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Flexible antenna sensors have gained significant momentum in recent times due to increase in demand for internet of things (IOT) technology. Conventional flexible antenna-based wireless sensors fabricated on plastic substrates are neither biodegradable nor recyclable, use expensive and sophisticated equipment and eco-unfriendly solution processing to fabricate radiating element thus generating e-waste and causing environment contamination. Here we fabricated a 2.4 GHZ paper-based rectangular patch antenna in which aluminium tape is used as radiating patch and ground pane and cellulose filter paper is used as dielectric substrate that separates radiating patch and ground plane. This aluminium on paper antenna exhibits excellent average sensitivity ∼3.23 and ∼3.34 to 1.67% of compressive and tensile bending strain respectively and shows stable performance after hundreds of bending cycles. The performance of antenna sensor was evaluated by subjecting it to microstrains to identify small cracks, folding it with different angles to sense the angle of bending and by interfacing it with hand gloves to detect human motion. Due to versatility in sensing, robustness and flexibility, these antennas can be used as use-and-recycle wireless disposable electromechanical sensors for wearable electronics, human machine interfacing (HMI), crack detection of oils/flammable gas pipelines, and intelligent wireless monitoring of movements.

Fe3O4nanoparticle-infiltrated chromatography paper is prepared using a low-cost blending method. Upon characterizing the basic material properties of the Fe3O4/paper nanocomposite, beam-, accordion- and star-shaped actuators are constructed using the nanocomposite and the corresponding actuation performance is investigated experimentally. The beam-shaped actuator exhibits a reversible flexural deformation due to low magnetic hysteresis loop of the Fe3O4/paper nanocomposite, maintaining a stable response after 100 cycles. The accordion-shaped actuator can reach a maximum strain of 100% while the star-shaped actuator can capture a spitball twice heavier than itself.

Cellulose is earth-abundant and has exceptional intrinsic mechanical properties. Cellulose-based materials, however, exhibit a large variation in their mechanical properties (e.g., strength, toughness), which calls for the understanding of the sensitivity of these materials to flaws, an area that remains largely unexplored. In this paper, we report a systematic study of the flaw sensitivity of cellulose paper by measuring the fractocohesive lengths of cellulose paper made of cellulose fibers with various diameters (from nanometers to microns) and lengths (from sub-microns to millimeters). Unlike the strength of cellulose paper which depends strongly on the diameter of the constituent cellulose fibers, the flaw sensitivity of cellulose paper is closely related to the aspect ratio (length/diameter) of the cellulose fibers. The larger the aspect ratio of the cellulose fibers, the larger the fractocohesive length, and thus the more flaw tolerant the cellulose paper is. Findings in this paper shed light on designing cellulose-based materials with desirable mechanical performance that is pivotal for the widespread use of this sustainable material.

Clutch mechanisms that are lightweight and have low power consumption are crucial to enhancing the functionality of many robotic systems. We present the design, characterization, and modeling of a switchable clutch based on the self-amplified friction between thin flexible sheets. The clutch consists of interleaved paper sheets, which maintaining a locked state akin to that of interleaved books. Unlocking is achieved by applying rotation to the distal ends of the interleaved assembly, counteracting the self-amplified normal force within the layers. A 60-layer paper-based interleaved clutch, weighing 9 g, exhibits a locking force capacity of ∼550 N, along with an unlocked state force of ∼1 N. Through the incorporation of rubber bands, the clutch achieves bistable switching and self-resetting capabilities. In addition, we demonstrate an application of the clutch by integrating it into a wearable posture corrector.

