True Strain Calculator

Engineering strain measures elongation relative to the original length, assuming a constant geometry. However, as materials stretch, their cross-sectional area shrinks. True strain (also known as natural strain) accounts for this instantaneous change by integrating incremental deformations. The primary formula for true strain (ε_t) based on engineering strain (e) is: ε_t = ln(1 + e). Additionally, true stress (σ_t) is derived from engineering stress (σ_e) and engineering strain using the relation: σ_t = σ_e × (1 + e), assuming volume remains constant during plastic deformation.

Consider a metallic rod subjected to a tensile test where the engineering strain (e) is measured at 0.15 (a 15% elongation) and the engineering stress (σ_e) is 250 MPa. To find the true strain, we apply the logarithmic formula: ε_t = ln(1 + 0.15) = ln(1.15) ≈ 0.1398. To find the corresponding true stress, we calculate σ_t = 250 MPa × (1 + 0.15) = 250 × 1.15 = 287.5 MPa. This reveals that the actual stress and strain experienced by the atomic lattice differ significantly from engineering metrics as the specimen stretches.

Always ensure your engineering strain values are expressed as decimals rather than percentages before applying the natural logarithm. Be mindful that these specific conversion formulas assume volume constancy, which holds true for plastic deformation in metals but may vary for porous or highly compressible materials. Use true stress-strain curves for advanced finite element analysis and accurate post-yield material modeling.