Calculate True Strain

Precise instantaneous deformation analysis for engineering and materials science.

What is Calculate True Strain?

To calculate true strain (also known as logarithmic strain or Hencky strain) is to measure the instantaneous deformation of a material. Unlike engineering strain, which references the original dimensions of a component, true strain accounts for the continuously changing geometry during the deformation process. This makes it a critical metric in large-strain applications such as metal forming, plastic deformation analysis, and non-linear finite element modeling.

Engineers and materials scientists calculate true strain because it provides a more accurate physical representation of material behavior, especially when the volume of the material remains constant during plastic flow. While engineering strain is sufficient for small deformations within the elastic limit, it loses accuracy as the specimen undergoes significant stretching or compression.

A common misconception is that true strain and engineering strain are interchangeable. At low strain levels (less than 1%), the numerical difference is negligible. However, as deformation increases, the divergence becomes significant, with true strain being lower than engineering strain in tension and higher in magnitude during compression.

Calculate True Strain Formula and Mathematical Explanation

The mathematical derivation to calculate true strain involves integrating the incremental change in length over the instantaneous length. The formula is expressed as:

ε = ∫ (dL / L) from L₀ to L = ln(L / L₀)

Alternatively, if you already have the engineering strain (e), you can convert it using:

ε = ln(1 + e)

Variable	Meaning	Unit	Typical Range
L₀	Initial Length	mm or inch	10 – 500
L	Final/Current Length	mm or inch	L₀ ± 50%
e	Engineering Strain	Dimensionless	0 to 0.5 (Tension)
ε	True Strain	Dimensionless	-1.0 to 1.0

Table 1: Key variables used to calculate true strain in mechanical testing.

Practical Examples (Real-World Use Cases)

Example 1: Tensile Testing of Aluminum

An engineer performs a tensile test on an aluminum rod with an initial length (L₀) of 50 mm. After applying a load, the rod stretches to a final length (L) of 65 mm. To calculate true strain:

• Engineering Strain (e) = (65 – 50) / 50 = 0.3 or 30%.
• True Strain (ε) = ln(65 / 50) = ln(1.3) ≈ 0.2624.

In this case, the engineering strain overestimates the actual physical deformation compared to the true strain calculation.

Example 2: Compression of a Polymer Block

A polymer block with an initial height of 100 mm is compressed to 80 mm. To calculate true strain:

• Engineering Strain (e) = (80 – 100) / 100 = -0.2.
• True Strain (ε) = ln(80 / 100) = ln(0.8) ≈ -0.2231.

Note that for compression, the true strain has a larger magnitude than the engineering strain.

How to Use This Calculate True Strain Calculator

Using our tool to calculate true strain is straightforward and designed for professional accuracy:

1. Enter Initial Length: Input the original dimension of your material (L₀) before any load was applied.
2. Enter Final Length: Input the current or final dimension (L) after deformation.
3. Select Method: Use the dropdown to toggle between length-based or area-based calculations (useful for volume-conservative plastic deformation).
4. Review Results: The primary result shows the true strain (ε). Intermediate values provide the engineering strain (e) and percentage elongation for comparison.
5. Analyze the Chart: The dynamic SVG chart illustrates where your data point sits relative to the divergence of true and engineering strain.

Key Factors That Affect Calculate True Strain Results

• Material Ductility: Highly ductile materials undergo significant plastic deformation where the choice to calculate true strain vs engineering strain becomes critical for accuracy.
• Strain Rate: In dynamic loading, the rate at which you calculate true strain impacts the flow stress of the material.
• Temperature: Elevated temperatures generally increase ductility, leading to larger strain values before fracture.
• Volume Conservation: In the plastic region, materials are often assumed to be incompressible. This allows engineers to calculate true strain using cross-sectional area changes if length is hard to measure.
• Neck Concentration: Once “necking” begins in a tensile test, the calculate true strain becomes a local value rather than a global average.
• Measurement Precision: Since true strain uses a logarithmic scale, small errors in length measurement at high strains can result in significant data skew.

Frequently Asked Questions (FAQ)

Why is true strain always smaller than engineering strain in tension?

Because engineering strain uses a constant denominator (the original length), whereas true strain uses an increasing denominator (the instantaneous length) in its integral definition.

When should I use engineering strain instead?

Engineering strain is standard for structural design where deformations are very small (elastic region), as it simplifies calculations and follows Hooke’s Law linearly.

Can true strain be negative?

Yes, if the material is compressed (final length < initial length), the natural log of a fraction less than one results in a negative value.

Is true strain the same as Hencky strain?

Yes, Hencky strain is simply another name for the logarithmic or true strain commonly used in metallurgy.

How does calculate true strain relate to true stress?

True stress is the load divided by the instantaneous area. When you calculate true strain and true stress together, you get a “Flow Curve” which describes plastic behavior.

Does the unit of length matter?

No, as long as both initial and final lengths are in the same units (mm, cm, inch), the strain remains a dimensionless ratio.

What is the additive property of true strain?

One major advantage is that total true strain is the sum of incremental true strains (ε_total = ε1 + ε2), which is not true for engineering strain.

What is the limit of true strain?

Theoretically, it can go to infinity as L increases, but physically it is limited by the material’s fracture point.

Related Tools and Internal Resources

• Engineering Strain Calculator – Basic linear deformation tool for small displacements.
• Tensile Strength Tool – Calculate ultimate tensile strength and yield points.
• Material Science Basics – A guide to stress-strain relationships.
• Ductility Calculator – Measure percentage elongation and reduction in area.
• Plastic Strain Guide – Detailed look at permanent deformation in metals.
• Stress-Strain Curve Generator – Plot experimental data points dynamically.