The deformation of single crease origami units under partial stretch loads along the crease extension direction is influenced by their plates’ bending stiffness. For their application, it is of great significance to analyze the non-uniform deformation pattern of origami units and clarify the efficiency of partial driving on global unfolding. In this paper, the unfolding behavior of single crease origami units under partial stretch is systematically investigated. From the bending phenomenon of paper models, a parametrical simulation analysis is performed to analyze deformation patterns and virtual crease distribution. Furthermore, the overall uniform motion efficiency of origami units with local driving is discussed, while the criterion of uniform unfolding motion of the crease is defined. The feasible ranges of partial load factors corresponding to single crease origami units with different initial crease angles are also clarified under the constraint of the required uniform motion range. Mechanical and kinematic models are also established based on equivalent rigid plate nonlinear crease elements and equivalent single-vertex six-crease patterns, which can accurately identify the deformation characteristics of the single-crease origami unit under partial stretch. Furthermore, the flattening analysis of derived single-vertex six-crease origami units and their arrays is also carried out to investigate the influence of sector angles and crease rotation stiffness. Two different decay characteristics are observed, corresponding to the fully flattened planar state and the non-fully flattened planar state, respectively. A motion snap that occurs before the fully flattened planar state is also identified. The findings can be regarded as the research basis for the complex mechanical behavior of origami structures composed of single crease origami units.

Curved beams with bistable and negative stiffness properties can be used to design multi-stable metamaterials or honeycomb structures. Consequently, the deformation patterns and mechanical properties of curved beams under load have attracted many attentions. However, due to the nonlinear characteristics of variable thickness double curved beams, it is impossible to exhaust all possible structural forms through experimental and theoretical approaches. This paper presents a machine learning (ML) method for designing and optimizing double curved beam structures. The ML model is used to establish the underlying mapping relationship between thickness parameters and mechanical properties. After optimizing the double curved beam in different directions, the optimal thickness distributions of the backward snapping force and energy absorption are obtained. Double curved beams with optimal thickness distributions are used to construct multi-stable honeycomb structures, demonstrating the optimization process from single cell structure to periodic structure. Under the same mass, compared to the constant thickness honeycomb structure, the optimized variable thickness honeycomb structures exhibit a 140% increase in backward snapping force and a 57% increase in energy absorption. The objective of this study is to utilize machine learning technique to obtain a general approach for optimizing model of ‘multi-parameter input’ to ‘single-parameter output’, which is valuable for guiding the optimization and design of metamaterial structures in the future. This paper is a good case study of the mechanical structure performance optimization, whose implementation path is given detailly in appendix. Other disciplines with similar optimization goals can also use this method to carry out researches.

Dislocation slip-based crystal plasticity models have been a great success in connecting the fundamental physics with the macroscopic deformation of crystalline materials. Pioneered by Taylor in his work on “plastic strain in metals” (Taylor, 1938), and further advanced by Bishop and Hill (1951a, 1951b), the Taylor–Bishop–Hill theory laid the foundation of today’s constitutive models on crystal plasticity. An intriguing part of those modeling is to determine the active slip systems—which system to be involved in and how much it contributes to the deformation. In this paper, we developed a machine learning-based algorithm to determine accurately and efficiently the active slip systems in crystal plasticity constitutive models. Applications to the common three polycrystalline metals, face-centered cubic (FCC) copper, body-centered cubic (BCC) α-iron, and hexagonal close-packed (HCP) AZ31B, demonstrate that even a simple neural network could give rise to accurate and efficient results in comparing with traditional routines. There seems to be plenty of space for further reducing the computation time and hence scaling up the simulating samples.

The complete hyperelastic behavior of dielectric elastomers (DEs) refers to the large-range non-linear behavior under multiple loading modes, including uniaxial extension, biaxial extension, and triaxial-stressed deformation. Using hyperelastic models to encapsulate the complete behavior has always been hard due to not only the lack of measurement methods but also the incompleteness of the hyperelasticity theory. Among these obstacles, measuring the equi-biaxial behavior has been a crucial one as the existing methods fail to balance the measuring accuracy and the easy popularization. In this paper, an electromechanical coupling method (EMC method) is proposed to characterize the DE materials with the expectation of both a better complete-behavior coverage and a simpler experimental setup. The proposed method takes a theoretical investigation into the equi-biaxially pre-strained circular dielectric elastomer actuator (PCDEA) and deduces a special form of stress-strain relationship to bridge the gap between the easy-to-setup PCDEA experiments and model characterization. Experiments are then carried out on the classical VHB4910 acrylic film, and various hyperelastic models are evaluated with the proposed EMC characterization method on their fitting capability. Among these models, the Ogden 2-terms model fits all sets of measured data well. Validations are then carried out via DE actuators under more complex loading modes and the EMC-characterized Ogden 2-terms model provides precise behavior predictions with an average R2of 97.2 %. Thus, this research not only offers useful insights for a more practical complete-behavior-characterization method, but also provides a hyperelastic model for VHB4910 which is worthy of reference.

