The formula to calculate True Strain (\(\epsilon_T\)) is:
\[ \epsilon_T = \ln\left(\frac{l_i}{L_0}\right) \]
Where:
True strain is the instantaneous elongation per unit length.
Instantaneous length is the length after application of load.
Original Length refers to the material's initial size or dimension before any external forces are applied.
Let's assume the following values:
Using the formula:
\[ \epsilon_T = \ln\left(\frac{l_i}{L_0}\right) \]
Evaluating:
\[ \epsilon_T = \ln\left(\frac{0.02}{5}\right) \]
The True Strain is -5.5215.
| Instantaneous Length (m) | Original Length (m) | True Strain |
|---|---|---|
| 0.01 | 1 | -4.6052 |
| 0.01 | 2 | -5.2983 |
| 0.01 | 3 | -5.7038 |
| 0.01 | 4 | -5.9915 |
| 0.01 | 5 | -6.2146 |
| 0.01 | 6 | -6.3969 |
| 0.01 | 7 | -6.5511 |
| 0.01 | 8 | -6.6846 |
| 0.01 | 9 | -6.8024 |
| 0.01 | 10 | -6.9078 |
| 0.02 | 1 | -3.9120 |
| 0.02 | 2 | -4.6052 |
| 0.02 | 3 | -5.0106 |
| 0.02 | 4 | -5.2983 |
| 0.02 | 5 | -5.5215 |
| 0.02 | 6 | -5.7038 |
| 0.02 | 7 | -5.8579 |
| 0.02 | 8 | -5.9915 |
| 0.02 | 9 | -6.1092 |
| 0.02 | 10 | -6.2146 |
| 0.03 | 1 | -3.5066 |
| 0.03 | 2 | -4.1997 |
| 0.03 | 3 | -4.6052 |
| 0.03 | 4 | -4.8929 |
| 0.03 | 5 | -5.1160 |
| 0.03 | 6 | -5.2983 |
| 0.03 | 7 | -5.4525 |
| 0.03 | 8 | -5.5860 |
| 0.03 | 9 | -5.7038 |
| 0.03 | 10 | -5.8091 |
| 0.04 | 1 | -3.2189 |
| 0.04 | 2 | -3.9120 |
| 0.04 | 3 | -4.3175 |
| 0.04 | 4 | -4.6052 |
| 0.04 | 5 | -4.8283 |
| 0.04 | 6 | -5.0106 |
| 0.04 | 7 | -5.1648 |
| 0.04 | 8 | -5.2983 |
| 0.04 | 9 | -5.4161 |
| 0.04 | 10 | -5.5215 |
| 0.05 | 1 | -2.9957 |
| 0.05 | 2 | -3.6889 |
| 0.05 | 3 | -4.0943 |
| 0.05 | 4 | -4.3820 |
| 0.05 | 5 | -4.6052 |
| 0.05 | 6 | -4.7875 |
| 0.05 | 7 | -4.9416 |
| 0.05 | 8 | -5.0752 |
| 0.05 | 9 | -5.1930 |
| 0.05 | 10 | -5.2983 |
| 0.06 | 1 | -2.8134 |
| 0.06 | 2 | -3.5066 |
| 0.06 | 3 | -3.9120 |
| 0.06 | 4 | -4.1997 |
| 0.06 | 5 | -4.4228 |
| 0.06 | 6 | -4.6052 |
| 0.06 | 7 | -4.7593 |
| 0.06 | 8 | -4.8929 |
| 0.06 | 9 | -5.0106 |
| 0.06 | 10 | -5.1160 |
| 0.07 | 1 | -2.6593 |
| 0.07 | 2 | -3.3524 |
| 0.07 | 3 | -3.7579 |
| 0.07 | 4 | -4.0456 |
| 0.07 | 5 | -4.2687 |
| 0.07 | 6 | -4.4510 |
| 0.07 | 7 | -4.6052 |
| 0.07 | 8 | -4.7387 |
| 0.07 | 9 | -4.8565 |
| 0.07 | 10 | -4.9618 |
| 0.08 | 1 | -2.5257 |
| 0.08 | 2 | -3.2189 |
| 0.08 | 3 | -3.6243 |
| 0.08 | 4 | -3.9120 |
| 0.08 | 5 | -4.1352 |
| 0.08 | 6 | -4.3175 |
| 0.08 | 7 | -4.4716 |
| 0.08 | 8 | -4.6052 |
| 0.08 | 9 | -4.7230 |
| 0.08 | 10 | -4.8283 |
| 0.09 | 1 | -2.4079 |
| 0.09 | 2 | -3.1011 |
| 0.09 | 3 | -3.5066 |
| 0.09 | 4 | -3.7942 |
| 0.09 | 5 | -4.0174 |
| 0.09 | 6 | -4.1997 |
| 0.09 | 7 | -4.3539 |
| 0.09 | 8 | -4.4874 |
| 0.09 | 9 | -4.6052 |
| 0.09 | 10 | -4.7105 |
| 0.1 | 1 | -2.3026 |
| 0.1 | 2 | -2.9957 |
| 0.1 | 3 | -3.4012 |
| 0.1 | 4 | -3.6889 |
| 0.1 | 5 | -3.9120 |
| 0.1 | 6 | -4.0943 |
| 0.1 | 7 | -4.2485 |
| 0.1 | 8 | -4.3820 |
| 0.1 | 9 | -4.4998 |
| 0.1 | 10 | -4.6052 |