Zero modes activation to reconcile floppiness, rigidity, and multistability into an all-in-one class of reprogrammable metamaterials.

Existing mechanical metamaterials are typically designed to either withstand loads as a stiff structure, shape morph as a floppy mechanism, or trap energy as a multistable matter, distinct behaviours that correspond to three primary classes of macroscopic solids. Their stiffness and stability are sealed permanently into their architecture, mostly remaining immutable post-fabrication due to the invariance of zero modes. Here, we introduce an all-in-one reprogrammable class of Kagome metamaterials that enable the in-situ reprogramming of zero modes to access the apparently conflicting properties of all classes. Through the selective activation of metahinges via self-contact, their architecture can be switched to acquire on-demand rigidity, floppiness, or global multistability, bridging the seemingly uncrossable gap between structures, mechanisms, and multistable matters. We showcase the versatile generalizations of the metahinge and remarkable reprogrammability of zero modes for a range of properties including stiffness, mechanical signal guiding, buckling modes, phonon spectra, and auxeticity, opening a plethora of opportunities for all-in-one materials and devices.

Anisotropic Morphing in Bistable Kirigami through Symmetry Breaking and Geometric Frustration.

Shape morphing in bistable kirigami enables remarkable functionalities appealing to a diverse range of applications across the spectrum of length scale. At the core of their shape shifting lies the architecture of their repeating unit, where highly deformable slits and quasi-rigid rotating units often exhibit multiple symmetries that confer isotropic deployment obeying uniform scaling transformation. In this work, symmetry breaking in bistable kirigami is investigated to access geometric frustration and anisotropic morphing, enabling arbitrarily scaled deployment in planar and spatial bistable domains. With an analysis on their symmetry properties complemented by a systematic investigation integrating semi-analytical derivations, numerical simulations, and experiments on elastic kirigami sheets, this work unveils the fundamental relations between slit symmetry, geometric frustration, and anisotropic bistable deployment. Furthermore, asymmetric kirigami units are leveraged in planar and flat-to-3D demonstrations to showcase the pivotal role of shear deformation in achieving target shapes and functions so far unattainable with uniformly stretchable kirigami. The insights provided in this work unveil the role of slit symmetry breaking in controlling the anisotropic bistable deployment of soft kirigami metamaterials, enriching the range of achievable functionalities for applications spanning deployable space structures, wearable technologies, and soft machines.

Semantic segmentation for tooth cracks using improved DeepLabv3+ model.

Objective: Accurate and prompt detection of cracked teeth plays a critical role for human oral health. The aim of this paper is to evaluate the performance of a tooth crack segmentation model (namely, FDB-DeepLabv3+) on optical microscopic images. Method: The FDB-DeepLabv3+ model proposed here improves feature learning by replacing the backbone with ResNet50. Feature pyramid network (FPN) is introduced to fuse muti-level features. Densely linked atrous spatial pyramid pooling (Dense ASPP) is applied to achieve denser pixel sampling and wider receptive field. Bottleneck attention module (BAM) is embedded to enhance local feature extraction. Results: Through testing on a self-made hidden cracked tooth dataset, the proposed method outperforms four classical networks (FCN, U-Net, SegNet, DeepLabv3+) on segmentation results in terms of mean pixel accuracy (MPA) and mean intersection over union (MIoU). The network achieves an increase of 11.41% in MPA and 12.14% in MIoU compared to DeepLabv3+. Ablation experiments shows that all the modifications are beneficial. Conclusion: An improved network is designed for segmenting tooth surface cracks with good overall performance and robustness, which may hold significant potential in computer-aided diagnosis of cracked teeth.

Tunable sequential pathways through spatial partitioning and frustration tuning in soft metamaterials.

