A simplified variational model for the formation of convoluted accommodation structures, as seen in the hinge zones of larger-scale geological folds, is presented. The model encapsulates some important and intriguing nonlinear features, notably: infinite critical loads, formation of plastic hinges, and buckling on different length-scales. An inextensible elastic beam is forced by uniform overburden pressure and axial load into a V-shaped geometry dictated by formation of a plastic hinge. Using variational methods developed by Dodwell et al., upon which this paper leans heavily, energy minimisation leads to representation as a fourth-order nonlinear differential equation with free boundary conditions. Equilibrium solutions are found using numerical shooting techniques. Under the Maxwell stability criterion, it is recognised that global energy minimisers can exist with convoluted physical shapes. For such solutions, parallels can be drawn with some of the accommodation structures seen in exposed escarpments of real geological folds.