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We designed and fabricated a simple setup for the controlled crumpling of nanopatterned, surface-porous flat metallic sheets for the fabrication of volume-porous biomaterials and showed that crumpling can be considered as an efficient alternative to origami-inspired folding. Before crumpling, laser cutting was used to introduce pores to the sheets. We then fabricated titanium (Ti) nanopatterns through reactive ion etching on the polished Ti sheets. Thereafter, nanopatterned porous Ti sheets were crumpled at two deformation velocities (i.e., 2 and 100 mm/min). The compression tests of the scaffolds indicated that the elastic modulus of the specimens vary in the range of 11.8–13.9 MPa. Micro-computed tomography scans and computational simulations of crumpled scaffolds were performed to study the morphological properties of the resulting meta-biomaterials. The porosity and pore size of the scaffolds remained within the range of those reported for trabecular bone. Finally, the in vitro cell preosteoblasts culture demonstrated the cytocompatibility of the nanopatterned scaffolds. Moreover, the aspect ratio of the cells residing on the nanopatterned surfaces was found to be significantly higher than those cultured on the control scaffolds, indicating that the nanopatterned surface may have a higher potential for inducing the osteogenic differentiation of the preosteoblasts., Biomaterials & Tissue Biomechanics, Support Biomechanical Engineering

Shape-shifting materials are a powerful tool for the fabrication of reconfigurable materials. Upon activation, not only a change in their shape but also a large shift in their material properties can be realized. As compared with the 4D printing of 2D-to-3D shape-shifting materials, the 4D printing of reconfigurable (i.e., 3D-to-3D shape-shifting) materials remains challenging. That is caused by the intrinsically 2D nature of the layer-by-layer manner of fabrication, which limits the possible shape-shifting modes of 4D printed reconfigurable materials. Here, we present a single-step production method for the fabrication and programming of 3D-to-3D shape-changing materials, which requires nothing more than a simple modification of widely available fused deposition modeling (FDM) printers. This simple modification allows the printer to print on curved surfaces. We demonstrate how this modified printer can be combined with various design strategies to achieve high levels of complexity and versatility in the 3D-to-3D shape-shifting behavior of our reconfigurable materials and devices. We showcase the potential of the proposed approach for the fabrication of deployable medical devices including deployable bifurcation stents that are otherwise extremely challenging to create., Biomaterials & Tissue Biomechanics, Emerging Materials

The design of advanced functional devices often requires the use of intrinsically curved geometries that belong to the realm of non-Euclidean geometry and remain a challenge for traditional engineering approaches. Here, it is shown how the simple deflection of thick meta-plates based on hexagonal cellular mesostructures can be used to achieve a wide range of intrinsic (i.e., Gaussian) curvatures, including dome-like and saddle-like shapes. Depending on the unit cell structure, non-auxetic (i.e., positive Poisson ratio) or auxetic (i.e., negative Poisson ratio) plates can be obtained, leading to a negative or positive value of the Gaussian curvature upon bending, respectively. It is found that bending such meta-plates along their longitudinal direction induces a curvature along their transverse direction. Experimentally and numerically, it is shown how the amplitude of this induced curvature is related to the longitudinal bending and the geometry of the meta-plate. The approach proposed here constitutes a general route for the rational design of advanced functional devices with intrinsically curved geometries. To demonstrate the merits of this approach, a scaling relationship is presented, and its validity is demonstrated by applying it to 3D-printed microscale meta-plates. Several applications for adaptive optical devices with adjustable focal length and soft wearable robotics are presented., Biomaterials & Tissue Biomechanics, Micro and Nano Engineering

