Table of Contents
What Is True Strain?
True strain (also called logarithmic or natural strain) is the integral of incremental strain referenced to the instantaneous length of the specimen. Unlike engineering strain, which references the original length, true strain accounts for the continuously changing gauge length during deformation.
True strain is preferred in plasticity theory and metal forming because it is additive for sequential deformations. If a bar is stretched from length A to B, then B to C, the total true strain equals the sum of the individual true strains, which is not the case for engineering strain.
Strain Formulas
Engineering vs True Strain Comparison
| Engineering Strain | True Strain | Difference (%) |
|---|---|---|
| 0.01 (1%) | 0.00995 | 0.5% |
| 0.05 (5%) | 0.04879 | 2.4% |
| 0.10 (10%) | 0.09531 | 4.7% |
| 0.20 (20%) | 0.18232 | 8.8% |
| 0.50 (50%) | 0.40546 | 18.9% |
| 1.00 (100%) | 0.69315 | 30.7% |
Frequently Asked Questions
When should I use true strain instead of engineering strain?
Use true strain for large deformations (greater than ~5%), plasticity calculations, metal forming simulations (FEA), and when combining sequential deformation steps. Engineering strain is adequate for small elastic deformations where the difference is negligible.
What is the stretch ratio?
The stretch ratio (or extension ratio) lambda = L/L0 is the ratio of deformed length to original length. It relates to true strain by epsilon_true = ln(lambda) and to engineering strain by e_eng = lambda - 1.
Can true strain be negative?
Yes, true strain is negative for compression (L less than L0). A specimen compressed to half its length has true strain = ln(0.5) = -0.693. This symmetry is another advantage over engineering strain, where compression to half gives -0.5 while stretching to double gives +1.0.