True Strain Calculator
Convert engineering strain and stress to true strain and true stress for material analysis
Calculate True Strain and True Stress
Dimensionless value (e.g., 0.1 for 10% strain)
Nominal stress based on original cross-sectional area
True Strain and Stress Results
Strain Analysis
Stress Analysis
Formulas Used
True Strain: ε = ln(1 + εₑ)
True Stress: σ = σₑ(1 + εₑ)
Where εₑ is engineering strain and σₑ is engineering stress
Strain Analysis
Example Calculation
Steel Tensile Test Example
Engineering Strain (εₑ): 0.05 (5% elongation)
Engineering Stress (σₑ): 400 MPa
Original Cross-sectional Area: Used for engineering stress
Instantaneous Area: Used for true stress calculation
Calculation Steps
True Strain: ε = ln(1 + 0.05) = ln(1.05) = 0.04879
True Stress: σ = 400 × (1 + 0.05) = 400 × 1.05 = 420 MPa
Strain Difference: (0.05 - 0.04879)/0.05 × 100% = 2.42%
Stress Difference: (420 - 400)/400 × 100% = 5.00%
Stress-Strain Curves
Engineering Curve
Based on original area
Shows apparent stress drop after necking
True Curve
Based on instantaneous area
Continues to increase until failure
Small Strain
Curves nearly identical
For strains < 1-2%
Applications
Material characterization beyond yield point
CAE software input (ABAQUS, ANSYS)
Strain hardening behavior modeling
Accurate plastic deformation analysis
When to Use True Values
Large deformation analysis (> 5%)
Plastic behavior characterization
Strain hardening studies
FEA material model inputs
Engineering values adequate for small strains
Understanding True Strain and True Stress
What is True Strain?
True strain (also called logarithmic or natural strain) represents the actual strain experienced by a material during deformation. Unlike engineering strain, which uses the original length as reference, true strain considers the continuous change in dimensions.
Key Differences
- •Engineering Strain: Based on original length (εₑ = ΔL/L₀)
- •True Strain: Based on instantaneous length (ε = ln(L/L₀))
- •True strain is always smaller than engineering strain
- •Difference becomes significant for large deformations
Mathematical Relationships
ε = ln(1 + εₑ)
σ = σₑ(1 + εₑ)
- ε: True strain (dimensionless)
- εₑ: Engineering strain (dimensionless)
- σ: True stress (Pa, MPa, etc.)
- σₑ: Engineering stress (Pa, MPa, etc.)
Note: For small strains (< 2%), engineering and true values are nearly identical.
Practical Applications
Material Testing
Essential for characterizing material behavior beyond the elastic limit and during plastic deformation phases.
FEA Simulation
Required input for accurate plastic material models in finite element analysis software like ABAQUS and ANSYS.
Manufacturing
Critical for metal forming processes, sheet metal operations, and any application involving large plastic deformations.