Elastic instabilities have been leveraged in soft metamaterials to attain novel functionalities such as mechanical memory and sequential pathways. Pathways have been realized in complex media or within a collection of hysteretic elements. However, much less has been explored in frustrated and partitioned soft metamaterials. In this work, we introduce spatial partitioning as a method to localize deformation in sub-regions of a large and soft metamaterial. The partitioning is achieved through the strategic arrangement of soft inclusions in a soft lattice, which form distinct regions behaving as mechanical units. We examine two partitions: an equally spaced layer partition with mechanical units connected in series, and a cross partition, represented by interconnected series of mechanical units in parallel. Sequential pathways are obtained by frustrating the partitioned metamaterial post-manufacture and are characterized by tracking the polarization change in each partition region. Through a combination of experiments and simulations, we demonstrate that partitioning enables tuning the pathway from longitudinal with weak interactions to a pathway exhibiting strong interactions rising from geometric incompatibility and central domain rotation. We show that tuning the level of uniform lateral pre-strain provides a wide range of tunability from disabling to modifying the sequential pathway. We also show that imposing a nonuniform confinement and altering the tilting of one or two of the domain edges enables to program the pathway, access a larger set of states, and tune the level of interaction between the regions.

In Situ Activation of Snap-Through Instability in Multi-Response Metamaterials through Multistable Topological Transformation.

Snap-through instability has been widely leveraged in metamaterials to attain non-monotonic responses for a specific subset of applications where conventional monotonic materials fail to perform. In the remaining more plentiful set of ordinary applications, snap-through instability is harmful, and current snapping metamaterials become inadequate because their capacity to snap cannot be suppressed post-fabrication. Here, a class of topology-transformable metamaterials is introduced to enable in situ activation and deactivation of the snapping capacity, providing a remarkable level of versatility in switching between responses from monotonic to monostable and bistable snap-through. Theoretical analysis, numerical simulations, and experiments are combined to unveil the role played by contact in the topological transformation capable of increasing the geometry incompatibility and confinement stiffness of selected architectural members. The strategy here presented for post-fabrication reprogrammability of matter and on-the-fly response switching paves the way to multifunctionality for application in multiple sectors from mechanical logic gates, and adjustable energy dissipators, to in situ adaptable sport equipment.

Modeling, design and tailoring of a tough, strong and stiff multilayered bone graft material.

Damage tolerance, stiffness, and strength are critical mechanical properties that are difficult to achieve concurrently in synthetic monolithic materials. This limits the range of certain applications, including in bone graft materials where bone-like mechanical reliance is desired. For example, calcium sulfate (CS) is a biologically compatible ceramic that possesses several properties of an ideal bone graft material, but its applications in medicine is limited by its brittleness. Brittleness may be alleviated by the addition of stronger and more ductile reinforcements, with the best mechanical improvements obtained when the layered architecture and the interfaces for these reinforcements are tailored. Here we propose a systematic modeling and design approach to tailor the architecture and properties of a multilayered bone graft material composed of a brittle ceramic and a more ductile material such as metals. More specifically, the volume fraction, moduli, number of layers, and the toughness of the interfaces between the different phases are tailored to maximize overall stiffness, strength, and energy absorption capacity. Our model predicts that when the stiffness of the reinforcement is higher (lower) than the ceramic, the beams with lower (higher) number of layers and higher (lower) volume fraction of metal are stronger. However, while the higher number of layers is always desired in terms of energy dissipation, the effects of other variables is more complex to understand and should thus be studied in conjunction with each other.

Genetic Deletion of Menin in Mouse Mesenchymal Stem Cells: An Experimental and Computational Analysis.

