# Stiffness

flexibilityrigidityrigidtorsional rigiditycompliancestiffflexiblecompliantstiffertorsional stiffness
Stiffness is the extent to which an object resists deformation in response to an applied force.wikipedia
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### Hooke's law

spring constantforce constantelasticity tensor
A description including all possible stretch and shear parameters is given by the elasticity tensor.
That is: F_s=kx, where k is a constant factor characteristic of the spring: its stiffness, and x is small compared to the total possible deformation of the spring.

### Young's modulus

Young’s modulusmodulustensile modulus
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 structure.
Young's modulus, or the Young modulus, is a mechanical property that measures the stiffness of a solid material.

### Euler–Bernoulli beam theory

Euler–Bernoulli beam equationbeam theoryEuler-Bernoulli beam equation
For example, a point on a horizontal beam can undergo both a vertical displacement and a rotation relative to its undeformed axis.
:The quantity A_{xx} is the extensional stiffness,B_{xx} is the coupled extensional-bending stiffness, and D_{xx} is the bending stiffness.

### Torsion (mechanics)

torsiontorsionaltorsionally

### Durotaxis

durotactic
In biology, the stiffness of the extracellular matrix is important for guiding the migration of cells in a phenomenon called durotaxis.
With information from the previous observations, Lo and colleagues formulated the hypothesis that individual cells can detect substrate stiffness by a process of active tactile exploration in which cells exert contractile forces and measure the resulting deformation in the substrate.

### Torsion constant

torsional
The torsion constant, together with material properties and length, describes a bar's torsional stiffness.

### Elastic modulus

modulus of elasticityelastic modulimodulus
The elastic modulus of a material is not the same as the stiffness of a component made from that material.

### Extracellular matrix

ECMmatrixextracellular matrices
In biology, the stiffness of the extracellular matrix is important for guiding the migration of cells in a phenomenon called durotaxis.
The ECM can exist in varying degrees of stiffness and elasticity, from soft brain tissues to hard bone tissues.

### Deformation (mechanics)

straindeformationshear strain
Stiffness is the extent to which an object resists deformation in response to an applied force.

### Force

forcesattractiveelastic force
Stiffness is the extent to which an object resists deformation in response to an applied force.

### Degrees of freedom (mechanics)

degrees of freedomdegree of freedompitch
For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as

### International System of Units

SISI unitsSI unit
In the International System of Units, stiffness is typically measured in newtons per meter.

### Newton (unit)

kNnewtonN
In the International System of Units, stiffness is typically measured in newtons per meter.

### Pound (force)

lbflb f pound-force
In Imperial units, stiffness is typically measured in pounds(lbs) per inch. In the SAE system, rotational stiffness is typically measured in inch-pounds per degree.

### Deflection (engineering)

deflectiondeflectionsdeflect
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).

### Displacement (vector)

displacementdisplacement vectordisplacements
For example, a point on a horizontal beam can undergo both a vertical displacement and a rotation relative to its undeformed axis.

### Matrix (mathematics)

matrixmatricesmatrix theory
When there are M degrees of freedom a M x M matrix must be used to describe the stiffness at the point.

### Multiplicative inverse

reciprocalinversereciprocals
The inverse of stiffness is flexibility or compliance, typically measured in units of metres per newton.

### Rheology

rheologicalrheologistrheological properties
In rheology, it may be defined as the ratio of strain to stress, and so take the units of reciprocal stress, e.g.

hPaMPakPa
1/Pa.

### Newton metre

N·mNmnewton-metre
In the SI system, rotational stiffness is typically measured in newton-metres per radian.

In the SI system, rotational stiffness is typically measured in newton-metres per radian.

### Degree (angle)

°degreesdegree
In the SAE system, rotational stiffness is typically measured in inch-pounds per degree.

### Moment (physics)

momentmomentsmoment arm

### Shear stress

shearshearingwall shear stress