Calculate True Strain

Material Deformation & Mechanics Analysis

Calculation Results

True Strain (ε) 0.0000

Engineering Strain (e) 0.0000

Elongation % 0.00%

Ratio (L/L₀) 0.000

Please enter valid positive numbers where the final length is greater than zero.

Understanding True Strain vs. Engineering Strain

In materials science and mechanical engineering, "Strain" measures the deformation of a material. While many students first learn Engineering Strain, True Strain (also known as logarithmic strain or Hencky strain) provides a more accurate representation of large plastic deformations.

The Formula

The True Strain ($\epsilon$) is calculated using the natural logarithm of the ratio of the instantaneous (final) length to the initial length:

ε = ln(L / L₀)

Where:

• L₀: The original length of the specimen before any force is applied.
• L: The instantaneous or final length of the specimen.

Why Use True Strain?

Engineering strain ($e = \Delta L / L_0$) is convenient for small deformations, but it fails to account for the changing cross-sectional area and the incremental nature of deformation in ductile materials. True strain is additive; if you stretch a rod from 10cm to 11cm, and then from 11cm to 12cm, the sum of the true strains for each step equals the total true strain from 10cm to 12cm. This is not true for engineering strain.

Example Calculation

If a metal wire with an initial length of 100 mm is pulled until it reaches 150 mm:

1. Engineering Strain: (150 – 100) / 100 = 0.50 (or 50%)
2. True Strain: ln(150 / 100) = ln(1.5) ≈ 0.4055

As seen here, as deformation increases, the difference between engineering and true strain becomes significant.