Volumetric Strain 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 for Volume Change is defined as the strain in the specimen for a given volume change.ⓘ Volumetric Strain with No Distortion [ε_v]

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Formula

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Volumetric Strain with No Distortion

Formula

`"ε"_{"v"} = ((1-2*"𝛎")*"σ"_{"v"})/"E"`

Example

`"0.000109"=((1-2*"0.3")*"52N/mm²")/"190GPa"`

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Volumetric Strain with No Distortion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Strain for Volume Change = ((1-2*Poisson's Ratio)*Stress for Volume Change)/Young's Modulus of Specimen
ε_v = ((1-2*𝛎)*σ_v)/E
This formula uses 4 Variables

Variables Used

Strain for Volume Change - Strain for Volume Change is defined as the strain in the specimen for a given 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.
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

ε_v = ((1-2*𝛎)*σ_v)/E --> ((1-2*0.3)*52000000)/190000000000

Evaluating ... ...

ε_v = 0.000109473684210526

STEP 3: Convert Result to Output's Unit

0.000109473684210526 --> No Conversion Required

FINAL ANSWER

0.000109473684210526 ≈ 0.000109 <-- Strain for Volume Change

(Calculation completed in 00.004 seconds)

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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!

< 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

Volumetric Strain with No Distortion Formula

Strain for Volume Change = ((1-2*Poisson's Ratio)*Stress for Volume Change)/Young's Modulus of Specimen
ε_v = ((1-2*𝛎)*σ_v)/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 Volumetric Strain with No Distortion?

Volumetric Strain with No Distortion calculator uses Strain for Volume Change = ((1-2*Poisson's Ratio)*Stress for Volume Change)/Young's Modulus of Specimen to calculate the Strain for Volume Change, Volumetric Strain with No Distortion formula is defined as the amount of deformation experienced by the body in the direction of force applied, divided by the initial dimensions of the body This is the strain when volume changes with zero distortion. Strain for Volume Change is denoted by ε_v symbol.

How to calculate Volumetric Strain with No Distortion using this online calculator? To use this online calculator for Volumetric Strain 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 Volumetric Strain with No Distortion calculation can be explained with given input values -> 0.000109 = ((1-2*0.3)*52000000)/190000000000.

FAQ

What is Volumetric Strain with No Distortion?

Volumetric Strain with No Distortion formula is defined as the amount of deformation experienced by the body in the direction of force applied, divided by the initial dimensions of the body This is the strain when volume changes with zero distortion and is represented as ε_v = ((1-2*𝛎)*σ_v)/E or Strain for Volume Change = ((1-2*Poisson's Ratio)*Stress for Volume Change)/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 Volumetric Strain with No Distortion?

Volumetric Strain with No Distortion formula is defined as the amount of deformation experienced by the body in the direction of force applied, divided by the initial dimensions of the body This is the strain when volume changes with zero distortion is calculated using Strain for Volume Change = ((1-2*Poisson's Ratio)*Stress for Volume Change)/Young's Modulus of Specimen. To calculate Volumetric Strain 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.

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