Computational analysis of liquid crystalline elastomer membranes: Changing Gaussian curvature without stretch energy

Liquid crystalline elastomers (LCEs) can undergo extremely large reversible shape changes when exposed to external stimuli, such as mechanical deformations, heating or illumination. The deformation of LCEs result from a combination of directional reorientation of the nematic director and entropic elasticity. In this paper, we study the energetics of initially flat, thin LCE membranes by stress driven reorientation of the nematic director. The energy functional used in the variational formulation includes contributions depending on the deformation gradient and the second gradient of the deformation. The deformation gradient models the in-plane stretching of the membrane. The second gradient regularises the non-convex membrane energy functional so that infinitely fine in-plane microstructures and infinitely fine out-of-plane membrane wrinkling are penalised. For a specific example, our computational results show that a non-developable surface can be generated from an initially flat sheet at cost of only energy terms resulting from the second gradients. That is, Gaussian curvature can be generated in LCE membranes without the cost of stretch energy in contrast to conventional materials. © 2013 Elsevier Ltd. All rights reserved.

The shape of helically creased cylinders

Creasing in thin shells admits large deformation by concentrating curvatures while relieving stretching strains over the bulk of the shell: after unloading, the creases remain as narrow ridges and the rest of the shell is flat or simply curved. We present a helically creased unloaded shell that is doubly curved everywhere, which is formed by cylindrically wrapping a flat sheet with embedded foldlines not axially aligned. The finished shell is in a state of uniform self-stress and this is responsible for maintaining the Gaussian curvature outside of the creases in a controllable and persistent manner. We describe the overall shape of the shell using the familiar geometrical concept of a Mohr's circle applied to each of its constituent features-the creases, the regions between the creases, and the overall cylindrical form. These Mohr's circles can be combined in view of geometrical compatibility, which enables the observed shape to be accurately and completely described in terms of the helical pitch angle alone. Copyright © 2013 by ASME.

Two-dimensional Cartesian air-gap element (CAGE) for dynamic finite-element modeling of electrical machines with a flat air gap

This paper extends the air-gap element (AGE) to enable the modeling of flat air gaps. AGE is a macroelement originally proposed by Abdel-Razek et al.for modeling annular air gaps in electrical machines. The paper presents the theory of the new macroelement and explains its implementation within a time-stepped finite-element (FE) code. It validates the solution produced by the new macroelement by comparing it with that obtained by using an FE mesh with a discretized air gap. It then applies the model to determine the open-circuit electromotive force of an axial-flux permanent-magnet machine and compares the results with measurements.