In mechanics, the flexural modulus or bending modulus ^[1] 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. ^[2] The flexural modulus defined using the 2-point (cantilever) and 3-point bend tests assumes a linear stress strain response. ^[3]

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: ^[1]

${\displaystyle E_{\mathrm {flex} }={\frac {L^{3}F}{4wh^{3}d}}}$

From elastic beam theory

${\displaystyle d={\frac {L^{3}F}{48IE}}}$

and for rectangular beam

${\displaystyle I={\frac {1}{12}}wh^{3}}$

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

For very small strains in isotropic materials – like glass, metal or polymer – flexural or bending modulus of elasticity is equivalent to the tensile modulus ( Young's modulus) or compressive modulus of elasticity. However, in anisotropic materials, for example wood, these values may not be equivalent. Moreover, composite materials like fiber-reinforced polymers ^{[4] [3]} or biological tissues ^[5] are inhomogeneous combinations of two or more materials, each with different material properties, therefore their tensile, compressive, and flexural moduli usually are not equivalent.

Related pages

• Stiffness

References

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