Defining relationships between geometry and behavior of bistable composite laminates

Abstract

Bistability is exhibited by an object when it can be resting in two stable equilibrium states. Certain composite laminates exhibit bistability by having two stable curvatures of opposite sign with the two axes of curvature perpendicular to each other. These laminates can be actuated from one state to the other. The actuation from the original post-cure shape to the second shape is called as ‘snap-through’ and the reverse actuation is called as ‘snap-back’. This phenomenon can be used in applications for morphing structures, energy harvesting, and other applications where there is a conflicting requirement of a structure that is load-carrying, light, and shape-adaptable. MW Hyer first reported this phenomenon in his paper in 1981. He found that thin unsymmetric laminates do not behave according to the predictions of the Classical Lamination Theory (CLT). The CLT is a linear theory and predicts the post-cure shape of thin unsymmetric laminates to be a saddle. MW Hyer developed a non-linear method called the “Extended Classical Lamination Theory” which accurately predicted the laminate to have two cylindrical shapes. Since then, a number of researchers have tried to identify the key parameters affecting the behavior of such laminates. Geometric parameters such as stacking sequence, fibre orientation, cure cycle, boundary conditions, and force of actuation, have all been studied. The objective of this research is to define a relation between the length, width and thickness of square and rectangular laminates required to achieve bistability. Using these relations, a 36 in × 36 in bistable laminate is fabricated with a thickness of 30 CFRP layers. Also, it is proved that a laminate does not lose bistability with an increase in aspect ratio, as long as both sides of the rectangular laminate are above a certain ‘critical length’. A bistable laminate with dimensions of 2 in × 50 in is fabricated. Further, for laminates that are bistable, it is necessary to be able to predict the curvature and force required for actuation. Therefore, a method is developed which allows us to predict the curvature of both stable shapes, as well as the force of actuation of laminates for which the thickness and dimensions are known. Finite Element Analysis is used to carry out the numerical calculations, which are validated by fabricating laminates. The curvature of these laminates is measured using a profilometer and the force of actuation is recorded using a universal test set-up.