True Strain Calculator - Logarithmic Strain

True (Logarithmic) Strain

True strain measures deformation using the natural logarithm of the length ratio. Unlike engineering strain, it accounts for the changing reference length during large deformations and is preferred in finite element analysis and metal forming.

Formulas

$$\varepsilon_{true} = \ln\left(\frac{L}{L_0}\right) = \ln(1 + \varepsilon_{eng})$$

Here $L_0$ is initial length, $L$ is final length, and $\varepsilon_{eng} = (L - L_0)/L_0$ is engineering strain. For small strains (below about 5%), true and engineering strain are nearly equal.

When to Use True Strain

True strain is additive for sequential deformations and matches stress-strain curves from tensile tests that report logarithmic values. Use engineering strain for small elastic deformations; switch to true strain for plastic forming, rubber elasticity, and large stretches.

Related tools: Earthquake Calculator and PERT Calculator.

Frequently Asked Questions

How is true strain different from engineering strain?

Engineering strain uses the original length as reference: $\varepsilon_{eng} = \Delta L / L_0$. True strain integrates infinitesimal stretches: $\varepsilon_{true} = \ln(L/L_0)$.

At what strain do they diverge?

Below about 5% strain the difference is small. At 10% engineering strain, true strain is about 9.5%. At 50%, true strain is 40.5% while engineering strain is 50%.

Can true strain be negative?

Yes. Compression (shorter final length) gives negative true strain, since $L/L_0 < 1$ and $\ln(L/L_0) < 0$.

What units does length use?

Any consistent length unit works (mm, m, in) because true strain is dimensionless. The ratio $L/L_0$ is what matters.

Why is ln(1 + ε_eng) used?

Since $L/L_0 = 1 + \varepsilon_{eng}$, taking the natural log converts engineering strain directly to true strain without needing both lengths.

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True Strain

True (Logarithmic) Strain

Formulas

When to Use True Strain

Frequently Asked Questions

Related Tools

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