3D-printing biomimetic structures to reveal the mechanics of natural systems

Michael M Porter 

Natural Engineering Lab, Department of Mechanical Engineering, Clemson University; Zucker Graduate Education Center, N. Charleston, SC, 29405

Biological systems are notoriously difficult to study because many are protected or have limited access; they also exhibit a high variability of forms and properties (no two organisms ever grow exactly alike). For these reasons, many researchers use artificial models to help understand natural phenomena. However, in contrast to the many established technologies used to investigate biological systems – such as microscopes to visualize the microstructures of tissues or treadmills to measure the running speeds of animals – additive manufacturing, or 3D-printing, has only recently entered the field as a new tool of discovery in biological research.

In short, many biologists, engineers, and designers are working together to create biomimetic models of natural systems to explore their properties and behaviors. This is different from the original intent of biomimicry: “to [innovate] sustainable solutions to human challenges by emulating nature’s time-tested patterns and strategies” (The Biomimicry Institute, 2017). Instead, artificial models of biological systems are designed with CAD software and built with 3D printers, then tested in controlled laboratory environments. The result: a surplus of data to explain biological phenomena without the need for controversial in vivo or invasive testing, and designs that lie outside of the natural morphospace can be created and compared with their natural counterparts to reveal the mechanisms that control their mechanics.

In recent years, many research groups have created biomimetic analogues of natural materials, structures, and organisms to explore their biomechanics. Here, I highlight a few representative studies that mimic the dermal armors of various fishes via 3D-printing.

Figure 1 shows schematic illustrations of a diversity of fish armors. They can be broadly classified as (A) elasmoid scales, (B) ganoid scales, (C) placoid scales, (D) carapace scutes, and (E) bony plates. Commonly found in striped bass, gars, sharks, boxfishes, seahorses and many other fishes, these armored systems are composed of relatively rigid structures embedded in a more compliant skin and interconnected by various articulation patterns. The interfaces of the rigid elements range from simple overlaps and abutted sutures to more complex peg-and-socket joints. 

Fig. 1. Representative schematics of common protective armors among living fishes. (A) Overlapping elasmoid scales common among most teleosts, such as striped bass; (B) interlocking ganoid scales common among gars and bichirs; (C) partially imbricated placoid scales common among sharks; (D) tessellating carapace scutes common among boxfishes; (E) interlocking and overlapping bony plates common among seahorses and related syngnathid fishes. Figures and caption taken from (Porter et al., 2017).

To better understand the mechanics of these structures, several researchers have performed studies on 3D-printed proxies of the natural armors. In most cases, the natural complexity of the dermal armors is reduced or simplified. This is because 3D-printing currently has many limitations; most machines can only print a few materials (most often polymers) with Young’s moduli up to only a few GPa at resolutions on the order of ~100 μm. However, these design constraints are not necessarily a bad thing. The reduced structures lend themselves nicely to validate analytical and computation results; they can also be built such that only one mechanism is investigated at a time, a strategy that is simply not possible with only natural specimens.

Below are several figures taken from (Porter et al., 2017) highlighting recent reports that used 3D-printing to study the mechanics of some fish-inspired structures.

Figure 2 shows several versions of overlapping elasmoid-like structures created to explore their mechanics. The biomimetic models were created by: (A) 3D-printing the plates, then casting them in a silicon rubber (Browning et al., 2013); (B) 3D-printing the plates, then gluing them on a silicon base (Ghosh et al., 2014); (C) 3D-printing the plates and supporting matrix with a multi-material machine (Rudykh et al., 2015). In these studies, it was found that interference and frictional contact between adjacent scales cause them to rotate and bend, store energy, and strike a balance of combined protection and flexibility.

Fig. 2. Elasmoid scales provide body mobility and puncture resistance. (A) Three representative 3D-printed models used to evaluate the effects of scale size, inclination, and overlap; (B) 3D-printed model of overlapping scales used to validate analytical models describing the effect of frictional sliding during bending; (C) multi-material 3D-printed model of hard scales embedded in a soft substrate subjected to 3-point bending. (D-F) Diagrams illustrating the two-dimensional micromechanical behavior of overlapping fishscales in concave bending, which are dependent on the rotation and bending stiffnesses of the scales. Symbols in (D-F): scale length (l), separation distance (rl), radius of curvature of the skin (R) and scale (Rs), scale rotation angle (theta), scale attachment stiffness (K), and scale rigidity (EI). Scale bars: (A) 25 mm; (C) 10 mm. Images adapted from (A) (Browning et al., 2013); (B) (Ghosh et al., 2014); (C) (Rudykh et al., 2015); (D-F) (Vernerey and Barthelat, 2014). Figures and caption taken from (Porter et al., 2017).