Mechanical metamaterials are usually designed to exhibit novel properties and functionalities that are rare or even unprecedented. What is common among most previous designs is the quasi-static nature of their mechanical behavior. Here, we introduce a previously unidentified class of strain rate-dependent mechanical metamaterials. The principal idea is to laterally attach two beams with very different levels of strain rate-dependencies to make them act as a single bi-beam. We use an analytical model and multiple computational models to explore the instability modes of such a bi-beam construct, demonstrating how different combinations of hyperelastic and viscoelastic properties of both beams, as well as purposefully introduced geometric imperfections, could be used to create robust and highly predictable strain rate-dependent behaviors of bi-beams. We then use the bi-beams to design and experimentally realize lattice structures with unique strain rate-dependent properties including switching between auxetic and conventional behaviors and negative viscoelasticity., Biomaterials & Tissue Biomechanics

Deployable meta-implants aim to minimize the invasiveness of orthopaedic surgeries by allowing for changes in their shape and size that are triggered by an external stimulus. Multi-stability enables deployable implants to transform their shape from some compact retracted state to the deployed state where they take their full sizes and are load-bearing. We combined multiple design features to develop a new generation of deployable orthopaedic implants. Kirigami cut patterns were used to create bi-stability in flat sheets which can be folded into deployable implants using origami techniques. Inspired by Russian dolls, we designed multi-layered specimens that allow for adjusting the mechanical properties and the geometrical features of the implants through the number of the layers. Because all layers are folded from a flat state, surface-related functionalities could be applied to our deployable implants. We fabricated specimens from polylactic acid, titanium sheets, and aluminum sheets, and demonstrated that a deployment ratio of up to ≈2 is possible. We performed experiments to characterize the deployment and load-bearing behavior of the specimens and found that the above-mentioned design variables allow for adjustments in the deployment force and the maximum force before failure. Finally, we demonstrate the possibility of decorating the specimens with micropatterns., Biomaterials & Tissue Biomechanics

Self-folding of complex origami-inspired structures from flat states allows for the incorporation of a multitude of surface-related functionalities into the final 3D device. Several self-folding techniques have therefore been developed during the last few years to fabricate such multi-functional devices. The vast majority of such approaches are, however, limited to simple folding sequences, specific materials, or large length scales, rendering them inapplicable to microscale (meta)materials and devices with complex geometries, which are often made from materials other than the ones for which these approaches are developed. Here, we propose a mechanical self-folding technique that only requires global stretching for activation, is applicable to a wide range of materials, allows for sequential self-folding of multi-storey constructs, and can be downscaled to microscale dimensions. We combined two types of permanently deforming kirigami elements, working on the basis of either multi-stability or plastic deformation, with an elastic layer to create self-folding basic elements. The folding angles of these elements could be controlled using the kirigami cut patterns as well as the dimensions of the elastic layer and be accurately predicted using our computational models. We then assembled these basic elements in a modular manner to create multiple complex 3D structures (e.g., multi-storey origami lattices) in different sizes including some with microscale feature sizes. Moreover, starting from a flat state enabled us to incorporate not only precisely controlled, arbitrarily complex, and spatially varied micropatterns but also flexible electronics into the self-folded 3D structures. In all cases, our computational models could capture the self-folding behavior of the assemblies and the strains in the connectors of the flexible electronic devices, thereby guiding the rational design of our specimens. This approach has numerous potential applications including fabrication, Biomaterials & Tissue Biomechanics

Buckling, which was once considered the epitome of design failure, has been harnessed during the last few years to develop mechanical metamaterials with advanced functionalities. Soft robotics in general and soft actuators in particular could greatly benefit from such designer materials. Unlocking the great potential of buckling-driven materials is, however, contingent on resolving the main limitation of the designs presented to date, namely the limited range of their programmability. Here, we present multi-material buckling-driven metamaterials with high levels of programmability. We combined rational design approaches based on predictive computational models with advanced multi-material additive manufacturing techniques to 3D print cellular materials with arbitrary distributions of flexible and stiff materials in the central and corner parts of their unit cells. Using the geometry and spatial distribution of material properties as the main design parameters, we developed soft mechanical metamaterials behaving as mechanisms whose actuation force and actuation amplitude could be adjusted both independently and concomitantly within wide ranges. Our designs also resulted in the emergence of a new lowest instability mode, i.e. double-side buckling, in addition to the already known modes of side-buckling and symmetric compaction. Finally, we proposed a general approach to pre-dispose our soft mechanical metamaterials such that they can reliably actuate their higher instability modes without any need for additional boundary conditions or fixtures. To demonstrate this approach, we created a cellular mechanism with a rotational buckling pattern that clones the functionality of mechanical machines. The potential of the presented designs in robotics is then demonstrated by applying them as a force switch, kinematic controllers, and a pick and place end-effector., Biomaterials & Tissue Biomechanics

