Module Of Resilience Calculator

Module Of Resilience Formula:

\[ U_r = \frac{\sigma_y^2}{2E} \]

Module Of Resilience (U_r):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Module Of Resilience?

Module Of Resilience (U_r) is a material property that represents the maximum amount of energy per unit volume that a material can absorb without undergoing permanent deformation. It is a measure of a material's ability to absorb energy elastically.

2. How Does the Calculator Work?

The calculator uses the Module Of Resilience formula:

\[ U_r = \frac{\sigma_y^2}{2E} \]

Where:

\( \sigma_y \) — Yield strength of the material (Pa)
\( E \) — Young's modulus of the material (Pa)
\( U_r \) — Module of resilience (J/m³)

Explanation: The formula calculates the area under the stress-strain curve up to the yield point, representing the elastic energy storage capacity of a material.

3. Importance of Module Of Resilience Calculation

Details: Calculating module of resilience is crucial for material selection in engineering applications where energy absorption and elastic deformation are important factors, such as in springs, shock absorbers, and structural components.

4. Using the Calculator

Tips: Enter yield strength in Pascals (Pa), Young's modulus in Pascals (Pa). Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between resilience and toughness?
A: Resilience measures energy absorption up to the yield point (elastic deformation), while toughness measures total energy absorption including plastic deformation up to fracture.

Q2: What are typical values for module of resilience?
A: Values vary widely by material. For example, steel has higher resilience than cast iron, while rubber can have very high resilience values.

Q3: How does temperature affect module of resilience?
A: Generally, module of resilience decreases with increasing temperature as materials tend to become less stiff and yield at lower stresses.

Q4: Can this calculation be used for all materials?
A: This formula applies to materials with a well-defined yield point. For materials without a clear yield point, alternative methods may be needed.

Q5: Why is module of resilience important in spring design?
A: Springs need to absorb and release energy efficiently, so materials with high module of resilience are preferred as they can store more elastic energy per unit volume.