# Flexural modulus

In mechanics (mechanics is a branch of physics), the flexural modulus or bending modulus[1] is the ratio of stress to strain in flexural deformation, or the tendency for a material to bend. It is determined from the slope of a stress-strain curve produced by a flexural test (such as the ASTM D 790), and uses units of force per area.[2] It is an intensive property.

Flexural modulus measurement

For a 3-point test of a rectangular beam behaving as an isotropic linear material, where w and h are the width and height of the beam, L is the distance between the two outer supports and d is the deflection due to the load F applied at the middle of the beam, the flexural modulus:

$E_{\mathrm{bend}} = \frac {L^3 m}{4 b d^3}$

From elastic beam theory $d = \frac {L^3 F}{48 I E }$ and for rectangular beam $I = \frac{1}{12}wh^3$

thus $E_{\mathrm{bend}} = E$ (Elastic modulus)

Ideally, flexural or bending modulus of elasticity is equivalent to the tensile or compressive modulus of elasticity. In reality, these values may be different, especially for plastic materials.