Strain Energy due to Change in Volume with No Distortion 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%
✖Stress for Volume Change is defined as the stress in the specimen for a given volume change.ⓘ Stress for Volume Change [σ_v]			+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%

✖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 with No Distortion [U_v]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Theories of Failure Formulas PDF PDF Image

Strain Energy due to Change in Volume with No Distortion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Strain Energy for Volume Change = 3/2*((1-2*Poisson's Ratio)*Stress for Volume Change^2)/Young's Modulus of Specimen
U_v = 3/2*((1-2*𝛎)*σ_v^2)/E
This formula uses 4 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.
Stress for Volume Change - (Measured in Pascal) - Stress for Volume Change is defined as the stress in the specimen for a given volume change.
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.

STEP 1: Convert Input(s) to Base Unit

Poisson's Ratio: 0.3 --> No Conversion Required
Stress for Volume Change: 52 Newton per Square Millimeter --> 52000000 Pascal (Check conversion here)
Young's Modulus of Specimen: 190 Gigapascal --> 190000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U_v = 3/2*((1-2*𝛎)*σ_v^2)/E --> 3/2*((1-2*0.3)*52000000^2)/190000000000

Evaluating ... ...

U_v = 8538.94736842105

STEP 3: Convert Result to Output's Unit

8538.94736842105 Joule per Cubic Meter -->8.53894736842105 Kilojoule per Cubic Meter (Check conversion here)

FINAL ANSWER

8.53894736842105 ≈ 8.538947 Kilojoule per Cubic Meter <-- Strain Energy for Volume Change

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Mechanical » Machine Design » Design Against Static Load » Theories of Failure » Distortion Energy Theory » Strain Energy due to Change in Volume with No Distortion

Credits

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

Sagar S Kulkarni has verified this Calculator and 200+ more calculators!

< 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

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

Total Strain Energy per Unit Volume

LaTeX Go Total Strain Energy = Strain Energy for Distortion+Strain Energy 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 with No Distortion Formula

LaTeX Go

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

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 with No Distortion?

Strain Energy due to Change in Volume with No Distortion calculator uses Strain Energy for Volume Change = 3/2*((1-2*Poisson's Ratio)*Stress for Volume Change^2)/Young's Modulus of Specimen to calculate 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 calculate Strain Energy due to Change in Volume with No Distortion using this online calculator? To use this online calculator 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. Here is how the Strain Energy due to Change in Volume with No Distortion calculation can be explained with given input values -> 8.5E-9 = 3/2*((1-2*0.3)*52000000^2)/190000000000.

FAQ

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

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 and is represented as U_v = 3/2*((1-2*𝛎)*σ_v^2)/E or Strain Energy for Volume Change = 3/2*((1-2*Poisson's Ratio)*Stress for Volume Change^2)/Young's Modulus of Specimen. 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, Stress for Volume Change is defined as the stress in the specimen for a given volume change & Young's Modulus of Specimen is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

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

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 is calculated using Strain Energy for Volume Change = 3/2*((1-2*Poisson's Ratio)*Stress for Volume Change^2)/Young's Modulus of Specimen. To calculate Strain Energy due to Change in Volume with No Distortion, you need Poisson's Ratio (𝛎), Stress for Volume Change (σ_v) & Young's Modulus of Specimen (E). With our tool, you need to enter the respective value for Poisson's Ratio, Stress for Volume Change & Young's Modulus of Specimen 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, Stress for Volume Change & Young's Modulus of Specimen. 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 = ((1-2*Poisson's Ratio))/(6*Young's Modulus of Specimen)*(First Principal Stress+Second Principal Stress+Third Principal Stress)^2

Home

FREE PDFs

🔍 Search