Reconfigurable surfaces contribute to multi-task robotic platforms, such as reconfigurable phased array antennas with variable aperture, by morphing between multiple specified shapes. Controlling each tile to approximate the variating shape of target surfaces requires a large number of accurate actuators. Previous research has demonstrated employing bistable-element-assembly to form reconfigurable surfaces for significant actuation simplification but suffering from low out-of-plane stiffness resulting in the lack of load-bearing capacity for carrying functional units with good mechanical accuracy. This paper proposes a design framework for tile-assembling bistable (TAB) surfaces with bi-compatible truss attachment for two prescribable stable configurations. The bistability comes from joining surface tiles with bistable elements, which contributes to easy actuation with fewer inaccurate actuators. Bi-compatible truss structures, which are only kinematically compatible at the two prescribed states, are introduced to enhance the out-of-plane stiffness of the TAB surface and improve its load-bearing capacity. Additionally and consequently, the kinematic determinacy of the reconfigurable surfaces is increased by the truss introduction, where bistable elements control the metric while truss structures dictate the principal curvature of the surface. This diminishes the redundant degrees of freedom with enhanced shape-approximation and reconfiguration-coordination. Four prototypes are designed and manufactured, which are a three-tile by three-tile (3 × 3) TAB surface that is stable at flat and spherical configurations, a 5 × 5 TAB surface with flat and spherical stable configurations, a 3 × 3 TAB surface that is stable at the flat and saddle configurations, and a 3 × 3 TAB surface that is stable at the sphere and saddle shapes. The out-of-plane stiffness, easiness of actuation, and shape accuracy of all prototypes are evaluated and show promises for real engineering applications.

This paper presents the results of an interfacial fracture study of Perovskite Light Emitting Devices (PLEDs). The interfacial robustness of the interfaces between the active layer and the adjacent layers of PLEDs is explored in an effort to simulate the effects of applied loads on pre-existing defects that are present in PLEDs. The dependence of interfacial fracture toughness on mode mixity (ratio of mode I and mode II) was studied using Brazil disk testing. The crack microstructure interactions associated with crack growth were then studied along with the underlying fracture modes and toughening mechanisms. The underlying toughening mechanisms were then modeled before discussing the implications of the current work for the design of mechanically robust PLEDs.

Although bending a sheet of paper is an easy operation, stretching is more limited and it leads to rupture and tears. However, well-designed cuts on the sheet can induce a large effective stretchability. This kirigami technique offers a large scope of engineering applications ranging from deployable structures to compliant electronics. We are here interested in the axisymmetric configuration where cuts are designed along concentric circles. Applying an increasing transverse load at the center of the sheet results into a 3D axisymmetric structure of growing amplitude which eventually saturates. We first describe the linear response of the structure and determine the evolution of the deployed shape until its asymptotic geometrical limit. Reversing the problem in the linear regime, we propose, a design procedure for the cuts leading to a desired 3D shape. The structure can also be deployed by inflating an inner balloon. Exploring further the interplay between mechanics and geometry, we finally describe the maximum volume of inflated kirigami structures as a function of the cutting pattern.

