Variables

Strain Energy for Distortion

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

Symbol: U_d

Measurement: Energy DensityUnit: kJ/m³

Note: Value should be greater than 0.

Formulas to find Strain Energy for Distortion

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 Distortion

Go Distortion Strain Energy for Yielding

U d = \frac{(1 + 𝛎)}{3 \cdot E} \cdot {σ y}^{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 Strain Energy due to Change in Volume given Volumetric Stress

U v = \frac{3}{2} \cdot σ v \cdot ε v

Go Stress due to Change in Volume with No Distortion

σ v = \frac{σ 1 + σ 2 + σ 3}{3}

How to Evaluate Distortion Strain Energy?

Distortion Strain Energy evaluator uses Strain Energy for Distortion = ((1+Poisson's Ratio))/(6*Young's Modulus of Specimen)*((First Principal Stress-Second Principal Stress)^2+(Second Principal Stress-Third Principal Stress)^2+(Third Principal Stress-First Principal Stress)^2) to evaluate the Strain Energy for Distortion, Distortion Strain Energy formula is defined as the energy stored in a body due to deformation. This energy is the energy stored when volume does not change with distortion. Strain Energy for Distortion is denoted by U_d symbol.

How to evaluate Distortion Strain Energy using this online evaluator? To use this online evaluator for Distortion Strain Energy, 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 Distortion Strain Energy

What is the formula to find Distortion Strain Energy?

The formula of Distortion Strain Energy is expressed as Strain Energy for Distortion = ((1+Poisson's Ratio))/(6*Young's Modulus of Specimen)*((First Principal Stress-Second Principal Stress)^2+(Second Principal Stress-Third Principal Stress)^2+(Third Principal Stress-First Principal Stress)^2). Here is an example- 0.00156 = ((1+0.3))/(6*190000000000)*((35200000-47000000)^2+(47000000-65000000)^2+(65000000-35200000)^2).

How to calculate Distortion Strain Energy?

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 Distortion Strain Energy using the formula - Strain Energy for Distortion = ((1+Poisson's Ratio))/(6*Young's Modulus of Specimen)*((First Principal Stress-Second Principal Stress)^2+(Second Principal Stress-Third Principal Stress)^2+(Third Principal Stress-First Principal Stress)^2).

What are the other ways to Calculate Strain Energy for Distortion?

Here are the different ways to Calculate Strain Energy for Distortion-

Strain Energy for Distortion=((1+Poisson's Ratio))/(3*Young's Modulus of Specimen)*Tensile Yield Strength^2

Can the Distortion Strain Energy be negative?

No, the Distortion Strain Energy, measured in Energy Density cannot be negative.

Which unit is used to measure Distortion Strain Energy?

Distortion Strain Energy 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 Distortion Strain Energy can be measured.

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Distortion Strain Energy Formula

​GoDistortion Strain Energy for Yielding Formula

Distortion Strain Energy Example

Distortion Strain Energy Solution

Distortion Strain Energy Formula Elements

Other Formulas to find Strain Energy for Distortion

Other formulas in Distortion Energy Theory category

How to Evaluate Distortion Strain Energy?

FAQs on Distortion Strain Energy

Variable Name

GoDistortion Strain Energy for Yielding Formula