As a new class of smart materials, shape memory polymers and their composites (SMPs and SMPCs) can respond to specific external stimulus and remember the original shape. There are many types of stimulus methods to actuate the deformation of SMPs and SMPCs, of which the thermal-and electro-responsive components and structures are common. In this review, the general mechanism of SMPs and SMPCs are first introduced, the stimulus methods are then discussed to demonstrate the shape recovery effect, and finally, the applications of SMPs and SMPCs that are reinforced with fiber materials in aerospace are reviewed. SMPC hinges and booms are discussed in the part on components; the booms can be divided again into foldable SMPC truss booms, coilable SMPC truss booms and storable tubular extendible member (STEM) booms. In terms of SMPC structures, the solar array and deployable panel, reflector antenna and morphing wing are introduced in detail. Considering the factors of weight, recovery force and shock effect, SMPCs are expected to have great potential applications in aerospace.

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