It is well known that spiders have an extraordinary auditory sensitivity. However, significant differences in the acoustic impedance between air and solids (spiders) would reduce the acoustic energy transmitted from air to spiders, and by intuition this might result in a significant decrease in the acoustic sensitivity of spiders. This mechanism has been long troubled in researchers’ minds that how hunting spiders could have an outstanding auditory sensitivity. In this paper, the auditory sensing mechanisms of hunting spiders are studied by theoretical analysis and simulation. The results show that the acoustic impedance can be adjusted by spiders’ hairs with particular features to realize the acoustic impedance matching between air and spiders, which could make spiders’ hairs easily send signals to the nervous system of spiders, thus significantly promoting the acoustic energy transfer from air to spiders. Both the appropriate length and deflection angle of hairs are critical to determine the acoustic impedance/acoustic transmission coefficient. In parallel, verification test is carried out on an innovative bionic hair array. The experiment result shows that the acoustic impedance is significantly descended by the bionic hair array with the spiders' acoustic hairs' features, which provides a sufficient proof of the acoustic impedance matching by spiders' hairs. Consequently, this work clearly discloses the acoustic sensing mechanism for the extraordinary auditory sensitivity of hunting spiders, which may have a great significance for the development of artificial auditory technology and sound stealth devices.

The force-displacement relationship is a fundamental mechanical property of materials, and the ability to inversely customize a prespecified relationship is useful for complex energy absorption systems, substrates of wearable electronics, and programmable vibration control. The recent development of mechanical metamaterials introduces graded strength into porous frameworks, which, however, can only achieve designable strain-hardening behavior. This is because the soft layers always deform prior to the hard layers due to the minimum energy gradient principle, regardless of the spatial arrangement of the component strength. Inspired by the “Domino effect” of tube inversion where its deformation sequence is governed by its kinematic compatibility, this paper introduces graded strength into a progressive and sequential tube inversion process, and correspondingly achieves arbitrarily prescribable force-displacement curves. Parametric study, numerical simulations for 9 different target curves, theoretical modeling leading to an inverse design framework, and experiments are carried out. This strategy paves the way for the inverse design of materials with arbitrary nonlinear mechanical responses essential for various novel applications.

Multistable morphing structures can reconfigure between different stable states that are separated by energy barriers, and one-degree-of-freedom (1-DOF) mechanisms have many merits, like simple actuation. This paper combines the two and proposes a new family of reconfigurable compliant linkages with many (2−6) 1-DOF kinematic paths that are separated by energy barriers. This new type of design is an extension of multistable structures, where each stable state corresponds to not just one configuration but a 1-DOF configuration space, i.e., a kinematic path. Components of the linkages are made elastically compliant, therefore enabling the switch between two isolated compatible paths with multi-stability. A generation-selection hybrid design algorithm to follow prescribed reconfigurable paths is proposed, and a minimum energy path (MEP) finding method to guide actuation to switch between different kinematic paths is developed. Four design examples with 2–3 reconfigurable paths and their experiments are presented, and the effectiveness of this method is verified. This work provides a fresh perspective to design the single-DOF reconfigurable mechanisms with larger design space, more reconfigurable kinematic paths, and easier reconfiguration actuation.

Origami has emerged as a powerful methodology for developing intelligent transformable robots. Although there is considerable progress in origami techniques to enable the design of a broad range of geometries, there is a dearth of effective actuation mechanisms which can eliminate the complex process of assembling external actuators. This paper illustrates a soft active origami robot based on electrostatic attraction. The time-varying electrostatic forces induced by AC voltage can lead to vibration of the origami structure. Inertia forces induced by vibration will then result in a traction, which can overcome the friction and facilitate the robot’s forward motion. This robot is composed of two paper strips coated with compliant electrodes which act as both the body (or skeleton) and the actuator, significantly simplifying the fabrication and decreasing the structural complexity, weight (∼7 g) and cost (∼1US$). A theoretical model is developed to interpret the actuation mechanism and the simulations are qualitatively consistent with the experiments. This soft active origami robot exhibits interesting attributes such as robustness, scalability and adaptability. This robot also demonstrates its capability to perform surveillance tasks in a 2D plane. This work investigates a new actuating mechanism for driving an origami structure, which results in simple and rapid prototyping of a soft robot. Soft active origami structures are expected to offer inexpensive solutions to space and/or swarm robots, due to properties of simple structure, low weight, low volume and low cost.

