Strain Calculations

1. Normal Strain

ε = ΔL / L₀

ΔL: Change in length [mm] — L₀: Original length [mm]

2. True Strain

εtrue = ln(L / L₀)

3. Shear Strain

γ = Δx / L

Alternatively, γ = tan(θ) for small angles

4. Volumetric Strain

εv = ΔV / V₀

5. Thermal Strain

εT = α × ΔT

α: Coefficient of thermal expansion — ΔT: Temperature change [°C]

6. Total Strain

ε = εe + εp

Elastic + Plastic strain

7. Elastic Strain

εe = σ / E

8. Plastic Strain

εp = ε - εe

9. Principal Strains

ε1,2 = (εx + εy)/2 ± √[((εx - εy)/2)² + γxy²]

10. Plane Strain Condition

εz = 0

Used in thick walls or long structures where deformation in one direction is negligible.

11. Strain Tensor (3D)

ε = [[εxx, γxy/2, γxz/2], [γxy/2, εyy, γyz/2], [γxz/2, γyz/2, εzz]]