Figure 3 shows 3D-printed models that replicate the morphology of ganoid scales. In this study, the biomimetic models were scaled up for visualization and manual manipulation. It was found that the morphology of the plates changes across the body of a bichir fish, providing more protection near its head and more flexibility near its tail. These mechanisms were further exploited to design customized armors to cover different body curvatures, including a human shoulder (Duro-Royo et al., 2015).  

Fig. 3. Ganoid scales provide protection and flexibility. (A-D) 3D-printed replicas of scales from near the head (A, B) and tail (C, D) of a bichir fish (Polypterus senegalus); (E) schematic illustrating the transition from protection near the head of the fish in blue to flexibility near the tail of the fish in red. (F) Illustrations of different body curvatures observed in swimming fishes. The arrows in (B & D) indicate the direction of insertion of the peg-and-socket joints. The coordinate axes indicate the anteroposterior (u), ventrodorsal (v), and lateral (n) directions, with respect to the body of the fish. Images adapted from (Duro-Royo et al., 2015). Figures and caption taken from (Porter et al., 2017).

Figure 4 shows 3D-printed arrays of topologically interlocked structures, which are similar to the overlapping edges of many ganoid scales. Adding the topological interlocks enhances the stiffness, strength and resilience of the structures because contact at the inclined interfaces of the plates redistributes the puncture load through the entire tessellation. For more details on this and related structures, refer to (Martini et al., 2017).

Fig. 4. Effect of scale geometry on puncture resistance. (A) A 5 x 5 array of simple square scales made of stiff ABS plastic resting on a softer silicon substrate, punctured by a sharp steel needle; (B) the same system, with the addition of 45° angles on the sides of the scales to generate topological interlocking between the scales. (C) Puncture force-deflection curves for simple and interlocked scales with associated sequences of pictures. Both systems fail by sudden tilting of the indented scale. However, tilting is delayed in the interlocked scales, which increases the puncture resistance by a factor of four. Scale bars: 10 mm. Figures and caption taken from (Porter et al., 2017).

Figure 5 shows biomimetic models of shark skin used for hydrodynamic studies. Natural shark skin, shown in panel (A), is composed of several placoid scales that are shaped like tiny hydrofoils. These structures pin vorticities, which reduce static drag and increase the swimming speed of the cartilaginous fishes. In different studies, synthetic models of the shark-like skins were tested to reveal the mechanical effects of the scales (Wen et al., 2014), their patterning (Wen et al., 2015) and their bristled form (Lang et al., 2008).

Fig. 5. Placoid scales (dermal denticles) reduce drag in shark skins. (A) Scanning electron micrograph of a natural shark skin (Sphyrna tiburo); (B) computer model of biomimetic denticles designed for 3D-printing; (C) micrograph of a biomimetic shark skin, showing scale engagement in concave bending and scale separation in convex bending. (D) Image of a computer-rendered model of bristled scales used to create a synthetic prototype for experimental testing; (E) schematic illustration of the fluid roller bearing effect of drag reduction by bristled scales, showing the primary, secondary, and tertiary vorticities. The axes in (D) indicate the anteroposterior (x), lateral (y), and ventrodorsal (z) directions. Scale bars: (A) 200 μm; (C & D) each denticle is scaled up from the natural ~200 μm to (C) ~1.5 mm long and (D) ~20 mm long. Images adapted from (A-C) (Wen et al., 2014) and (D & E) (Lang et al., 2008). Figures and caption taken from (Porter et al., 2017).

Figures 6 & 7 show images from two studies on 3D-printed models of boxfishes. In the first (Fig 6), 3D-printed models of boxfish bodies were tested in a flow tank to validate computational fluid dynamics studies on their swimming performance. It was found that the boxy shape of the fish increases drag, but enhances maneuverability due to instabilities that promote tighter turning (Wassenbergh et al., 2015). In the second (Fig 7), multi-material models of a boxfish carapace were compressed to reveal the mechanisms that protect the animal from crushing. It was found that the boxy shape promotes buckling of the body; the sutured interfaces between its armored scutes enhances its resistance to crushing (Kenneson, 2016).