Cutting mechanics in soft solids have been a subject of study for several decades, an interest fuelled by the multitude of its applications, including material testing, manufacturing, and biomedical technology. Wire cutting of a parallelepiped sample is the simplest model system to analyse the cutting resistance of a soft material. However, even for this simple system, the complex failure mechanisms that underpin cutting are still not completely understood. Several models that connect the critical cutting force to the radius of the wire and the key mechanical properties of the cut material have been proposed. An almost ubiquitous simplifying assumption is a state of plane (and anti-plane) strain in the material. In this paper, we show that this assumption can lead to erroneous conclusions because even such a simple cutting problem is essentially three-dimensional. A planar approximation restricts the analysis to the stress distribution in the midplane of the sample. However, through threedimensional finite element modelling, we reveal that the maximal tensile stress – and thus the likely location of cut initiation – is located in the front face of the sample (end effect). Friction reduces the magnitude of this tensile stress, but this detrimental effect can be counteracted by large “slice-to-push”(shear-to-indentation) ratios. The introduction of the “end effect” helps reconcile a recent controversy around the role of friction in wire cutting, for it implies that slicing can indeed reduce required cutting forces, but only if the slice-push ratio and the friction coefficient are sufficiently large.

In some rocks and crystals, the fracture toughness in one direction would be lower than the other directions, and the fracture behavior in the materials with anisotropic fracture toughness profile may be very different from the isotropic materials. The weak plane model is suitable to describe the fracture toughness property in such materials. Because of the attraction of weak plane direction, the fracture might never enter a sector of directions near the weak plane, instead, these kinds of fracture would deflect to the weak plane direction immediately. Such material-level crack forbidden area, which is protected by the weak plane, is demonstrated in this paper. The size of the forbidden area is found to be only related to one material constant, the fracture toughness ratio, and is independent of the angle between the fracture and the weak plane, or the ratio of stress intensity factors near the crack tip. An approximate expression of the crack forbidden area is also derived in this paper for the simplified model. The study on the crack forbidden area would be helpful to control the crack path in the anisotropic fracture toughness materials and protect parts of the medium by designing the material properties.

This paper reports an untethered soft robot using soft electrostatic actuators. The robot consists of a deformable body driven by dielectric elastomer actuators, and two paper-based feet driven by electroadhesion actuators. The use of light-weight batteries and small-volume amplifiers contributes to the development of this untethered soft robot. Inspired by inchworms, this untethered soft robot can achieve locomotion through alternate expansion/contraction of its deformable body and adhesion/detachment of its two paper-based feet. The strong electroadhesion ensures a stable locomotion, and the large voltage-induced deformation and fast response of the robotic body leads to a velocity of 0.02 body length/s. This velocity is higher than that of untethered soft crawling robots based on pneumatic actuators or ionic polymer metal composites. The deformation of the robotic body is studied through finite element analysis. Compared to traditional hard robots, soft robots are found to be more susceptible to dissipative processes, including charging/discharging the actuators, dielectric relaxation and viscoelastic effects. These dissipative effects on this untethered soft robot are also investigated in this paper.

In this paper, deep learning neural networks is used to predict the band structure of metamaterial lattices, and proactive inverse design is employed in bandgap modulation. A parametric design of the metamaterial lattice is proposed to achieve a rich design space. The corresponding band structure data is calculated by finite element method (FEM) to construct the data set. We successfully bypass complex theoretical or numerical methods to establish the mapping relationship between the lattice geometry parameters of metamaterials and the band structure data by constructing and training fully connected neural networks and convolutional neural networks (CNN). By combining the trained neural network model into an inverse design method of bandgap tuning, the geometric parameters of the metamaterial lattice can be obtained directly by inputting the target band structure. Finally, three object band structures are designed and verified by finite element simulation and experiment, which verifies the effectiveness of the inverse design method. This design approach can be extended to design other metamaterial properties.

In this paper, based on the original Gray–Scott model, we propose a modified Gray–Scott model by introducing a target term into the reaction–diffusion equations. We apply this modified model in the context of shape transformation problems. To expedite the process from the source shape to the target shape, we utilize the explicit Euler method to solve our proposed modified Gray–Scott model, making our approach simpler and more efficient. To validate the feasibility of our method, we conduct simulation experiments in both two-dimensional (2D) and three-dimensional (3D) spaces. By progressing through experiments of increasing complexity, we demonstrate the natural effectiveness of our simulation method as a viable approach for shape transformation. To demonstrate the efficiency of the method, we provide the runtime consumed by the simulated shape transformation experiment. Additionally, to assess the correspondence between the ground truth values of the target shape and the simulated results, we calculate the corresponding area change rate and volume change rate in 2D and 3D spaces to prove that our proposed method can effectively transform into the target shape.

