Distortion Strain Energy Calculator

✖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.ⓘ Poisson's Ratio [𝛎]			+10% -10%
✖Young's Modulus of Specimen is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus of Specimen [E]			+10% -10%
✖First Principal Stress is the first one among the two or three principal stresses acting on a biaxial or triaxial stressed component.ⓘ First Principal Stress [σ₁]			+10% -10%
✖Second Principal Stress is the second one among the two or three principal stresses acting on a biaxial or triaxial stressed component.ⓘ Second Principal Stress [σ₂]			+10% -10%
✖Third Principal Stress is the third one among the two or three principal stresses acting on a biaxial or triaxial stressed component.ⓘ Third Principal Stress [σ₃]			+10% -10%

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

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Formula

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Distortion Strain Energy

Formula

`"U"_{"d"} = ((1+"𝛎"))/(6*"E")*(("σ"_{"1"}-"σ"_{"2"})^2+("σ"_{"2"}-"σ"_{"3"})^2+("σ"_{"3"}-"σ"_{"1"})^2)`

Example

`"1.56kJ/m³"=((1+"0.3"))/(6*"190GPa")*(("35N/mm²"-"47N/mm²")^2+("47N/mm²"-"65N/mm²")^2+("65N/mm²"-"35N/mm²")^2)`

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Distortion Strain Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
U_d = ((1+𝛎))/(6*E)*((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2)
This formula uses 6 Variables

Variables Used

Strain Energy for Distortion - (Measured in Joule per Cubic Meter) - Strain Energy for Distortion with no volume change is defined as the energy stored in the body per unit volume due to deformation.
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.
Young's Modulus of Specimen - (Measured in Pascal) - Young's Modulus of Specimen is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
First Principal Stress - (Measured in Pascal) - First Principal Stress is the first one among the two or three principal stresses acting on a biaxial or triaxial stressed component.
Second Principal Stress - (Measured in Pascal) - Second Principal Stress is the second one among the two or three principal stresses acting on a biaxial or triaxial stressed component.
Third Principal Stress - (Measured in Pascal) - Third Principal Stress is the third one among the two or three principal stresses acting on a biaxial or triaxial stressed component.

STEP 1: Convert Input(s) to Base Unit

Poisson's Ratio: 0.3 --> No Conversion Required
Young's Modulus of Specimen: 190 Gigapascal --> 190000000000 Pascal (Check conversion here)
First Principal Stress: 35 Newton per Square Millimeter --> 35000000 Pascal (Check conversion here)
Second Principal Stress: 47 Newton per Square Millimeter --> 47000000 Pascal (Check conversion here)
Third Principal Stress: 65 Newton per Square Millimeter --> 65000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U_d = ((1+𝛎))/(6*E)*((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2) --> ((1+0.3))/(6*190000000000)*((35000000-47000000)^2+(47000000-65000000)^2+(65000000-35000000)^2)

Evaluating ... ...

U_d = 1560

STEP 3: Convert Result to Output's Unit

1560 Joule per Cubic Meter -->1.56 Kilojoule per Cubic Meter (Check conversion here)

FINAL ANSWER

1.56 Kilojoule per Cubic Meter <-- Strain Energy for Distortion

(Calculation completed in 00.008 seconds)

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

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Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 13 Distortion Energy Theory Calculators

Distortion Strain Energy

Go 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)

Tensile Yield Strength by Distortion Energy Theorem Considering Factor of Safety

Go Tensile Yield Strength = Factor of Safety*sqrt(1/2*((First Principal Stress-Second Principal Stress)^2+(Second Principal Stress-Third Principal Stress)^2+(Third Principal Stress-First Principal Stress)^2))

Tensile Yield Strength by Distortion Energy Theorem

Go Tensile Yield Strength = sqrt(1/2*((First Principal Stress-Second Principal Stress)^2+(Second Principal Stress-Third Principal Stress)^2+(Third Principal Stress-First Principal Stress)^2))

Tensile Yield Strength for Biaxial Stress by Distortion Energy Theorem Considering Factor of Safety

Go Tensile Yield Strength = Factor of Safety*sqrt(First Principal Stress^2+Second Principal Stress^2-First Principal Stress*Second Principal Stress)

Strain Energy due to Change in Volume given Principal Stresses

Go 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

Strain Energy due to Change in Volume with No Distortion

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

Distortion Strain Energy for Yielding

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

Volumetric Strain with No Distortion

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

Stress due to Change in Volume with No Distortion

Go Stress for Volume Change = (First Principal Stress+Second Principal Stress+Third Principal Stress)/3

Total Strain Energy per Unit Volume

Go Total Strain Energy per Unit Volume = Strain Energy for Distortion+Strain Energy for Volume Change

Strain Energy due to Change in Volume given Volumetric Stress

Go Strain Energy for Volume Change = 3/2*Stress for Volume Change*Strain for Volume Change

Shear Yield Strength by Maximum Distortion Energy Theorem

Go Shear Yield Strength = 0.577*Tensile Yield Strength

Shear Yield Strength by Maximum Distortion Energy Theory

Go Shear Yield Strength = 0.577*Tensile Yield Strength

Distortion Strain Energy Formula

What is strain energy?

Strain energy is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation. When the applied force is released, the whole system returns to its original shape. It is usually denoted by U.

How to Calculate Distortion Strain Energy?

Distortion Strain Energy calculator 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 calculate 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 calculate Distortion Strain Energy using this online calculator? To use this online calculator 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. Here is how the Distortion Strain Energy calculation can be explained with given input values -> 1.6E-9 = ((1+0.3))/(6*190000000000)*((35000000-47000000)^2+(47000000-65000000)^2+(65000000-35000000)^2).

FAQ

What is Distortion Strain Energy?

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 and is represented as U_d = ((1+𝛎))/(6*E)*((σ₁-σ₂)^2+(σ₂-σ₃)^2+(σ₃-σ₁)^2) or 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). 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, Young's Modulus of Specimen is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, First Principal Stress is the first one among the two or three principal stresses acting on a biaxial or triaxial stressed component, Second Principal Stress is the second one among the two or three principal stresses acting on a biaxial or triaxial stressed component & Third Principal Stress is the third one among the two or three principal stresses acting on a biaxial or triaxial stressed component.

How to calculate Distortion Strain Energy?

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 is calculated using 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 calculate Distortion Strain Energy, you need Poisson's Ratio (𝛎), Young's Modulus of Specimen (E), First Principal Stress (σ₁), Second Principal Stress (σ₂) & Third Principal Stress (σ₃). With our tool, you need to enter the respective value for Poisson's Ratio, Young's Modulus of Specimen, First Principal Stress, Second Principal Stress & Third Principal Stress and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Strain Energy for Distortion?

In this formula, Strain Energy for Distortion uses Poisson's Ratio, Young's Modulus of Specimen, First Principal Stress, Second Principal Stress & Third Principal Stress. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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