Loss-of-function mutations in the MEN1 tumor-suppressor gene cause the multiple endocrine neoplasia type 1 syndrome. Menin, the MEN1 gene product, is expressed in many tissues, including bone, where its function remains elusive. We conditionally inactivated menin in mesenchymal stem cells (MSCs) using paired-related homeobox 1 (Prx1)-Cre and compared resultant skeletal phenotypes of Prx1-Cre;Men1 f/f menin-knockout mice (KO) and wild-type controls using in vivo and in vitro experimental approaches and mechanics simulation. Dual-energy X-ray absorptiometry demonstrated significantly reduced bone mineral density, and 3-dimensional micro-CT imaging revealed a decrease in trabecular bone volume, altered trabecular structure, and an increase in trabecular separation in KO mice at 6 and 9 months of age. Numbers of osteoblasts were unaltered, and dynamic histomorphometry demonstrated unaltered bone formation; however, osteoclast number and activity and receptor activator of NF-κB ligand/osteoprotegerin (RANKL/OPG) mRNA profiles were increased, supporting increased osteoclastogenesis and bone resorption. In vitro, proliferative capabilities of bone marrow stem cells and differentiation of osteoblasts and mineralization were unaltered; however, osteoclast generation was increased. Gross femur geometrical alterations observed included significant reductions in length and in mid-metaphyseal cross-sectional area. Atomic force microscopy demonstrated significant decreases in elasticity of both cortical and trabecular bone at the nanoscale, whereas three-point bending tests demonstrated a 30% reduction in bone stiffness; finite element analysis showed morphological changes of the femur microgeometry and a significantly diminished femur flexural rigidity. The biomechanical results demonstrated the detrimental outcome of the accelerated osteoclastic bone resorption. Our studies have a twofold implication; first, MEN1 deletion from MSCs can negatively regulate bone mass and bone biomechanics, and second, the experimental and computational biomechanical analyses employed in the present study should be applicable for improved phenotypic characterization of murine bone. Furthermore, our findings of critical menin function in bone may underpin the more severe skeletal phenotype found in hyperparathyroidism associated with loss-of-function of the MEN1 gene. © 2022 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

Rigidly flat-foldable class of lockable origami-inspired metamaterials with topological stiff states.

Origami crease patterns have inspired the design of reconfigurable materials that can transform their shape and properties through folding. Unfortunately, most designs cannot provide load-bearing capacity, and those that can, do so in certain directions but collapse along the direction of deployment, limiting their use as structural materials. Here, we merge notions of kirigami and origami to introduce a rigidly foldable class of cellular metamaterials that can flat-fold and lock into several states that are stiff across multiple directions, including the deployment direction. Our metamaterials rigidly fold with one degree of freedom and can reconfigure into several flat-foldable and spatially-lockable folding paths due to face contact. Locking under compression yields topology and symmetry changes that impart multidirectional stiffness. Additionally, folding paths and mixed-mode configurations can be activated in situ to modulate their properties. Their load-bearing capacity, flat-foldability, and reprogrammability can be harnessed for deployable structures, reconfigurable robots, and low-volume packaging.

Bi-Shell Valve for Fast Actuation of Soft Pneumatic Actuators via Shell Snapping Interaction.

Rapid motion in soft pneumatic robots is typically achieved through actuators that either use a fast volume input generated from pressure control, employ an integrated power source, such as chemical explosions, or are designed to embed elastic instabilities in the body of the robot. This paper presents a bi-shell valve that can fast actuate soft actuators neither relying on the fast volume input provided by pressure control strategies nor requiring modifications to the architecture of the actuator. The bi-shell valve consists of a spherical cap and an imperfect shell with a geometrically tuned defect that enables shell snapping interaction to convert a slowly dispensed volume input into a fast volume output. This function is beyond those of current valves capable to perform fluidic flow regulation. Validated through experiments, the analysis unveils that the spherical cap sets the threshold of the snapping pressure along with the upper bounds of volume and energy output, while the imperfect shell interacts with the cap to store and deliver the desired output for rapid actuation. Geometry variations of the bi-shell valve are provided to show that the concept is versatile. A final demonstration shows that the soft valve can quickly actuate a striker.

Topology optimization of 3D-printed structurally porous cage for acetabular reinforcement in total hip arthroplasty.

Aseptic loosening and mechanical failure of acetabular reinforcement components are among the main causes of their reduced service life. Current acetabular implants typically feature a structural solid layer that provides load bearing capacity, coated with a foam of uniform porosity to reduce stress shielding and implant loosening. This paper presents an alternative concept for a 3D printed cage that consists of a multifunctional fully porous layer with graded attributes that integrate both structural function and bone in-growth properties. The design comprises a hemispherical cup affixed to a superior flange with architecture featuring an optimally graded porosity. The methodology here presented combines an upscaling mechanics scheme of lattice materials with density-based topology optimization, and includes additive manufacturing constraints and bone ingrowth requirements in the problem formulation. The numerical results indicate a 21.4% reduction in the maximum contact stress on the bone surface, and a 26% decrease in the bone-implant interface peak micromotion, values that are indicative of enhanced bone ingrowth and implant long-term stability.

