Total Strain Energy per Unit Volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Strain Energy per Unit Volume = Strain Energy for Distortion+Strain Energy for Volume Change
UTotal = Ud+Uv
This formula uses 3 Variables
Variables Used
Total Strain Energy per Unit Volume - (Measured in Joule per Cubic Meter) - Total Strain Energy per Unit Volume is defined as the sum of strain energy corresponding to distortion with no change in volume and strain energy corresponding to volume change with no distortion.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Strain Energy for Distortion: 15 Kilojoule per Cubic Meter --> 15000 Joule per Cubic Meter (Check conversion here)
Strain Energy for Volume Change: 16 Kilojoule per Cubic Meter --> 16000 Joule per Cubic Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
UTotal = Ud+Uv --> 15000+16000
Evaluating ... ...
UTotal = 31000
STEP 3: Convert Result to Output's Unit
31000 Joule per Cubic Meter -->31 Kilojoule per Cubic Meter (Check conversion here)
FINAL ANSWER
31 Kilojoule per Cubic Meter <-- Total Strain Energy per Unit Volume
(Calculation completed in 00.004 seconds)

Credits

Created by Vaibhav Malani
National Institute of Technology (NIT), Tiruchirapalli
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Verified by Sagar S Kulkarni
Dayananda Sagar College of Engineering (DSCE), Bengaluru
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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

Total Strain Energy per Unit Volume Formula

Total Strain Energy per Unit Volume = Strain Energy for Distortion+Strain Energy for Volume Change
UTotal = Ud+Uv

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 also 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 Total Strain Energy per Unit Volume?

Total Strain Energy per Unit Volume calculator uses Total Strain Energy per Unit Volume = Strain Energy for Distortion+Strain Energy for Volume Change to calculate the Total Strain Energy per Unit Volume, Total strain energy per unit volume formula is defined as the sum of strain energy corresponding to distortion with no change in volume and strain energy corresponding to volume change with no distortion. Total Strain Energy per Unit Volume is denoted by UTotal symbol.

How to calculate Total Strain Energy per Unit Volume using this online calculator? To use this online calculator for Total Strain Energy per Unit Volume, enter Strain Energy for Distortion (Ud) & Strain Energy for Volume Change (Uv) and hit the calculate button. Here is how the Total Strain Energy per Unit Volume calculation can be explained with given input values -> 3.1E-8 = 15000+16000.

FAQ

What is Total Strain Energy per Unit Volume?
Total strain energy per unit volume formula is defined as the sum of strain energy corresponding to distortion with no change in volume and strain energy corresponding to volume change with no distortion and is represented as UTotal = Ud+Uv or Total Strain Energy per Unit Volume = Strain Energy for Distortion+Strain Energy for Volume Change. Strain Energy for Distortion with no volume change is defined as the energy stored in the body per unit volume due to deformation & Strain Energy for Volume Change with no distortion is defined as the energy stored in the body per unit volume due to deformation.
How to calculate Total Strain Energy per Unit Volume?
Total strain energy per unit volume formula is defined as the sum of strain energy corresponding to distortion with no change in volume and strain energy corresponding to volume change with no distortion is calculated using Total Strain Energy per Unit Volume = Strain Energy for Distortion+Strain Energy for Volume Change. To calculate Total Strain Energy per Unit Volume, you need Strain Energy for Distortion (Ud) & Strain Energy for Volume Change (Uv). With our tool, you need to enter the respective value for Strain Energy for Distortion & Strain Energy for Volume Change 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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