Strain

Theory

Engineering strain ε = ΔL/L₀ is dimensionless, expressed as mm/mm or %. True strain ε_true = ln(L/L₀) is more accurate at large deformations. Lateral strain accompanies axial strain; their ratio defines Poisson's ratio. Strain is also a second-rank tensor but scalar treatment suffices for uniaxial loading.

Application

Strain gauges measure surface strain; stress is then inferred via E. In FDM, layer-to-layer thermal shrinkage induces residual strains causing warping. For elastomeric filaments (TPU), strain to failure (>300%) is the primary design variable rather than strength.

Common mistakes

Engineering strain becomes inaccurate above ~10% deformation: use true strain instead. Thermal strain α·ΔT from printing temperatures adds to mechanical strain; ignoring it gives incorrect shrinkage models. Strain varies point-to-point; do not treat it as a single scalar for complex geometries.

Related terms: Stress, Young's Modulus, Poisson's Ratio, Elongation at Break, Stress-Strain Curve