# Flexural modulus

In mechanics, the flexural modulus or bending modulus is an intensive property that is computed as the ratio of stress to strain in flexural deformation, or the tendency for a material to resist bending. It is determined from the slope of a stress-strain curve produced by a flexural test (such as the ASTM D790), and uses units of force per area. The flexural modulus defined using the 3-point bend test assumes a linear stress strain response.

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, I is the second moment of area of the beam's cross-section, 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:

$E_{\mathrm {bend} }={\frac {L^{3}F}{4wh^{3}d}}$ From elastic beam theory

$d={\frac {L^{3}F}{48IE}}$ 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 modulus (Young's modulus) or compressive modulus of elasticity. In reality, these values may be different, especially for polymers which are often viscoelastic (time dependent) materials. Equivalence of the flexural modulus with Young's modulus also assumes equivalent compressive and tensile moduli as bend specimens have both tensile and compressive strain. Polymers in particular often have drastically different compressive and tensile moduli for the same material.