# 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.

### 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.

### Newton metre

**N·mNmnewton-metre**

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

### Radian

**radiansradmicroradian**

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**