The one-dimensional energy functional of a bent beam made of a single crystal was derived within continuum dislocation theory. By relaxing the continuously differentiable minimiser of this energy functional, a sequence of piecewise smooth deflections and piecewise constant plastic distortions were constructed which reduced the energy and exhibited polygonization. The number of polygons could be estimated by comparing the surface energy of small-angle tilt boundaries with the contribution of the gradient terms from the weak minimiser in the bulk energy.

Polygonization as Low Energy Dislocation Structure. K.C.Le, Q.S.Nguyen: Continuum Mechanics and Thermodynamics, 2010, 22[4], 291-8