crumpled thin sheets exhibit extraordinary characteristics such as a high strength combined with a low volume ratio. This review focuses on the physics of crumpled thin sheets, including the crumpling mechanics, crumpling methods, and the mechanical behavior of crumpled thin sheets. Most of the physical and mechanical properties of crumpled thin sheets change with the compaction ratio, which creates the opportunity to obtain the properties that are needed for a specific application simply by changing the compaction ratio. This also enables obtaining unusual combinations of material properties, which cannot be easily found in nature. Furthermore, crumpling starts from a flat surface, which could first be decorated with (nano-) patterns or functionalized through other surface treatment techniques, many of which are only applicable to flat surfaces. Ultimately, the crumpling of thin sheets could be used for creating disordered mechanical metamaterials, which are less sensitive to geometric imperfections compared to ordered designs of mechanical metamaterials that are based, for example, on origami or lattice structures., Biomaterials & Tissue Biomechanics

Biomimetic composites are usually made by combining hard and soft phases using, for example, multi-material additive manufacturing (AM). Like other fabrication methods, AM techniques are limited by the resolution of the device, hence, setting a minimum length scale. The effects of this length scale on the performance of hard-soft composites are not well understood. Here, we studied how this length scale affects the fracture toughness behavior of single-edge notched specimens made using random, semi-random, and ordered arrangements of the hard and soft phases with five different ratios of hard to soft phases. Increase in the length scale (40 to 960 μm) was found to cause a four-fold drop in the fracture toughness. The effects of the length scale were also modulated by the arrangement and volumetric ratio of both phases. A decreased size of the crack tip plastic zone, a crack path going through the soft phase, and highly strained areas far from the crack tip were the main mechanisms explaining the drop of the fracture toughness with the length scale., Biomaterials & Tissue Biomechanics, Mechatronic Design

Soft mechanical metamaterials working on the basis of instability have numerous potential applications in the context of "machine materials." Controlling the onset of instability is usually required when rationally designing such metamaterials. We study the isolated and modulated effects of geometrical design and material distribution on the onset of instability in multimaterial cellular metamaterials. We use multimaterial additive manufacturing to fabricate cellular specimens whose unit cells are divided into void space, a square element, and an intermediate ligament. The ratio of the elastic modulus of the ligament to that of the square element [(EL)/(ES)] is changed by using different material types. Computational models are also developed, validated against experimental observations, and used to study a wide range of possible designs. The critical stress can be adjusted independently from the critical strain by changing the material type while keeping [(EL)/(ES)] constant. The critical strain shows a power-law relationship with [(EL)/(ES)] within the range [(EL)/(ES)]=0.1-10. The void shape design alters the critical strain by up to threefold, while the combined effects of the void shape and material distribution cause up to a ninefold change in the critical strain. Our findings highlight the strong influence of material distribution on the onset of the instability and buckling mode., Biomaterials & Tissue Biomechanics

Nature is full of materials that exhibit astonishing properties that are not available in engineering materials. The study of the underlying structure of such materials has revealed that geometry plays an important role in achieving such properties. Unusual physical and mechanical properties such as structural coloring in butterfly wings and shock absorption in woodpecker skull are examples of how geometry could be used for functionalization of materials. At the same time, recent advancements in (additive) manufacturing techniques have enabled us to fabricate engineering materials whose ultrastructure is geometrically very complex. It is therefore now possible to design engineering materials with unusual properties. In this dissertation, two types of geometrical designs are used for development of mechanical metamaterials with unusual properties. That includes 1. Cellular structures working on the basis of mechanical instability, and 2. Origami-based designs. The dissertation has been organized in two parts each covering one of the above-mentioned design types..., Biomaterials & Tissue Biomechanics