Nano-indentation reveals a potential role for gradients of cell wall stiffness in directional movement of the resurrection plant Selaginella lepidophylla.

As a physical response to water loss during drought, inner Selaginella lepidophylla stems curl into a spiral shape to prevent photoirradiation damage to their photosynthetic surfaces. Curling is reversible and involves hierarchical deformation, making S. lepidophylla an attractive model with which to study water-responsive actuation. Investigation at the organ and tissue level has led to the understanding that the direction and extent of stem curling can be partially attributed to stiffness gradients between adaxial and abaxial stem sides at the nanoscale. Here, we examine cell wall elasticity to understand how it contributes to the overall stem curling. We compare the measured elastic moduli along the stem length and between adaxial and abaxial stem sides using atomic force microscopy nano-indentation testing. We show that changes in cortex secondary cell wall development lead to cell wall stiffness gradients from stem tip to base, and also between adaxial and abaxial stem sides. Changes in cortical cell wall morphology and secondary cell wall composition are suggested to contribute to the observed stiffness gradients.

Encoding kirigami bi-materials to morph on target in response to temperature.

Shape morphing in response to an environmental stimulus, such as temperature, light, and chemical cues, is currently pursued in synthetic analogs for manifold applications in engineering, architecture, and beyond. Existing strategies mostly resort to active, namely smart or field responsive, materials, which undergo a change of their physical properties when subjected to an external stimulus. Their ability for shape morphing is intrinsic to the atomic/molecular structure as well as the mechanochemical interactions of their constituents. Programming shape changes with active materials require manipulation of their composition through chemical synthesis. Here, we demonstrate that a pair of off-the-shelf passive solids, such as wood and silicone rubber, can be topologically arranged in a kirigami bi-material to shape-morph on target in response to a temperature stimulus. A coherent framework is introduced to enable the optimal orchestration of bi-material units that can engage temperature to collectively deploy into a geometrically rich set of periodic and aperiodic shapes that can shape-match a predefined target. The results highlight reversible morphing by mechanics and geometry, thus contributing to relax the dependence of current strategies on material chemistry and fabrication.

Three-dimensional functional gradients direct stem curling in the resurrection plant Selaginella lepidophylla.

Upon hydration and dehydration, the vegetative tissue of Selaginella lepidophylla can reversibly swell and shrink to generate complex morphological transformations. Here, we investigate how structural and compositional properties at tissue and cell wall levels in S. lepidophylla lead to different stem curling profiles between inner and outer stems. Our results show that directional bending in both stem types is associated with cross-sectional gradients of tissue density, cell orientation and secondary cell wall composition between adaxial and abaxial stem sides. In inner stems, longitudinal gradients of cell wall thickness and composition affect tip-to-base tissue swelling and shrinking, allowing for more complex curling as compared to outer stems. Together, these features yield three-dimensional functional gradients that allow the plant to reproducibly deform in predetermined patterns that vary depending on the stem type. This study is the first to demonstrate functional gradients at different hierarchical levels combining to operate in a three-dimensional context.

Material anisotropy and elasticity of cortical and trabecular bone in the adult mouse femur via AFM indentation.

