Annulus Twist as a verification test

Illustrated below is the solution to an idealized problem of a linear elastic annulus (blue) subjected to twisting motion caused by rotating the T-bar an angle \alpha .  The motion is presumed to be applied slowly enough that equilibrium is satisfied.

This simple problem is taken to be governed by the equations of equilibrium \vec{\nabla}\cdot\sigma=0 , along with the plane strain version of Hooke’s law in which Cauchy stress is taken to be linear with respect to the small strain tensor (symmetric part of the displacement gradient).  If this system of governing equations is implemented in a code, the code will give you an answer, but it is up to you to decide if that answer is a reasonable approximation to reality. This observation helps to illustrate the distinction between verification (i.e., evidence that the equations are solved correctly) and validation (evidence that physically applicable and physically appropriate equations are being solved).  The governing equations always have a correct answer (verification), but that answer might not be very predictive of reality (validation).

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