mechanics Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...

and

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

, pure shear is a

three-dimensional In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (''coordinates'') are required to determine the position (geometry), position of a point (geometry), poi ...

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