Bistable laminates with non-cylindrical curved shapes

Abstract

Thermally-cured fiber-reinforced polymeric laminates can exhibit bistable cylindrical shapes when their plies are configured orthogonally. Such “cross-ply” laminates have been studied extensively through modeling and experiments. However, bistable laminates with non-cylindrical shapes, especially through non-orthogonal ply orientations, have received little attention due to inherent design limitations. This paper presents an approach for developing non-cylindrical curved shapes based on bistability in mechanically-prestressed laminates; prestress is applied by laminating prestrained fiber-reinforced elastomeric laminae on either face of an initially stress-free isotropic layer. An analytical laminated-plate model is developed based on strain energy minimization and stable shapes are calculated for various orientations of the prestrained laminae. The modeled shapes are in agreement with the measured shapes of physical rectangular laminates within 11%. The minimum polynomial order for the calculation of non-cylindrical shapes is fourth; a simplified constitutive model for prestrained-elastomers is developed to reduce computation time. The domain of bistability is investigated taking into account the combined effect of prestrain orientation and the ratio of prestrains, laminate size, and aspect ratio. Modeling of snap-through actuation requirements shows that actuation effort is maximum when one of the prestressed laminae is on a diagonal and the angle between prestrains is 45°.