# Why is pure shear a "shear"?

That is, a force acts along a surface of an element at it is elongated, turning a rectangle into a rhombus. Apparently this is called "simple shear".

But then I found out there is something called "pure shear", which is illustrated in this picture:

So pure shear, on the other hand, is a "flattening" of a body; the element is squeezed flatter on one axis and elongated on another. There is no change in angle between the lines, as there was in the simple shear case.

My question is: Why are these two things both called "shear strains"? What do they have in common, besides that neither change the area of the element? What is "pure" about "pure shear" and "simple" about "simple shear"?

Simple shear is caused when the force is acting along the surface of the element, without normal forces. But what about pure shear? It involves squeezing in one axis and elongating on other, so it must be caused by normal forces, right? But if this is right, then it wouldn't make sense to put this in the same category ("shear") as simple shear, as one would be caused by normal forces that act directly on the surfaces of the element, and the other by forces along the surfaces of the element.

In mechanics and geology, pure shear is a three-dimensional 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.

Example of pure shear in fracture mechanics:

• Mode I – Opening mode (a tensile stress normal to the plane of the crack),

• Mode II – Sliding mode (a shear stress acting parallel to the plane of the crack and perpendicular to the crack front), and

• Mode III – Tearing mode (a shear stress acting parallel to the plane of the crack and parallel to the crack front).

Ref.

You can actually take a look here: Shear, pure and simple for a mathematical description.