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 object ...

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 Ea ...

, 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 informa ...

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. 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 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 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 Green-Lagrange strain 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