1. What is the Modulus Of Resilience?

The Modulus Of Resilience (U_r) is a measure of a material's ability to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered. It represents the maximum energy per unit volume that can be absorbed without creating a permanent distortion.

2. How Does the Calculator Work?

The calculator uses the Modulus Of Resilience equation:

Where:

• \( \sigma_y \) — Yield stress of the material (Pa)
• \( E \) — Modulus of elasticity of the material (Pa)
• \( U_r \) — Modulus of resilience (J/m³)

Explanation: The equation 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 Modulus Of Resilience Calculation

Details: Calculating the modulus of resilience is crucial for material selection in engineering applications where energy absorption and elastic recovery are important, such as in springs, shock absorbers, and structural components subjected to dynamic loading.

4. Using the Calculator

Tips: Enter yield stress in Pascals (Pa), modulus of elasticity in Pascals (Pa). Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

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

Q2: What are typical values for modulus of resilience?
A: Values vary significantly by material. For example, steel has a higher modulus of resilience than rubber, though rubber can undergo much larger elastic deformations.

Q3: How does temperature affect modulus of resilience?
A: Generally, as temperature increases, both yield strength and modulus of elasticity decrease, which affects the modulus of resilience. The specific relationship depends on the material.

Q4: Can modulus of resilience be measured experimentally?
A: Yes, through tensile testing by measuring the area under the stress-strain curve up to the yield point.

Q5: Why is modulus of resilience important in spring design?
A: Springs need to store and release energy efficiently without permanent deformation, making high modulus of resilience a desirable property for spring materials.