Stiffness is the rigidity of an object — the extent to which it resists deformation in response to an applied force.^{[1]}
The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.^{[2]}
Contents

Calculations 1

Compliance 2

Rotational stiffness 3

Relationship to elasticity 4

Applications 5

See also 6

References 7
Calculations
The stiffness, k, of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as

k=\frac {F} {\delta}
where,

F is the force applied on the body

δ is the displacement produced by the force along the same degree of freedom (for instance, the change in length of a stretched spring)
In the International System of Units, stiffness is typically measured in newtons per meter. In Imperial units, stiffness is typically measured in pounds(lbs) per inch.
Generally speaking, deflections (or motions) of an infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple DOF (maximum of six DOF at a point). For example, a point on a horizontal beam can undergo both a vertical displacement and a rotation relative to its undeformed axis. When there are M degrees of freedom a M x M matrix must be used to describe the stiffness at the point. The diagonal terms in the matrix are the directrelated stiffnesses (or simply stiffnesses) along the same degree of freedom and the offdiagonal terms are the coupling stiffnesses between two different degrees of freedom (either at the same or different points) or the same degree of freedom at two different points. In industry, the term influence coefficient is sometimes used to refer to the coupling stiffness.
It is noted that for a body with multiple DOF, the equation above generally does not apply since the applied force generates not only the deflection along its own direction (or degree of freedom), but also those along other directions.
For a body with multiple DOF, in order to calculate a particular directrelated stiffness (the diagonal terms), the corresponding DOF is left free while the remaining should be constrained. Under such a condition, the above equation can be used to obtain the directrelated stiffness for the degree of freedom which is unconstrained. The ratios between the reaction forces (or moments) and the produced deflection are the coupling stiffnesses.
A description including all possible stretch and shear parameters is given by the elasticity tensor.
Compliance
The inverse of stiffness is compliance (or sometimes elastic modulus), typically measured in units of metres per newton. In rheology it may be defined as the ratio of strain to stress,^{[3]} and so take the units of reciprocal stress, e.g. 1/Pa.
Rotational stiffness
A body may also have a rotational stiffness, k, given by

k=\frac {M} {\theta}
where

M is the applied moment

θ is the rotation
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:

shear stiffness  ratio of applied shear force to shear deformation

torsional stiffness  ratio of applied torsion moment to angle of twist
Relationship to elasticity
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 structure. 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

k=\frac {AE} {L}
where

A is the crosssectional area,

E is the (tensile) elastic modulus (or Young's modulus),

L is the length of the element.
Similarly, the rotational stiffness of a straight section is

k=\frac {GJ} {L}
where

"J" is the torsion constant for the section,

"G" is the rigidity modulus of the material
Note that in SI, these units yield k : \frac{N \cdot m}{rad}. 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.
Applications
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.
In biology, the stiffness of the extracellular matrix is important for guiding the migration of cells in a phenomenon called durotaxis.
See also
References

^ Baumgart F. (2000). "Stiffnessan unknown world of mechanical science?". Injury (Elsevier) 31.

^ Martin Wenham (2001), "Stiffness and flexibility", 200 science investigations for young students, p. 126,

^ V. GOPALAKRISHNAN and CHARLES F. ZUKOSKI; "Delayed flow in thermoreversible colloidal gels"; Journal of Rheology; Society of Rheology, U.S.A.; July/August 2007; 51 (4): pp. 623–644.
This article was sourced from Creative Commons AttributionShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, EGovernment Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a nonprofit organization.