Meta-biomaterials exhibit unprecedented or rare combinations of properties not usually found in nature. Such unusual mechanical, mass transport, and biological properties could be used to develop novel categories of orthopedic implants with superior performance, otherwise known as meta-implants. Here, we use bi-stable elements working on the basis of snap-through instability to design deployable meta-implants. Deployable meta-implants are compact in their retracted state, allowing them to be brought to the surgical site with minimum invasiveness. Once in place, they are deployed to take their full-size load-bearing shape. We designed five types of meta-implants by arranging bi-stable elements in such a way to obtain a radially-deployable structure, three types of auxetic structures, and an axially-deployable structure. The intermediate stable conditions (i.e. multi-stability features), deployment force, and stiffness of the meta-implants were found to be strongly dependent on the geometrical parameters of the bi-stable elements as well as on their arrangement., Biomaterials & Tissue Biomechanics

Shape-shifting of flat materials into the desired 3D configuration is an alternative design route for fabrication of complex 3D shapes, which provides many benefits such as access to the flat material surface and the ability to produce well-described motions. The advanced production techniques that primarily work in 2D could then be used to add complex surface features to the flat material. The combination of complex 3D shapes and surface-related functionalities has a wide range of applications in biotechnology, actuators/sensors, and engineering of complex metamaterials. Here, we categorize the different programming strategies that could be used for planning the shape-shifting of soft matter based on the type of stresses generated inside the flat material and present an overview of the ways those mechanisms could be used to achieve the desired 3D shapes. Stress gradients through the thickness of the material, which generate out-of-plane bending moments, and compressive in-plane stresses that result in out-of-plane buckling constitute the major mechanisms through which shape-shifting of the flat matter could be programmed. We review both programming strategies with a focus on the underlying physical principles, which are highly scalable and could be applied to other structures and materials. The techniques used for programming the time sequence of shape-shifting are discussed as well. Such types of so-called “sequential” shape-shifting enable achieving more complex 3D shapes, as the kinematics of the movements could be planned in time to avoid collisions. Ultimately, we discuss what 3D shapes could be achieved through shape-shifting from flat soft matter and identify multiple areas of application., Biomaterials & Tissue Biomechanics

Architectured materials with rationally designed geometries could be used to create mechanical metamaterials with unprecedented or rare properties and functionalities. Here, we introduce "shape-matching" metamaterials where the geometry of cellular structures comprising auxetic and conventional unit cells is designed so as to achieve a pre-defined shape upon deformation. We used computational models to forward-map the space of planar shapes to the space of geometrical designs. The validity of the underlying computational models was first demonstrated by comparing their predictions with experimental observations on specimens fabricated with indirect additive manufacturing. The forward-maps were then used to devise the geometry of cellular structures that approximate the arbitrary shapes described by random Fourier's series. Finally, we show that the presented metamaterials could match the contours of three real objects including a scapula model, a pumpkin, and a Delft Blue pottery piece. Shape-matching materials have potential applications in soft robotics and wearable (medical) devices., Biomaterials & Tissue Biomechanics

Rationally designed meta-biomaterials present unprecedented combinations of mechanical, mass transport, and biological properties favorable for tissue regeneration. Here we introduce hybrid meta-biomaterials with rationally-distributed values of negative (auxetic) and positive Poisson’s ratios, and use them to design meta-implants that unlike conventional implants do not retract from the bone under biomechanical loading. We rationally design and additively manufacture six different types of meta-biomaterials (three auxetic and three conventional), which then serve as the parent materials to six hybrid meta-biomaterials (with or without transitional regions). Both single and hybrid meta-biomaterials are mechanically tested to reveal their full-field strain distribution by digital image correlation. The best-performing hybrid metabiomaterials are then selected for the design of meta-implants (hip stems), which are tested under simulated-implantation conditions. Full-field strain measurements clearly show that, under biomechanical loading, hybrid meta-implants press onto the bone on both the medial and lateral sides, thereby improving implant–bone contact and potentially implant longevity., Biomaterials & Tissue Biomechanics

