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Modulus of resilience Formula

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Modulus of Resilience is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding. Check FAQs

U r = \frac{{σ y}^{2}}{2 \cdot E}

U_r - Modulus of Resilience?σ_y - Yield Strength?E - Young's Modulus?

Modulus of resilience Example

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Here is how the Modulus of resilience equation looks like with Values.

Here is how the Modulus of resilience equation looks like with Units.

Here is how the Modulus of resilience equation looks like.

4.1E+7 = \frac{35^{2}}{2 \cdot 15}

4.1E+7MPa = \frac{{35N/mm²}^{2}}{2 \cdot 15N/m}

4.1E+7 = \frac{35^{2}}{2 \cdot 15}

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Modulus of resilience Solution

Follow our step by step solution on how to calculate Modulus of resilience?

FIRST Step Consider the formula

U r = \frac{{σ y}^{2}}{2 \cdot E}

Next Step Substitute values of Variables

∴

U r = \frac{{35N/mm²}^{2}}{2 \cdot 15N/m}

Next Step Convert Units

∴

U r = \frac{{3.5E+7Pa}^{2}}{2 \cdot 15N/m}

Next Step Prepare to Evaluate

∴

U r = \frac{{3.5E+7}^{2}}{2 \cdot 15}

Next Step Evaluate

∴

U r = 40833333333333.3Pa

Next Step Convert to Output's Unit

∴

U r = 40833333.3333333MPa

LAST Step Rounding Answer

∴

U r = 4.1E+7MPa

Modulus of resilience Formula Elements

Variables

Modulus of Resilience

Modulus of Resilience is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding.

Symbol: U_r

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Resilience

Yield Strength

Yield strength can be defined as follows, a straight line is constructed parallel to elastic portion of stress–strain curve at strain offset of 0.002.

Symbol: σ_y

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Yield Strength

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: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Young's Modulus

Other formulas in Failure Testing in Materials category

Go Percent elongation

%EL = (l f - L 0) \cdot \frac{100}{L 0}

Go Percent reduction in area

%RA = (A 0 - A f) \cdot \frac{100}{A 0}

Go Percent cold work

%CW = 100 \cdot \frac{A 0 - A d}{A 0}

Go Critical stress for crack propagation

σ c = \sqrt{2 \cdot E \cdot \frac{γ s}{π \cdot a}}

How to Evaluate Modulus of resilience?

Modulus of resilience evaluator uses Modulus of Resilience = Yield Strength^2/(2*Young's Modulus) to evaluate the Modulus of Resilience, Modulus of resilience is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding. Modulus of Resilience is denoted by U_r symbol.

How to evaluate Modulus of resilience using this online evaluator? To use this online evaluator for Modulus of resilience, enter Yield Strength (σ_y) & Young's Modulus (E) and hit the calculate button.

FAQs on Modulus of resilience

What is the formula to find Modulus of resilience?

The formula of Modulus of resilience is expressed as Modulus of Resilience = Yield Strength^2/(2*Young's Modulus). Here is an example- 40.83333 = 35000000^2/(2*15).

How to calculate Modulus of resilience?

With Yield Strength (σ_y) & Young's Modulus (E) we can find Modulus of resilience using the formula - Modulus of Resilience = Yield Strength^2/(2*Young's Modulus).

Can the Modulus of resilience be negative?

No, the Modulus of resilience, measured in Stress cannot be negative.

Which unit is used to measure Modulus of resilience?

Modulus of resilience is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Modulus of resilience can be measured.

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Modulus of resilience Formula

Modulus of resilience Example

Modulus of resilience Solution

Modulus of resilience Formula Elements

Other formulas in Failure Testing in Materials category

How to Evaluate Modulus of resilience?

FAQs on Modulus of resilience

Variable Name