mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects r ...

and

geology Geology () is a branch of natural science concerned with Earth and other astronomical objects, the features or rocks of which it is composed, and the processes by which they change over time. Modern geology significantly overlaps all other Ear ...

, pure shear is a

three-dimensional Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...

homogeneous flattening of a body. It is an example of irrotational

strain Strain may refer to: Science and technology * Strain (biology), variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes * Strain (chemistry), a chemical stress of a molecule * Strain (injury), an injury to a mu ...

in which body is elongated in one direction while being shortened

perpendicularly In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...

. For soft materials, such as rubber, a strain state of pure shear is often used for characterizing hyperelastic and fracture mechanical behaviour. Pure shear is differentiated from

simple shear Simple shear is a deformation in which parallel planes in a material remain parallel and maintain a constant distance, while translating relative to each other. In fluid mechanics In fluid mechanics, simple shear is a special case of deformati ...

in that pure shear involves no rigid body rotation. The deformation gradient for pure shear is given by:

F = \begin1&\gamma&0 \\\gamma&1&0\\0&0&1\end

Note that this gives a

Green-Lagrange strain In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains and/or rotations are large enough to invalidate assumptions inherent in infinitesimal stra ...

of:

E = \frac\begin\gamma^2&2\gamma&0\\2\gamma&\gamma^2&0\\0&0&0\end

Here there is no rotation occurring, which can be seen from the equal off-diagonal components of the strain tensor. The linear approximation to the

shows that the small strain tensor is:

\epsilon = \frac\begin0&2\gamma&0\\2\gamma&0&0\\0&0&0\end

which has only shearing components.

References

Fluid mechanics Continuum mechanics {{geology-stub

See also

References