Strain Energy due to Change in Volume given Principal Stresses 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 Volume Change with no distortion is defined as the energy stored in the body per unit volume due to deformation.ⓘ Strain Energy due to Change in Volume given Principal Stresses [U_v]

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Strain Energy due to Change in Volume given Principal Stresses Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Strain Energy for Volume Change - (Measured in Joule per Cubic Meter) - Strain Energy for Volume Change with no distortion 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_v = ((1-2*𝛎))/(6*E)*(σ₁+σ₂+σ₃)^2 --> ((1-2*0.3))/(6*190000000000)*(35000000+47000000+65000000)^2

Evaluating ... ...

U_v = 7582.1052631579

STEP 3: Convert Result to Output's Unit

7582.1052631579 Joule per Cubic Meter -->7.58210526315789 Kilojoule per Cubic Meter (Check conversion here)

FINAL ANSWER

7.58210526315789 ≈ 7.582105 Kilojoule per Cubic Meter <-- Strain Energy for Volume Change

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Machine Design » Design Against Static Load » Theories of Failure » Distortion Energy Theory » Strain Energy due to Change in Volume given Principal Stresses

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

Vaibhav Malani has created this Calculator and 600+ more calculators!

Verified by Sagar S Kulkarni

Dayananda Sagar College of Engineering (DSCE), Bengaluru

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< Distortion Energy Theory Calculators

Stress due to Change in Volume with No Distortion

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

Total Strain Energy per Unit Volume

LaTeX 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

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

Shear Yield Strength by Maximum Distortion Energy Theory

LaTeX Go Shear Yield Strength = 0.577*Tensile Yield Strength

Strain Energy due to Change in Volume given Principal Stresses Formula

LaTeX Go

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 Strain Energy due to Change in Volume given Principal Stresses?

Strain Energy due to Change in Volume given Principal Stresses calculator 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 calculate 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 calculate Strain Energy due to Change in Volume given Principal Stresses using this online calculator? To use this online calculator 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. Here is how the Strain Energy due to Change in Volume given Principal Stresses calculation can be explained with given input values -> 7.6E-9 = ((1-2*0.3))/(6*190000000000)*(35000000+47000000+65000000)^2.

FAQ

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

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 and is represented as U_v = ((1-2*𝛎))/(6*E)*(σ₁+σ₂+σ₃)^2 or 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. 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 Strain Energy due to Change in Volume given Principal Stresses?

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 is calculated using 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 calculate Strain Energy due to Change in Volume given Principal Stresses, 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 Volume Change?

In this formula, Strain Energy for Volume Change uses Poisson's Ratio, Young's Modulus of Specimen, First Principal Stress, Second Principal Stress & Third Principal Stress. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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