The design process of 3D mechanical metamaterials is still an emerging field and in this paper, we propose for the first time, a new design and optimisation approach based on 3D projections of 4D geometries (4-polytopes) and evolutionary algorithms. We find that through iterative parametric optimisation, 4-polytope projected mechanical metamaterials can be optimised to achieve both high specific stiffness and high specific yield strengths. Samples manufactured using a low-stereolithography method were tested in compression. We find that optimised tesseracts (8-cell structures) had a higher specific yield strength (22.8 kN m/kg) than that of honeycomb structures tested out-of-plane (19.4 kN m/kg) and a specific stiffness of (0.68 MN m/kg) which is more than 3-fold that of gyroid structures. The compressive strength to solid-modulus ratio of the 8-cell tesseract is very high (3×10−3), exceeding that of out-of-plane honeycombs, which are themselves closer in value to 5-cell pentatopes (2×10−3). 8-cell and 5-cell structures are in the region of one order of magnitude higher than 16-cell and 24-cell structures (∼2×10−4–8×10−4) and are hence comparable to nanostructured metamaterials. The 8-cell tesseracts are 18% stiffer, 43% stronger, and 19% tougher in compression than out-of-plane honeycomb structures, but unlike honeycombs, 8-cell tesseracts are 3D structures with cubic symmetry. Architecture has a profound effect on the relative consistency of properties with cubically symmetric structures displaying the greatest levels of consistency in terms of both strength and stiffness reduction as a function of pore space. The results presented in this paper showcase the potential of this new class of mechanical metamaterial based on 3D projected 4-polytopes.

Electronic medical devices have become more powerful in recent years. These medical devices contain arrays of electronic components, which required high-performance heat sinks to prevent from overheating and damaging. For the design of high-performance medical heat sinks, the temperature distribution should be evaluated. Thus, in this paper, the Generalized Differential Transformation Method (GDTM) is applied to the medical heat sink with a convex parabolic convective fin with variable thermal conductivity and mass transfer. In the first section of the current paper, the general heat balance equation related to the medical heat sink with convex parabolic fins is derived. Because of the fractional type of derivative, the concept of GDTM is employed to derive analytical solutions. The major aim of this study, which is exclusive for this article, is to find the closed-form analytical solution for the fractional differential equation in considered heat sink for the first time. In the next step, multiobjective optimization of the considerable fin is performed for minimum volume and maximum thermal efficiency. For evaluation of optimum design at various environmental conditions, the multiobjective optimizations are performed for a wide range of environmental conditions. In the final step, the results of multiobjective optimization in various environmental conditions are applied to the genetic programming tool and suitable analytical correlations are created for optimum geometrical design.

We studied the mechanical response of a recently developed new class of mechanical metamaterials based on the paper art of cutting, kirigami. Specially, the geometrical and structural design of representative cut units, via combined line cut, cut-out, and hierarchy of the structure, was explored for achieving both extreme stretchability and/or compressibility in kirigami metamaterials through experiments, alongside geometrical modeling and finite element simulations. The kirigami design was tested on constituent materials including non-stretchable copy papers and highly stretchable silicone rubber to explore the role of constituent material properties. The cut unit in the shape of solid rectangles with the square shape as a special case was demonstrated for achieving the extreme stretchability via rigid rotation of cut units. We found that compared to the square cut units, the theoretically predicted maximum stretchability via unit rotation in rectangle units (aspect ratio 2:1) increased dramatically from about 41% to 124% for the level 1 cut structure without hierarchy, and from about 62% to 156% for the level 2 hierarchical cut structure, which was validated by both experiments and simulations. To demonstrate the achievement of both extreme stretchability and compressibility, we replaced the solid square cut units with porous squares and re-entrant lattice shapes in silicone rubber based metamaterials. We found that a porous structure can enable an extreme compressibility of as high as 81%.

