Poisson's ratio is a dimensionless constant used for stress and deflection analysis of structures such as beams, plates, shells and rotating discs. When bending a piece of metal, one surface of the material stretches in tension while the opposite surface compresses. It follows that there is a line or region of zero stress between the two surfaces, called the neutral axis. The material of the beam is linearly elastic, homogeneous and isotropic. The proportional limit is not exceeded.
All deflections are small, so that planar cross-sections remain planar before and after bending.
The reported flexural modulus is usually the initial modulus from the stress-strain curve in tension. One of the methods to reduce maximum stress is to keep the strain energy in the beam constant while changing the beam profile. Additional beam profiles are trapezoidal, tapered and torsion. Yielding Yielding occurs when the design stress exceeds the material yield strength. The Von Mises yield criterion states that yielding occurs when the Von Mises stress, exceeds the yield strength in tension.