True Strain Calculator

Calculate True Strain and Deformation

Enter the initial and final dimensions or engineering strain to calculate true strain and related deformation parameters.

Example Calculations

Common true strain calculations for different materials and scenarios

Tensile Deformation

Tensile Deformation

Steel rod under tensile loading

Initial Length: 100 mm

Final Length: 110 mm

Engineering Strain: 0.1

Initial Area: 50 mm²

Engineering Stress: 200 MPa

Compressive Deformation

Compressive Deformation

Aluminum block under compression

Initial Length: 50 mm

Final Length: 45 mm

Engineering Strain: -0.1

Initial Area: 25 mm²

Engineering Stress: 150 MPa

Large Deformation

Large Deformation

Rubber material with large strain

Initial Length: 20 mm

Final Length: 40 mm

Engineering Strain: 1

Initial Area: 10 mm²

Engineering Stress: 5 MPa

Small Deformation

Small Deformation

Precision measurement scenario

Initial Length: 1000 mm

Final Length: 1001 mm

Engineering Strain: 0.001

Initial Area: 100 mm²

Engineering Stress: 50 MPa

Other Titles
Understanding True Strain: A Comprehensive Guide
Learn about true strain, its relationship with engineering strain, and its applications in material science and engineering

What is True Strain?

  • Definition and Concept
  • Mathematical Foundation
  • Physical Significance
True strain, also known as logarithmic strain or natural strain, is a measure of deformation that accounts for the instantaneous change in length relative to the current length, rather than the original length. Unlike engineering strain, which assumes small deformations and linear behavior, true strain provides a more accurate representation of material behavior under large deformations.
Mathematical Definition
True strain is defined as the natural logarithm of the ratio of final length to initial length: εtrue = ln(L/L₀) = ln(1 + εengineering), where L is the final length, L₀ is the initial length, and ε_engineering is the engineering strain.
Advantages of True Strain
True strain offers several advantages over engineering strain: it provides additive strain values for sequential deformations, gives more accurate stress-strain relationships for large deformations, and better represents the actual material behavior in plastic deformation regions.

True Strain Examples

  • For a 10% elongation: ε_engineering = 0.1, ε_true = ln(1.1) ≈ 0.0953
  • For a 50% elongation: ε_engineering = 0.5, ε_true = ln(1.5) ≈ 0.4055

Step-by-Step Guide to Using the True Strain Calculator

  • Input Methods
  • Calculation Process
  • Result Interpretation
The True Strain Calculator offers two primary input methods: using length measurements or using engineering strain values. Choose the method that best fits your available data and measurement capabilities.
Method 1: Length Measurements
Enter the initial length (L₀) and final length (L) of your material. The calculator will automatically compute both engineering strain and true strain. Ensure both measurements use the same units (mm, cm, m, inches, etc.).
Method 2: Engineering Strain
If you already have the engineering strain value, simply enter it in the engineering strain field. The calculator will compute the corresponding true strain and other related parameters.
Additional Parameters
For complete stress analysis, you can also input initial cross-sectional area and engineering stress to calculate true stress, which is essential for understanding material behavior under large deformations.

Calculation Examples

  • Length method: L₀ = 100 mm, L = 110 mm → ε_engineering = 0.1, ε_true = 0.0953
  • Strain method: ε_engineering = 0.2 → ε_true = 0.1823

Real-World Applications of True Strain

  • Material Testing
  • Manufacturing Processes
  • Structural Analysis
True strain calculations are essential in various engineering and scientific applications where accurate deformation analysis is critical for understanding material behavior and predicting performance.
Material Testing and Characterization
In tensile testing, true strain provides more accurate stress-strain curves, especially in the plastic deformation region. This is crucial for determining material properties like ultimate tensile strength, yield strength, and ductility.
Manufacturing and Forming Processes
Metal forming operations such as rolling, drawing, and extrusion rely on true strain calculations to predict material behavior, optimize process parameters, and ensure product quality.
Structural and Mechanical Design
Engineers use true strain analysis in designing components that undergo significant deformations, such as springs, shock absorbers, and energy-absorbing structures.

Application Examples

  • Tensile testing of steel specimens for automotive applications
  • Analysis of metal forming processes in manufacturing
  • Design of energy-absorbing structures for crash safety

Common Misconceptions and Correct Methods

  • Strain vs. Stress
  • Linear vs. Non-linear Behavior
  • Measurement Accuracy
Understanding the differences between engineering and true strain, and knowing when to use each, is crucial for accurate material analysis and engineering design.
Engineering vs. True Strain
Engineering strain assumes small deformations and linear behavior, while true strain accounts for the actual geometric changes. For deformations less than 5%, the difference is negligible, but for larger deformations, true strain provides more accurate results.
Additive Property
Unlike engineering strain, true strain values are additive for sequential deformations. This property makes true strain particularly useful in multi-step forming processes.
Volume Conservation
In plastic deformation, materials often maintain constant volume. True strain calculations help verify this assumption and provide insights into material behavior.

Key Differences

  • For small deformations (<5%): ε_engineering ≈ ε_true
  • For large deformations: ε_true provides more accurate representation
  • Sequential deformations: ε_true_total = ε_true1 + ε_true2 + ...

Mathematical Derivation and Examples

  • Derivation Process
  • Relationship Equations
  • Practical Calculations
The mathematical relationship between engineering strain and true strain is fundamental to understanding deformation analysis and material behavior under various loading conditions.
Derivation of True Strain
True strain is derived by integrating the instantaneous strain over the deformation process: ε_true = ∫(dL/L) from L₀ to L = ln(L/L₀). This integration accounts for the changing reference length during deformation.
Relationship with Engineering Strain
The relationship between engineering strain (ε) and true strain (εtrue) is: εtrue = ln(1 + ε). For small strains, this can be approximated as: ε_true ≈ ε - ε²/2 + ε³/3 - ...
True Stress Relationship
True stress (σtrue) is related to engineering stress (σ) by: σtrue = σ(1 + ε) = σ × exp(ε_true). This relationship is crucial for accurate stress analysis in large deformations.

Mathematical Examples

  • ε = 0.1: ε_true = ln(1.1) ≈ 0.0953, difference ≈ 4.7%
  • ε = 0.5: ε_true = ln(1.5) ≈ 0.4055, difference ≈ 18.9%
  • ε = 1.0: ε_true = ln(2.0) ≈ 0.6931, difference ≈ 30.7%