Stress and strain measures for finite deformations

d ε = \frac{d l}{l}

and

ε = \int_{l_{0}}^{l} \frac{d l}{l} = \ln (\frac{l}{l_{0}}),

where l is the current length, $l_{0}$ is the original length, and $ε$ is the true strain or logarithmic strain.

The stress measure that is the conjugate to the true strain is called the true stress and is defined as

σ = \frac{F}{A},

where F is the force in the material and A is the current area. A ductile metal subjected to finite deformations will have the same stress-strain behavior in tension and compression if true stress is plotted against true strain.