3D printed, bio-inspired prototypes and analytical models for structured suture interfaces with geometrically-tuned deformation and failure behavior
Introduction
Geometrically structured interfaces are prevalent throughout nature and give rise to many remarkable mechanical properties in a number of biological materials (Bruet et al., 2008; Dunlop et al., 2011, Li et al., 2011, Li et al., 2012a, Li et al., 2013a, Weiner and Addadi, 1997, Zhang et al., 2012). For example, both computational (Zhang et al., 2012) and experimental studies (Bruck, 2004) reveal that geometrically interlocking interfaces enhance interfacial stiffness and strength, and interface waviness increases resistance to crack propagation (Li et al., 2012b).
A particularly fascinating example of geometrically structured interfaces is composite suture interfaces. Suture interfaces are mechanical structures often found in biology consisting of compliant, interlocking seams connecting stiffer components (Allen, 2007, Jaslow, 1990, Krauss et al., 2009, Saunders, 1999, Sun et al., 2004, Li et al., 2011). In nature, a wide range of suture interface geometries are observed, ranging from nearly flat suture interfaces in infant human skulls (Sun et al., 2004) to intricate, fractal-like designs in ammonites (Saunders and Work, 1996). Suture interface geometries are found to vary within species (Allen, 2007, De Stefano et al., 2009), within a certain structure across species (Song et al., 2010), through evolution (Saunders, 1999), or even with development (Pritchard et al., 1956, Sun et al., 2004, Yu et al., 2004). The diverse interface geometries hint at nature’s ability to utilize a limited set of natural materials to achieve a wide range of properties and functions simply through variation in geometry (Dunlop and Fratzl, 2010, Meyers et al., 2008, Ortiz and Boyce, 2008).
The geometry of suture interfaces has been shown, experimentally or through finite element analysis (FEA), to influence mechanical performance. Suture interfaces have been found to increase energy absorption (Jaslow, 1990), compliance (Hubbard et al., 1971), deformability, (Dunlop et al., 2011) and flexibility (Herring, 2008, Krauss et al., 2009). In addition, suture interfaces were shown to play an important role in the redistribution of strain in skulls (Moazen et al., 2009). Increased interdigitation in suture interfaces was found to increase bending strength (Jaslow, 1990) and decrease suture strain energy (Jasinoski et al., 2010). These studies confirm that geometric variation affects the effective mechanical behavior of the suture interface. However, a systematic, comprehensive experimentally-verified understanding of the underlying role geometry plays in the overall mechanical behavior, including stiffness, strength, toughness, and failure mechanisms of suture interfaces, is lacking. Recently, we developed a generalized analytical suture interface model for the case of in-plane loading of any suture interface with arbitrary geometry verified by finite element modeling (Li et al., 2011, Li et al., 2012a, Li et al., 2013a). This model gives analytical solutions for the effective stiffness, strength, and fracture toughness of suture interfaces with an unbonded tip interface in terms of a set of independent geometric parameters and material properties of the compliant seam and stiffer interdigitating “teeth”. Using this analytical model, it was predicted that the mechanical properties of suture interface systems have a highly nonlinear dependence on geometry and order of hierarchy. In addition, a general trapezoidal suture interface was predicted to possess significantly enhanced stiffness, strength, and fracture toughness relative to a flat interface. For a given set of materials, altering the geometry of the suture interfaces was found to result in a range of values for stiffness, strength, and fracture toughness, demonstrating the possibility of precise tailorability of mechanical properties through geometry.
The objectives of this study are threefold. On the theoretical side, the analytical model presented in Li et al. (2013a) is extended to include the behavior of suture interfaces with bonded tip interfacial layers. In nature, suture interface geometries typically consist of initially fully bonded interfaces, and therefore the effect of a fully bonded interface on the effective mechanical behavior is determined. Experimentally, the relationship between geometry and mechanical behavior of general trapezoidal suture interfaces is systematically explored, through the design and fabrication of bio-inspired prototypes via 3D printing and mechanical experiments. Previously, we have employed 3D printing fabricate co-continuous composite structures with enhancements in stiffness, strength, and energy dissipation (Wang et al., 2011) and subsequently this fabrication method has been rapidly emerging as a means to create physical prototypes of material structures to explore the roles of geometry and materiality on properties and performance (Browning et al., 2013, Dimas et al., 2013, Li et al., 2013b). Here, we exploit multi-material 3D printing to construct physical prototypes of a range of suture waveforms with soft, compliant interface layers adhering stiffer skeletal teeth and reveal the ability to tune the mechanical behavior (stiffness, strength, toughness, deformation and failure mechanisms) through the interplay between geometry and materiality. Four categories of bio-inspired representative periodic geometries that resemble suture interfaces in the linking girdles of diatoms (Fig. 1A) are chosen: anti-trapezoidal, rectangular, trapezoidal, and triangular (Fig. 1B and C). These four geometries were designed to possess the same tooth volume fraction and wavelength, and the same interfacial layer thickness and material combination. Hence, the only difference is the shape. Specifically, we focus on three design parameters, which include bonded vs. unbonded flat interfacial layer at the peaks of the teeth, tooth tip angle (θ), and a shape factor β (Fig. 1B) defined by Li et al. (2013a) to distinguish tooth shape. This study enables the extraction of design principles from the theoretical and experimental results for the design of new material interfaces with tailored mechanical behavior.
Section snippets
Materials and methods
Bio-inspired suture interfaces with and without bonded tip regions, with different tip angles, and with different geometries were designed within Solidworks (Dassault Systemes, France) and fabricated (Fig. 1C) with an Objet Connex500 3D multi-material printer (Stratasys Ltd., USA). VeroWhite, an acrylic-based photo-polymer, was used for the teeth, and TangoPlus, a rubber-like compliant material, was used for the interfacial layers. For each set of designs, the volume fraction and interface
Theory
The geometry of a general trapezoidal suture interface can be described by five independent parameters: the wavelength, λ, the tooth amplitude, A, the shape factor, β, the slant interface width, g, and the tip interface width, g0 (Fig. 1B). β determines the shape of the suture interface: anti-trapezoidal when , rectangular when β=0, trapezoidal when 0<β<θ, and triangular when β=θ, (Li et al., 2013a). The frequency of the waveforms can be quantified by the nondimensional tooth tip angle, θ
Sutures with bonded vs. unbonded tip interfaces
The effect of bonded tips on the mechanical behavior of suture interfaces is explored by testing four representative geometries of , , and , with and without bonded tip interfaces, that span the range of general trapezoidal suture interfaces: anti-trapezoidal, rectangular, trapezoidal, and triangular. The volume fractions of the flat tip interface with respect to the total volume are 7.6%, 5.2%, 2.7%, and 0% for anti-trapezoidal, rectangular, trapezoidal, and triangular
Conclusion
The dependence of the stiffness, strength, and toughness of suture interfaces on geometric parameters and material constituent properties was found through analytical modeling and experiment. By tailoring the geometric parameters, including having an unbonded or bonded tip region, tip angle, and geometry, a range of mechanical behaviors can be achieved. As shown in Table 1, for each property the underlying mechanism that improves the property corresponds to certain optimal geometric parameters.
Acknowledgements
This research was supported (in part) by the U.S. Army Research Office under contract W911NF-13-D-0001. In addition, this research was conducted with Government support under and awarded by DoD, Air Force Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a.
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Now at School of Engineering and Applied Sciences, Columbia University, New York, NY 10027, USA.