The precise control of both the mechanical deformation and wave propagation characteristics of metamaterial through design holds significant importance and presents a challenging task. This paper proposes a novel two-stage topological optimization design method for customizing both negative Poisson's ratio and locally resonant bandgap in the mechanical metamaterial. In the optimized model, the negative Poisson’s ratio structure is firstly obtained by optimizing the material distribution within the matrix region, then the metamaterial with the customized negative Poisson’s ratio and bandgap range is obtained through the second stage optimization. In the analysis of the metamaterial unit cell, the topology-dependent Poisson’s ratio is calculated based on the equivalent elastic matrix obtained through the homogenization method. The range of bandgap is estimated using the effective mass analytical model of the spring-mass system. Thus, the range of bandgap is determined by only a few geometric parameters instead of topological structure under given assumptions. The customized bandgap ranges can be extended by introducing more resonators into the unit cell and combining different unit cells into an assembled structure. Numerical examples are provided to demonstrate the efficacy of the proposed method.

A complete structure is composed of different components connected by various links/connections that plays extremely important role in maintaining the integrity of the structure, however, compared to the components, there is relatively less research on links/connections. Based on our accurate angle inversion of a detachable thin-walled cylindrical snap fit docking, we reformulate the elasticity of the snap fit and derive a new disassembly force and frictional energy dissipation of assembly/disassembly process. The studies shows that the irreversibility of frictional energy dissipation is the thermodynamic origin of snap-fit’s symmetry-breaking or asymmetry that is easy to assemble and not easy to disassemble. The results in this study are useful for the design of adjustable mechanical mechanism and/or snap-fit metamaterials. To make it easier for readers to use the formulas in this paper to solve their own problems, we provide a complete Maple program in the appendix.

In this paper, the impact energy dissipation characteristics of one-dimensional (1D) short single-walled carbon nanotube (SWNT) system are investigated via molecular dynamics (MD) simulation. It is found that 1D SWNT system has good force mitigation performance and extraordinarily high specific energy absorption (SEA) upon high-speed impact in the absence of plasticity, which is 1 to 2 orders advantageous over macroscale impact protection devices and structures. Moreover, a simple model based on the theorem of momentum can give an accurate prediction of force mitigation effect. The mechanism of this non-plastic impact energy dissipation lies in the transformation of impact energy to the kinetic and potential energy of SWNT molecules. Similar to macroscopic metallic rings, SWNTs can buckle under large force, which in fact enhances force mitigation capability of the system. A continuum model is established, able to predict the critical forces of SWNTs of different radii. Finally, system performance upon impact speeds in a broader range and the influence of parameters such as system length and SWNT radius are discussed. This work may be instructive to the design of novel impact energy mitigation system at nanoscale.

Mechanical stress within biological tissue can indicate an anomaly, or can be vital of its function, such as stresses in arteries. Measuring these stresses in tissue is challenging due to the complex, and often unknown, nature of the material properties. Recently, a method called the angled shear wave identitywas proposed to predict the stress by measuring the speed of two small amplitude shear waves. The method does not require prior knowledge of the material’s constitutive law, making it ideal for complex biological tissues. We extend this method, and the underlying identity, to include viscous dissipation, which can be significant for biological tissues. To generalise the identity, we consider soft viscoelastic solids described by a generalised Newtonian viscous stress, and account for transverse isotropy, a feature that is common in muscle tissue, for instance. We then derive the dispersion relationship for small-amplitude shear waves superimposed on a large static deformation. Similarly to the elastic case, the identity is recovered when the stress in the material is coaxial with the transverse anisotropy. A key result in this paper is that to predict the stress in a viscous material one would need to measure the wave attenuation as well as the wave speed. The case of viscoelastic materials with memory is also discussed.

