Origami structures are a traditional Japanese art that have recently found their way into engineering applications due to their powerful capability to transform flat 2D structures into complex 3D structures along their creases. This has given a rise to their application as designer materials with unprecedented mechanical characteristics, also known as metamaterials. Herein, gradient Miura-ori origami metamaterials are introduced as a method to preprogram out-of-plane curvatures. Several types of unit cell distributions in the origami lattice structure including checkered, linear gradient, concave radial gradient, convex radial gradient, and striped are considered. The results show that these distributions of Miura-ori origami can create single- or double curvatures including twisting, saddling, bending, local inflation, local twisting, local bending, and wavy shapes, when the origami metamaterial is loaded in compression. All the Gaussian curvatures (negative, positive, and zero) can be achieved using the proposed models. The approach helps tailoring complex preprogrammed surface geometries by employing linearly varying gradient distributions of Miura-ori origami.

Triply periodic minimal surfaces (TPMS) metamaterials and shape-memory polymer (SMP) smart materials are known for their beneficial attributes in novel scientific and industrial fields. Through TPMS designs, low weight accompanied by high surface area are achievable, which are known as crucial parameters in many fields, such as tissue engineering. Moreover, SMPs are well-suited to generate force or to recover their permanent shape by means of an external stimulus. Combining these properties is possible by fabricating TPMS-based metamaterials made out of SMPs, which can be applicable in numerous applications. By considering different level volume fraction of four types of TPMS-based lattices (diamond, gyroid, IWP, and primitive), we focus on the effect of micro-architecture on shape-memory characteristics (i.e., shape recovery, shape fixity, and force recovery) as well as mechanical properties (elastic modulus and Poisson's ratio) of these smart metamaterials. For this purpose, shape-memory effect (SME) is simulated employing thermo-visco-hyperelastic constitutive equations coupled with the time-temperature superposition principle. It is observed that by increasing the level volume fraction of each lattice type, the elastic modulus, shape fixity, and force recovery increase, while the shape recovery diminishes. Such behaviors can be attributed to different deformation modes (flexural or uniaxial) in SMP TPMS-based metamaterials. Furthermore, it is shown that the Poisson's ratio has a nonlinear behavior in these structures. The smart metamaterials introduced in this study have the advantage of providing the possibility of designing implants, especially in bone defects tailored with different micro-architectures depending on each patient's specific need.

The shape memory behavior of smart materials is widely used for stimulation or shape-shifting purposes. Shape memory polymers (SMPs) can shape and force recoveries accompanied by attractive attributes such as biocompatibility, biodegradability, and universality. In this paper, a thermoplastic elastomer (TPE) is used as a complementary material for 4D printed polylactic acid (PLA) structures to enhance their shape and force recovery properties and lower the stimulation temperature for more practical implementations. Two approaches are followed to provide SMP composites (SMPCs): multi-layered and multi-material lattices. In multi-layered lattices, specimens are comprised of separate layers and different ratios of SMP and TPE materials. For comparison, PLA-TPE filaments with the same ratios of multi-layered lattices are produced and used to fabricate multi-material lattices. Dynamic mechanical thermal analysis tests showed a reduction in the glass transition temperature of the manufactured PLA-TPE filament. X-ray diffraction test was conducted to prove that the crystallinity of the developed PLA-TPE material increases which explains the better shape memory effect in the multi-material specimens. Phase separation occurred in low ratios of TPE in PLA, discernible in field emission scanning electron microscope (FESEM) images, resultting in low quality in one of the developed PLA-TPE filaments. FESEM images also showed proper miscibility of TPE in PLA in higher ratios. Thermomechanical tests were done on printed specimens to examine and compare the shape and force recovery of the produced SMPCs. While the shape recovery of multi-material samples was not as good as multi-layered samples, both approaches have better shape recovery results than the PLA sample. Due to a lower glass transition temperature in multi-material lattices, their shape recovery process started at lower temperatures widening their potential practical applications. Force recovery of multi-material samples revealed a significant improvement which was due to more oriented crystalline polymer structures.