In
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:
Note that this gives a
Green-Lagrange strain of:
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:
which has only shearing components.
See also
*
Simple shear
*
Squeeze mapping
In linear algebra, a squeeze mapping, also called a squeeze transformation, is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is ''not'' a rotation or shear mapping.
For a fixed positive real number , th ...
References
Fluid mechanics
Continuum mechanics
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