This paper investigates the elastic properties of bone tissue in the adult mouse femur through Atomic Force Microscopy (AFM) indentation with the goal of understanding its microstructure and underlying mechanics at the nano length scale. Both trabecular and cortical bone types are studied. In particular, we examined the elasticity of cortical bone and individual trabeculae in the longitudinal and transverse directions of the samples. For cortical bone, the elastic modulus in the longitudinal direction was found to be 10-15% higher than that in the transverse direction; for trabecular bone, this difference was 42%. For the trabeculae, this value was found to be in a lower range (0.92 ± 0.22 GPa). As per the transverse elastic modulus, an average of 1.58 ± 0.36 GPa was measured for cortical bone, and 0.55 ± 0.21 GPa for trabecular bone. The anisotropy ratio was within the range of 1.2-1.5 for cortical bone and 1.7-2 for trabecular bone. While the elastic modulus of cortical bone varied along the length of the femur with up to 30% variation, no significant differences were observed within each transverse section. The effect of indentation frequency (1-500 Hz) on the longitudinal elastic moduli was also investigated for cortical and trabecular bone, with results showing a correlation between indentation frequency and elastic modulus. Statement of significance: This study examines the adult mouse femur with a twofold aim: to investigate the anisotropy and inhomogeneity of cortical and trabecular bone tissues and to elucidate their elastic behavior at the nanometer length scale. The elastic moduli of cortical bone and individual trabecula are measured in the longitudinal and transverse cross-sections via AFM indentation at selected locations and in specific directions of the adult mouse femur. The results provide insights into the relationship between mechanical properties and structural morphology of cortical and trabecular bone tissue.

Cervical fusion cage computationally optimized with porous architected Titanium for minimized subsidence.

Anterior cervical discectomy with fusion is a common surgical treatment that can relieve patients suffering from cervical spondylosis. This surgery is most commonly performed with the use of a cervical cage. One serious complication of the fusion cages commercially available in the market is subsidence of the cage with loss of the normal alignment of the spine and recurrent pain. This work presents the proof-of-concept of a fusion cage made of a graded porous titanium with microarchitecture minimizing the risk of subsidence associated with fully-solid implants. The optimized properties of the porous implant are obtained through a scheme combining multiscale mechanics and density-based topology optimization. Asymptotic homogenization is used to capture the effective properties of the porous material, which uses a tetrahedron based cell as building block. The stress levels and normal strains obtained under various loading conditions on the C7 superior surface of the vertebrae are used as indicators of subsidence. The results suggest a reduced risk of subsidence for the optimized implant versus the fully-solid implant. Under the most severe condition of combined loading, a collective improvement of the average von Mises stress up to 14% can be observed on the posterior, left, and right lateral regions of the C7 superior surface. Similarly, for the average normal strain, the optimized cage exhibits a more favourable distribution with a top gain of 21.7% at given locations.

Assessment of structural and hemodynamic performance of vascular stents modelled as periodic lattices.

This work considers vascular stents with tubular geometry assumed to follow a periodic arrangement of repeating unit cells. Structural and hemodynamic metrics are presented to assess alternative stent geometries, each defined by the topology of the unit cell. Structural metrics include foreshortening, elastic recoil and radial stiffness, whereas hemodynamic performance is described by a wall shear stress index quantifying the impact of in-stent restenosis. A representative volume element (RVE) modelling approach is used, and results are compared to those obtained from full simulations of entire stents. We demonstrate that the RVE approach can be used to quantify the impact of the topology of the repeating unit on the structural and hemodynamic properties of a stent, and thus support clinicians in making proper choices among alternative stent geometries.

Porous architected biomaterial for a tibial-knee implant with minimum bone resorption and bone-implant interface micromotion.

This investigation presents the numerical development of a fully porous tibial knee implant that is suggested to alleviate the clinical problems associated with current prostheses that are fully solid. A scheme combining multiscale mechanics and topology optimization is proposed to handle the homogenized analysis and property tailoring of the porous architecture with the aim of reducing the stiffness mismatch between the implant and surrounding bone. The outcome of applying this scheme is a graded lattice microarchitecture that can potentially offer the implant an improved degree of load bearing capacity while reducing concurrently bone resorption and interface micromotion. Asymptotic Homogenization theory is used to characterize the mechanics of its building block, a tetrahedron based unit cell, and the Soderberg fatigue criterion to represent the implant fatigue resistance under multiaxial physiological loadings. The numerical results suggest that the overall amount of bone resorption around the graded porous tibial stem is 26% lower than that around a conventional, commercially available, fully dense titanium implant of identical shape and size. In addition, an improved interface micromotion is observed along the tibial stem, with values at the tip of the stem as low as 17µm during gait cycle and 22µm for deep bend compared to a fully dense implant. This decrease in micromotion compared to that of an identical solid implant made of titanium can reasonably be expected to alleviate post-operative end of stem pain suffered by some patients undergoing surgery at the present time.

