Strain

The diagram shows the effect of applying a uniaxial stress to a
sample of initial area A ₀ . The Change in Length of the sample
normalized by its length is the longtitudinal strain produced by the
applied stress. The transverse dimensions of the sample also
change and when normalized by their initial values give the
transverse stresses.

For the longtitudinal case:

Engineering Strain = Nominal Strain = e_E = (Change in Length / Original Length)
i.e.: e_E = (dL / L₀ )

True Strain = e _T = Integral (dL / L) = Ln (L _i / L ₀ ) = Ln(e_E + 1)