Question

Derive the expression ε=ln(1+e), where ε is the true strain and e is the engineering strain. Note that this expression is not valid after the onset of necking

Answer 1

The formula for true strain after derivation from basic terms is; ε_t = In(1 + ε_e)

How to derive the expression for True Strain?

Formula for Engineering Stress is;

σ_e = Load/Area

Formula for true stress is;

σ_t = Force/Instantaneous Area

Formula for Engineering Strain is;

ε_e = ΔL/L₀

Formula for true strain is;

dε_t = dL/L

Total true strain is gotten from;

ε_t = ∫(dL/L) between boundaries of L_f and L_o

When we integrate between those boundaries, we have;

ε_t = In[(L₀ + ΔL)/L₀

⇒ ε_t = In[(1+ ΔL/L₀)

⇒ ε_t = In(1 + ε_e)

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