Curvature tuning through defect-based 4D printing


The latest developments in 4D printing have ushered in a new era of smart materials capable of changing shape and properties over time. Standard filament printing introduces residual stresses in the material along the printing direction. Upon heating, these stresses relax, inducing metric changes and deformation of the structure. For instance, a flat disk printed from successive rings adopts a conical shape after heating (see Figure 1a). In addition, thinner disk specimens tend to curl, suggesting a gradient of residual stress across the thickness. Traditionally, such deformations are undesired. Can we shift paradigms and harness printing procedures to program shape changes?

The quest for reverse deformation. Our exploration pivoted when we questioned, "How can we design structures to undergo reverse deformation?" (Figure 1b). Investigating the dynamic mechanical properties of printed filaments did not provide a definitive answer. Instead, a key insight came from analyzing the microstructure of these prints. Inspired by natural phenomena, such as leaves curling due to water evaporation or thin wood slices deforming upon drying (Figure 1c), we recognized the deliberate formation of micro-defects as crucial in driving shape transformations. This perspective shift allowed us to see imperfections not as obstacles but as facilitators of controlled deformation. Nature acted as our mentor, where gaps and spaces within biological structures allowed for controlled contractions. In printed filaments, these gaps emerged as spaces for contraction, offering a new outlook on the role of defects.

Fused Deposition Modeling as a platform for innovation. Two phenomena became central in advancing 4D printing with polymeric materials: anisotropic filament deformation and the formation of micro-defects during the printing process. We used fused deposition modeling as a dynamic platform for innovation in 4D printing, aiming to achieve complex shape transformations and to use imperfections as a design tool. By adjusting printing parameters such as bed temperature, nozzle temperature, and printing speed, we expanded the design possibilities for diverse shape-morphing behaviors.

Experimental journey. Our journey involved manipulating the spatial distribution of imperfections and residual stresses by varying printing speeds and integrating multi-materials. We aimed to reveal the potential within imperfections and residual stresses. Through a series of experiments, we demonstrated that imperfections could be exploited to achieve targeted shape transformations. The interaction between printing speed, micro-defects, and multi-material configurations paved the way for intricate positive curvatures, reverse deformations, and defying conventional limits (Figure 1d-left). We also intentionally introduced a softer material to affect local deformation, enabling us to control residual stresses and bending stiffness, thus accessing a range of curvature types. The combination of varying expansion factors, imperfection distributions, and multi-material printing resulted in complex 3D structures with complex geometries (Figure 1d-right). From negative to positive values of mean and Gaussian curvature, our defect-based metamaterials promise diverse applications, from soft robotics and mechanical metamaterials to innovative advancements in medical devices, particularly in drug delivery systems (Figure 1e).

Theoretical framework and computational models. To explain our experimental observations, we devised an analytical model to calculates out-of-plane deformation based on the anisotropic expansion factor of microstructures. We developed computational models to predict shape-changing behaviors, considering both imperfections and material properties. These theoretical approaches validated our experimental results and provided a deeper understanding of the mechanisms behind shape transformations in 4D printing (Figure 1e).

In conclusion, our research demonstrates how viewing printing imperfections as design elements can broaden our capabilities in creating sophisticated, programmable materials. This opens new avenues for the practical application use of defect-based metamaterials, inspiring further innovation and creativity in the field of 4D printing. We anticipate that our findings will extend the possibilities for smart materials and complex design strategies.

Figure 1: (a) The out-of-plane deformation of 2D structures, including triangles with horizontal filament patterns, squares, hexagons, and circles with concentric filament deposition, exhibited a similar dome-shaped transformations upon thermal activation. A uniform printing speed of 80 mm/s was used for these specimens. We extended our exploration by combining shapes, such as triangles and semi-circles, and 3D printing 2D planes with four distinct patterns: linear-horizontal, linear-vertical, concentric, and a combination of concentric and multi-material. The first deposited layers (F.D.L) are depicted in (a). (b) The distribution of residual stresses across the thickness played a pivotal role in determining the bending orientation of PLA disks. By employing a faster printing strategy for the initial layers, higher stress was introduced at the bottom layer of the PLA disks, resulting in inverse bending with an opposite localized curvature, as opposed to case where the higher gradient was at the top layer of PLA disks. (c) Nature-inspired observations revealed that shape-shifting commonly occurs due to drying processes and material shrinkage. Akin to a freshly cut slice of wood transforming from a flat state into a dome-like shape upon drying, similar out-of-plane shape transformations occurred when a 4D printed disk made of shape memory polymers was exposed to high temperatures. (d) The PLA disks were segmented into inner and outer regions, with the inner part printed at a minimum speed (20 mm/s) and the outer part at a maximum speed (80 mm/s). This segmentation resulted in discontinuous out-of-plane deformation, developing positive Gaussian curvature (κ>0) and negative mean curvature (H < 0) (i). Switching the printing speed of the inner and outer parts led to different shape transformations and local curvatures (ii). The peripheral edge of PLA disks was printed from a softer material (TPU), altering local mean and Gaussian curvatures (iii). Swapping the printing order of soft and hard polymers further changed the overall shape transformation and local curvature values (iv). (e) Precision in positioning imperfections in PLA disks, coupled with the integration of inverse bending and out-of-plane deformation concepts, enabled achieving more complex shape transformations (e–left). Introducing a soft polymeric phase and alternating the position of residual stress in the design of 4D printed disks led to even more intricate shapes (e–right).


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Physical Sciences > Materials Science > Biomaterials
Materials Engineering
Technology and Engineering > Mechanical Engineering > Materials Engineering
Structural Mechanics
Technology and Engineering > Mathematical and Computational Engineering Applications > Engineering Mechanics > Solid Mechanics > Structural Mechanics

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