Morphology of elastic nematic liquid crystal membranes.

Liquid crystalline phases found in many biological materials, such as actin, DNA, cellulose, and collagen can be responsible for the deformation of cell membranes. In this paper, cell membrane deformation is investigated through the coupling between liquid crystal anisotropy and membrane bending elasticity. The generalized shape equation for anisotropic interfaces, which resort to the Cahn-Hoffman capillarity vector, the Rapini-Papoular anchoring energy, and the Helfrich elastic energy, is applied to gain insight into the deformation of closed liquid crystal membranes. This study presents a general morphological phase diagram of membrane surface patterns, in which two characteristic regimes of membrane shapes can be classified with respect to the most dominant factor between liquid crystal anisotropy and bending elasticity. To that end, we consider a 2D nematic liquid crystal droplet immersed in a isotropic phase in the presence of an interfacial layer of surfactants, which leads to an additional elastic contribution to the free energy of the system. The presented results indicate that, depending on the bending elasticity of the cell membrane, the liquid crystal might be able to deform the cell, thereby resulting in anisotropic asymmetric shapes. As liquid crystal anisotropy dominates the bending elasticity, spindle-like or tactoid shapes, which are extensively observed in experiments, can be formed. The findings provide a foundational framework to better understand membrane topologies in living soft matters. Furthermore, the coupling between order and curvature of membranes shed new light into the design of novel functional soft materials.

Compensation strategy to reduce geometry and mechanics mismatches in porous biomaterials built with Selective Laser Melting.

The accuracy of Additive Manufacturing processes in fabricating porous biomaterials is currently limited by their capacity to render pore morphology that precisely matches its design. In a porous biomaterial, a geometric mismatch can result in pore occlusion and strut thinning, drawbacks that can inherently compromise bone ingrowth and severely impact mechanical performance. This paper focuses on Selective Laser Melting of porous microarchitecture and proposes a compensation scheme that reduces the morphology mismatch between as-designed and as-manufactured geometry, in particular that of the pore. A spider web analog is introduced, built out of Ti-6Al-4V powder via SLM, and morphologically characterized. Results from error analysis of strut thickness are used to generate thickness compensation relations expressed as a function of the angle each strut formed with the build plane. The scheme is applied to fabricate a set of three-dimensional porous biomaterials, which are morphologically and mechanically characterized via micro Computed Tomography, mechanically tested and numerically analyzed. For strut thickness, the results show the largest mismatch (60% from the design) occurring for horizontal members, reduces to 3.1% upon application of the compensation. Similar improvement is observed also for the mechanical properties, a factor that further corroborates the merit of the design-oriented scheme here introduced.

The twist-to-bend compliance of the Rheum rhabarbarum petiole: integrated computations and experiments.

Plant petioles can be considered as hierarchical cellular structures, displaying geometric features defined at multiple length scales. Their macroscopic mechanical properties are the cumulative outcome of structural properties attained at each level of the structural hierarchy. This work appraises the compliance of a rhubarb stalk by determining the stalk's bending and torsional stiffness both computationally and experimentally. In our model, the irregular cross-sectional shape of the petiole and the layers of the constituent tissues are considered to evaluate the stiffness properties at the structural level. The arbitrary shape contour of the petiole is generated with reasonable accuracy by the Gielis superformula. The stiffness and architecture of the constituent layered tissues are modeled by using the concept of shape transformers so as to obtain the computational twist-to-bend ratio for the petiole. The rhubarb stalk exhibits a ratio of flexural to torsional stiffness 4.04 (computational) and 3.83 (experimental) in comparison with 1.5 for isotropic, incompressible, circular cylinders, values that demonstrate the relative structural compliance to flexure and torsion.