Fig. 6. The shape of a boxfish carapace enhances swimming manueverability. (A) 3D-printed model of a boxfish carapace (~60 mm wide). (B & C) Computational fluid dynamics models of (B) the lead-edge pressure waves and (C) the trailing-edge vortices induced during swimming of a boxfish (Ostracion cubicus). The color scheme in (B) illustrates the distribution of negative pressure (blue) to postitive pressure (red) on the leading-edge of the carapace. The color scheme in (B) illustrates vorticity flows in the anti-clockwise (blue) and clockwise (red) directions for the front (left), dorsal (top, right) and lateral (bottom, right) views. Images adapted from (Van Wassenbergh et al., 2015). Figures and caption taken from (Porter et al., 2017).

Fig. 7. Carapace scutes provide body support in boxfishes. (A-C) Micro-computed tomography images of the hierarchical organization of a boxfish carapace (Lactoria cornuta), showing its (A) ventral surface, (B) tessellation pattern of predominantly hexagonal scutes, and (C) zigzag-like sutures between adjacenet scutes. (D) Load-displacement curves illustrating the compressive behaviors of three hypothetical models of 3D-printed boxfish carapaces. The inset (top, left) shows a representative 3D-printed model of a boxfish carapace (~70 mm wide) that was compressed ~15%, where the blue outline shows its orginial shape before loading. The slopes of the load-displacement curves before and after the scutes engage, which is a result of concave bending of the carapace sides, are denoted by the apparent moduli, E1' and E2'. (E-G) Magnified models of the three hypothetical carapaces tested, two with a biomimietc armor (orange) covering a flexible skin (yellow) having (E) sutured interfaces or (F) flat interfaces, and another with (G) a flexible skin only. Scale bars: (A) 5 mm; (B) 1 mm; (C) 50 μm; (E-G) 2 mm. Images adapted from (A-C) (Yang et al., 2015). Figures and caption taken from (Porter et al., 2017).

Figure 8 shows images of several sutured interfaces printed for mechanical testing. The 3D-printed models were created to validate analytical models that describe the stress response of the interfaces under loading (Li et al., 2011, 2012, 2013; Lin et al., 2014a, 2014b). It was found that triangular sutures are the best design for high strength and toughness; additional levels of hierarchy, shown in panel (B), further amplify their mechanical properties. In a similar study, jigsaw-like structures were also printed to validate analytical models (Malik et al., 2017).

Fig. 8. Suture geometries and hierarchies provide mechanical strength, stiffness, and toughness. (A) 3D-printed samples with first-order sutures, where β describes the suture angle measured with respect to the vertical axis of anti-trapezoidal (-11.3°), rectangular (0°), trapezoidal (11.3°), and triangular (22.6°) geometries. The inset (top, right) shows stretching of the softer interfacial layer that bonds the traingular sutures when subject to tension. (B) 3D-printed samples with varying levels of suture hierarchy, where N describes the level of hierarchy, as first (1), second (2), or third (3) order. Scale bars: (A) 10 mm (inset: 5 mm); (B) 10 mm. Images adapted from (A) (Lin et al., 2014a) and (B) (Lin et al., 2014b). Figures and caption taken from (Porter et al., 2017).

Figure 9 shows images of a seahorse skeleton and biomimetic models used to explain “why the seahorse tail is square” (Porter et al., 2015). In this study, natural square-prism and hypothetical cylindrical models of a seahorse tail skeleton were created to compare their mechanics in bending, twisting, and crushing. It was found that the square structure outperforms the cylindrical one as an armored and grasping appendage.

Fig. 9. Bony plates facilitate tail prehensility in seahorses. (A-C) Micro-computed tomographs of (A) a seahorse (Hippocampus reidi) and its tail in (B) bending, twisting, and (C) compression. For clarity, the vertebral column is colored magenta, and the bony plates are colored red, yellow, blue, and green. (D) Computer-generated images of a hypothetical cylindrical model and a natural square-prism model of a seahorse tail wrapped around a cylinder, illustrating their respective surface contact when grasping. (E, F) Images of 3D-printed prototypes compressed just before failure, which occurs when the spring struts disjoin from the 3D-printed plates, illustrating the (E) rotational hinge and (F) linear sliding mechanisms that occur at the overlapping joints of the cylindrical and square-prism structures, respectively. Scale bars: (A) 10 mm; (B & C) 2 mm; (E & F) 3D-printed models are ~60 mm wide. Images adapted from (A-C, E, F) (Porter et al., 2015). Figures and caption taken from (Porter et al., 2017).

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