Up until recently, the rational design of mechanical metamaterials has usually involved devising geometrical arrangements of micro-architectures that deliver unusual properties on the macro-scale. A less explored route to rational design is spatially distributing materials with different properties within lattice structures to achieve the desired mechanical properties. Here, we used computational models and advanced multi-material 3D printing techniques to rationally design and additively manufacture multi-material cellular solids for which the elastic modulus and Poisson's ratio could be independently tailored in different (anisotropic) directions. The random assignment of a hard phase to originally soft cellular structures with an auxetic, zero Poisson's ratio, and conventional designs allowed us to cover broad regions of the elastic modulus-Poisson's ratio plane. Patterned designs of the hard phase were also used and were found to be effective in the independent tuning of the elastic properties. Close inspection of the strain distributions associated with the different types of material distributions suggests that locally deflected patterns of deformation flow and strain localizations are the main underlying mechanisms driving the above-mentioned adjustments in the mechanical properties., Biomaterials & Tissue Biomechanics

Lattice structures are used in the design of metamaterials to achieve unusual physical, mechanical, or biological properties. The properties of such metamaterials result from the topology of the lattice structures, which are usually three-dimensionally (3D) printed. To incorporate advanced functionalities into metamaterials, the surface of the lattice structures may need to be ornamented with functionality-inducing features, such as nanopatterns or electronic devices. Given our limited access to the internal surfaces of lattice structures, free-form ornamentation is currently impossible. We present lattice structures that are folded from initially flat states and show that they could bear arbitrarily complex surface ornaments at different scales. We identify three categories of space-filling polyhedra as the basic unit cells of the cellular structures and, for each of those, propose a folding pattern. We also demonstrate “sequential self-folding” of flat constructs to 3D lattices. Furthermore, we folded auxetic mechanical metamaterials from flat sheets and measured the deformation-driven change in their negative Poisson’s ratio. Finally, we show how free-form 3D ornaments could be applied on the surface of flat sheets with nanometer resolution. Together, these folding patterns and experimental techniques present a unique platform for the fabrication of metamaterials with unprecedented combination of physical properties and surface-driven functionalities, Biomaterials & Tissue Biomechanics, ImPhys/Charged Particle Optics

Crumpled-based materials are relatively easy to fabricate and show robust mechanical properties for practical applications, including meta-biomaterials design aimed for improved tissue regeneration. For such requests, however, the structure needs to be porous. We introduce a crumpled holey thin sheet as a robust bio-metamaterial and measure the mechanical response of a crumpled holey thin Mylar sheet as a function of the hole size and hole area fraction. We also study the formation of patterns of crease lines and ridges. The area fraction largely dominated the crumpling mechanism. We also show, the crumpling exponents slightly increases with increasing the hole area fraction and the total perimeter of the holes. Finally, hole edges were found to limit and guide the propagation of crease lines and ridges., Biomaterials & Tissue Biomechanics

Materials and devices with advanced functionalities often need to combine complex 3D shapes with functionality-inducing surface features. Precisely controlled bio-nanopatterns, printed electronic components, and sensors/actuators are all examples of such surface features. However, the vast majority of the refined technologies that are currently available for creating functional surface features work only on flat surfaces. Here we present initially flat constructs that upon triggering by high temperatures change their shape to a pre-programmed 3D shape, thereby enabling the combination of surface-related functionalities with complex 3D shapes. A number of shape-shifting materials have been proposed during the last few years based on various types of advanced technologies. The proposed techniques often require multiple fabrication steps and special materials, while being limited in terms of the 3D shapes they could achieve. The approach presented here is a single-step printing process that requires only a hobbyist 3D printer and inexpensive off-the-shelf materials. It also lends itself to a host of design strategies based on self-folding origami, instability-driven pop-up, and ‘sequential’ shape-shifting to unprecedentedly expand the space of achievable 3D shapes. This combination of simplicity and versatility is a key to widespread applications., Biomaterials & Tissue Biomechanics

