Stiffness is the resistance of an elastic body to deformation by an applied force. It is an extensive material property.
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The stiffness, k, of a body is a measure of the resistance offered by an elastic body to deformation (bending, stretching or compression).
where
In the International System of Units, stiffness is typically measured in newtons per metre.
As both the applied force and displacement are vectors (respectively P and δ), in general their relationship is characterised by a stiffness matrix, k, where:
The displacement can, in general, refer to a point distinct from that where the force is applied and a complicated structure will not deflect purely in the same direction as an applied force. The stiffness matrix enables such systems to be characterised in straightforward terms.
The inverse of stiffness is compliance, typically measured in units of metres per newton. In rheology it may be defined as the ratio of strain to stress ^{[1]}, and so take the units of reciprocal stress, e.g. 1/Pa.
A body may also have a rotational stiffness, k, given by
where
In the SI system, rotational stiffness is typically measured in newtonmetres per radian.
In the SAE system, rotational stiffness is typically measured in inchpounds per degree.
Further measures of stiffness are derived on a similar basis, including:
In general, elastic modulus is not the same as stiffness. Elastic modulus is a property of the constituent material; stiffness is a property of a solid body. That is, the modulus is an intensive property of the material; stiffness, on the other hand, is an extensive property of the solid body dependent on the material and the shape and boundary conditions. For example, for an element in tension or compression, the axial stiffness is
where
For the special case of unconstrained uniaxial tension or compression, Young's modulus can be thought of as a measure of the stiffness of a material.
The stiffness of a structure is of principal importance in many engineering applications, so the modulus of elasticity is often one of the primary properties considered when selecting a material. A high modulus of elasticity is sought when deflection is undesirable, while a low modulus of elasticity is required when flexibility is needed.
