Material characterisation is typically performed by uniaxial tensile testing, where a material sample with defined geometry is tested under controlled conditions by means of a tensile testing machine. The sample is fixed at both extremes by the machine grips. While one of the ends remains fixed, the other follows a prescribed (and generally quasi-static) displacement until the sample failure is reached.
Tensile tests can be easily instrumented in order to obtain the equivalent magnitudes of stress and strain throughout the test. Stress can be obtained from load cell force measurement divided by the corss-sectional area of the sample, whereas strain can be obtained by the measurement of the length increment experienced by the material sample over a given longitudinal reference length (calibrated length).
Stress and strain values obtained from a sample tensile test can be expressed as lagrangian or eulerian magnitudes, depending on the type of assumed references. Lagrangian (engineering) magnitudes are defined from the initial values of the sectional area and the length of the sample, whereas eulerian (real) magnitudes are defined by the current values of area and length measured at each instant throughout the test.