Crumpled-based materials are relatively easy to fabricate and show robust mechanical properties for practical applications, including meta-biomaterials design aimed for improved tissue regeneration. For such requests, however, the structure needs to be porous. We introduce a crumpled holey thin sheet as a robust bio-metamaterial and measure the mechanical response of a crumpled holey thin Mylar sheet as a function of the hole size and hole area fraction. We also study the formation of patterns of crease lines and ridges. The area fraction largely dominated the crumpling mechanism. We also show, the crumpling exponents slightly increases with increasing the hole area fraction and the total perimeter of the holes. Finally, hole edges were found to limit and guide the propagation of crease lines and ridges.

Although the initial mechanical properties of additively manufactured porous biomaterials are intensively studied during the last few years, almost no information is available regarding the evolution of the mechanical properties of implant-bone complex as the tissue regeneration progresses. In this paper, we studied the effects of tissue regeneration on the static and fatigue behavior of selective laser melted porous titanium structures with three different porosities (i.e. 77, 81, and 85%). The porous structures were filled with four different polymeric materials with mechanical properties in the range of those observed for de novo bone (0.7 GPa, Accepted Author Manuscript, Biomaterials & Tissue Biomechanics

Recent research has shown the potential of rationally designed geometrical features for controlling the functionality of advanced materials. Of particular recent interest has been the use of geometry for controlling the buckling behaviour of soft materials under compression. However, the effects of geometry may be mixed with those of the mechanical properties. In this paper, we present a specific class of 2D cellular soft matter for which the geometry, independent from the mechanical properties of the bulk material, activates the instability pathways of the material, thereby controlling the instability threshold and the instability mode (instability pattern). The geometrical parameters include those characterizing the shape of the voids and the porosity of the cellular solid. A critical strain that solely depends on the geometry controls the transition to instability. Depending on the above-mentioned geometrical parameters, the onset of instability is followed by either symmetric compaction or side buckling. We provide instability maps that relate the geometrical parameters to the critical strain and the instability mode of the presented cellular soft material. These open up the possibility of using geometry for programming the functionalities of materials., Biomechanical Engineering, Mechanical, Maritime and Materials Engineering

Nature uses various activation mechanisms to program complex transformations in the shape and functionality of living organisms. Inspired by such natural events, we aimed to develop initially flat (i.e. two-dimensional) programmable materials that, when triggered by a stimulus such as temperature, could self-transform their shape into a complex three-dimensional geometry. A two-dimensional starting point enables full access to the surface, e.g. for (nano-)patterning purposes, which is not available in most other manufacturing techniques including additive manufacturing techniques and molding. We used different arrangements of bi- and multi-layers of a shape memory polymer (SMP) and hyperelastic polymers to program four basic modes of shape-shifting including self-rolling, self-twisting (self-helixing), combined self-rolling and self-wrinkling, and wave-like strips. The effects of various programming variables such as the thermomechanical properties of the hyperelastic layer, dimensions of the bi- and multi-layer strips, and activation temperature on the morphology of the resulting three-dimensional objects were studied experimentally and were found to cause as much as 10-fold change in the relevant dimensions. Some of the above-mentioned modes of shape-shifting were then integrated into other two-dimensional constructs to obtain self-twisting DNA-inspired structures, programmed pattern development in cellular solids, self-folding origami, and self-organizing fibers. Furthermore, the possibility of incorporating multiple surface patterns into one single piece of shape-transforming material is demonstrated using ultraviolet-cured photopolymers., Biomaterials & Tissue Biomechanics