A short way to phrase this question is:
Shear describes the translation of one part of a body relative to another given an applied force.
What is the equivalent rotational term? That is,
What describes the rotation of one part of a body relative to another given an applied moment of force?
In more detail:
I'm trying to find the right word for a particular type of distortion. I have an assembly of items connected to be approximately solid. I mount one flat to a wall, and put some force or moment onto the opposite flat side so that the assembly distorts. In particular, I want to correctly describe the relative rotation of the two flats (in any direction), and I want this term to describe only the rotation, and exclude any translation (so that if it only shears without twisting I'd like the quantity to be zero).
I thought of torsion, but definitions of torsion always seem to refer to a bar or an elongated axis of some type. Is a bar required for "torsion" to be meaningful? I thought of twist, but that doesn't necessarily imply a dynamic quantity, so, for example, one could freeze in a twist, and something can be twisted without forces applied. I don't think bend is correct because that could just refer to translation. Is there a better word that I'm not thinking of, or even a concise phrase?
If there is a word that matches my needs, a reference that I could review would be very helpful.
Why "bending" is not the word I need
Below is a sketch of two objects that are bending along the same curve (both by intuition and the equations), yet the rotation of the ends is different in each. I'm interested in a word or phrase for describing the rotation of the ends (or a tendency for the ends to rotate or not, etc).
Also, according to wikipedia, bending "characterizes the behavior of a slender structural element" under load, but I'm not interested in slender elements (and only drew the above to illustrate bending). The first is the common way a beam would bend, but not everything bends like a beam, and I am hoping to find a word that characterized the particular difference illustrated here.
Things that don't bend like normal beams
A reasonable model is a highly anisotropic material, rigid in one axis but less so in the others. For example, a bundle of parallel fiber optic cables.
I think another would be a tube filled with water at high pressure, like a fire hose. (I don't know how this bends, but I doubt it bends like a beam.)
Here's a sketch of a structure that doesn't bend like a beam, in that the side parallel to the wall stays parallel, even though the rest of the structure bends in a normal way. The black dots are meant to represent rotating joints. Even if this item were long and slender I think the ends would stay parallel. The point of the third picture is that you don't necessarily get to see what's on the inside (but it could still be important to describe that the two walls don't rotate with respect to each other in response to an applied force).