The formula to calculate Young's Modulus (E) is:
\[ E = 2G(1 + \nu) \]
Where:
Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Shear Modulus is the slope of the linear elastic region of the shear stress–strain curve.
Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5.
Let's assume the following values:
Using the formula:
\[ E = 2G(1 + \nu) \]
Evaluating:
\[ E = 2 \times 25000000000 \times (1 + 0.3) \]
Young's Modulus is 65000000000 N/m².
| Shear Modulus (Pa) | Poisson's Ratio | Young's Modulus (N/m²) |
|---|---|---|
| 20000000000 | 0.1 | 44,000,000,000.0000 |
| 20000000000 | 0.2 | 48,000,000,000.0000 |
| 20000000000 | 0.3 | 52,000,000,000.0000 |
| 20000000000 | 0.4 | 56,000,000,000.0000 |
| 20000000000 | 0.5 | 60,000,000,000.0000 |
| 25000000000 | 0.1 | 55,000,000,000.0000 |
| 25000000000 | 0.2 | 60,000,000,000.0000 |
| 25000000000 | 0.3 | 65,000,000,000.0000 |
| 25000000000 | 0.4 | 70,000,000,000.0000 |
| 25000000000 | 0.5 | 75,000,000,000.0000 |
| 30000000000 | 0.1 | 66,000,000,000.0000 |
| 30000000000 | 0.2 | 72,000,000,000.0000 |
| 30000000000 | 0.3 | 78,000,000,000.0000 |
| 30000000000 | 0.4 | 84,000,000,000.0000 |
| 30000000000 | 0.5 | 90,000,000,000.0000 |