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Strain Energy Stored per Unit Volume Formula

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Strain Energy Density is the energy dissipated per unit volume during the strain-hardening process, is equal to the area enclosed by the ascending branch of the stress-strain curve. Check FAQs

U density = \frac{σ^{2}}{2 \cdot E}

U_density - Strain Energy Density?σ - Direct Stress?E - Young's Modulus?

Strain Energy Stored per Unit Volume Example

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Here is how the Strain Energy Stored per Unit Volume equation looks like with Values.

Here is how the Strain Energy Stored per Unit Volume equation looks like with Units.

Here is how the Strain Energy Stored per Unit Volume equation looks like.

17929.21 = \frac{{26.78}^{2}}{2 \cdot 20000}

17929.21J/m³ = \frac{{26.78MPa}^{2}}{2 \cdot 20000MPa}

17929.21 = \frac{{26.78}^{2}}{2 \cdot 20000}

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Strain Energy Stored per Unit Volume Solution

Follow our step by step solution on how to calculate Strain Energy Stored per Unit Volume?

FIRST Step Consider the formula

U density = \frac{σ^{2}}{2 \cdot E}

Next Step Substitute values of Variables

∴

U density = \frac{{26.78MPa}^{2}}{2 \cdot 20000MPa}

Next Step Convert Units

∴

U density = \frac{{2.7E+7Pa}^{2}}{2 \cdot 2E+10Pa}

Next Step Prepare to Evaluate

∴

U density = \frac{{2.7E+7}^{2}}{2 \cdot 2E+10}

LAST Step Evaluate

∴

U density = 17929.21J/m³

Strain Energy Stored per Unit Volume Formula Elements

Variables

Strain Energy Density

Strain Energy Density is the energy dissipated per unit volume during the strain-hardening process, is equal to the area enclosed by the ascending branch of the stress-strain curve.

Symbol: U_density

Measurement: Energy DensityUnit: J/m³

Note: Value should be greater than 0.

Formulas to find Strain Energy Density

Direct Stress

Direct Stress is the stress developed due to force applied which is parallel or collinear to the axis of the component.

Symbol: σ

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Direct Stress

Young's Modulus

Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

Symbol: E

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Young's Modulus

Other formulas in Strain Energy stored per unit Volume category

Go Modulus of Elasticity of Member with known Strain Energy Stored per Unit Volume

E = \frac{σ^{2}}{2 \cdot U density}

Go Stress generated due to Strain Energy Stored per Unit Volume

σ = \sqrt{U density \cdot 2 \cdot E}

How to Evaluate Strain Energy Stored per Unit Volume?

Strain Energy Stored per Unit Volume evaluator uses Strain Energy Density = Direct Stress^2/(2*Young's Modulus) to evaluate the Strain Energy Density, The Strain Energy Stored per Unit Volume formula is defined as the energy gained by the material per unit volume when the member is subjected to a pull of given stress. Strain Energy Density is denoted by U_density symbol.

How to evaluate Strain Energy Stored per Unit Volume using this online evaluator? To use this online evaluator for Strain Energy Stored per Unit Volume, enter Direct Stress (σ) & Young's Modulus (E) and hit the calculate button.

FAQs on Strain Energy Stored per Unit Volume

What is the formula to find Strain Energy Stored per Unit Volume?

The formula of Strain Energy Stored per Unit Volume is expressed as Strain Energy Density = Direct Stress^2/(2*Young's Modulus). Here is an example- 17929.21 = 26780000^2/(2*20000000000).

How to calculate Strain Energy Stored per Unit Volume?

With Direct Stress (σ) & Young's Modulus (E) we can find Strain Energy Stored per Unit Volume using the formula - Strain Energy Density = Direct Stress^2/(2*Young's Modulus).

Can the Strain Energy Stored per Unit Volume be negative?

No, the Strain Energy Stored per Unit Volume, measured in Energy Density cannot be negative.

Which unit is used to measure Strain Energy Stored per Unit Volume?

Strain Energy Stored per Unit Volume is usually measured using the Joule per Cubic Meter[J/m³] for Energy Density. Kilojoule per Cubic Meter[J/m³], Megajoule per Cubic Meter[J/m³] are the few other units in which Strain Energy Stored per Unit Volume can be measured.

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