Currently simple and conventional structures are unable to meet increasingly critical and diverse applications, as well as establishment of constitutive relationship of complex structure is becoming a major challenge in materials and mechanics disciplines. To overcome these challenges, fractal structures have attracted much attention due to their abilities to establish constitutive relationships of complex structures. In this study, we design a spatial fractal framework by using high elasticity material and 3D printing method. The constitutive relationships of fractal framework are mathematically modeled. Effects of fractal levels, fractal dimension, and spatial pattern of structures on the mechanical behavior of the fractal framework and assembled spatial fractal structures are studied using both finite element analysis and experimental measurements. The constitutive relationships among stress, strain, fractal dimension, fractal levels, and spatial patterns of structures are proposed and discussed. This paper develops a novel method to establish constitutive relationships of complex structures, and provides theoretical and engineering basis for 3D printable spatial fractal structures undergoing auxetic elasticity.

We report significant improvements in the sensing scheme of a microelectromechanical system (MEMS) based nanomechanical tensile testing technique that has been previously demonstrated to allow direct microstructural observations inside a transmission electron microscope (TEM) at high magnifications while simultaneously measuring the stress and strain in the sample electronically. The particularity of the MEMS device is the presence of two capacitive sensors on either side of a specimen gap (across which nanostructures like nanowires and thin films can be manipulated and clamped), allowing independent measurement of applied load (stress) and crosshead displacement (strain). The improvement in the sensing technique lies in the independent, separate measurements of the signals from the two capacitive sensors (as opposed to the previous technique based on the differential measurement between the two sensors). The new technique (called technique 2 in this paper) provides independent electronic sensing of stress and strain without making any assumption about the material behavior and opens up the possibility of doing force controlled tests. The new sensing technique is demonstrated and compared to the previous one (called technique 1 in this paper) by performing ex-situ monotonic and stress relaxation tests on freestanding 100-nm-thick Au films. Important practical matters such as specimen clamping and signal drift are also discussed.

The recent surge of interest in soft robotics has led to interesting designs and fabrication of flexible actuators composed of soft matter. Modeling these actuators to obtain quantitative estimates of their dynamics is challenging. In the present paper, a rod-based model for a popular pneumatically activated soft robot arm is developed. The model is based on Euler’s theory of the elastica and is arguably the simplest possible model. Through a synthesis of experiment and theory, we find that the constitutive relations needed to accurately capture the deformation of the arm differ considerably from the simple classical relation that the bending moment is linearly proportional to a change in curvature. The present paper also provides a framework to evaluate whether future soft robot actuator designs can be captured using simple models.

Wrinkling, when a thin stiff film adhered to a compliant substrate deforms sinusoidally out of plane due to compression, is a well understood phenomenon in bi-layer systems. However, when there are more than two layers, the wrinkling behavior of the multi-layer system is, at present, not fully understood. In this paper, we provide an analytical solution for wrinkling in tri-layer systems where the additional layers can contribute to either the film stiffness or substrate stiffness. Then, we provide an algorithmic approach for extending our tri-layer analytical solution to systems with multiple additional layers. Our analytical solution and algorithmic approach are verified numerically using the finite element method. Using our methodology, wrinking can be predicted and controlled in multi-layer systems, with applications ranging from stretchable electronics to biomimetic design. In this paper, we demonstrate that our model can be used to understand wrinkling behavior in epidermal electronics.

This paper demonstrates a new soft structure that uses a meso- or macro-scale elastic instability to generate a shape-memory effect similar to that exhibited by a ferroelastic material. It demonstrates the phase transitions, state switching, and shape-memory effects in this system, both in experiment and in simulation. The new class of materials described in the paper is potentially useful, since it comprises what are effectively “shape-memory alloys” of arbitrarily low modulus and arbitrarily large remnant strain. The reproduction of properties of materials usually associated with atomic- or molecular-level changes in structure using meso-scale structural opens the door to development of new, soft materials with new properties and functions.

In this paper, we demonstrate the feasibility of controlling the shape changing sequence of shape memory polymers created from digital manufacturing by exploiting multi-shape memory effects. We create shape memory polymer components with precise architectures by 3D printing. After subjecting them to model-based thermomechanical programming steps, the components assume specified configurations in a precisely controlled shape changing sequence. The use of the 3D printing technique enables the digital manufacturing route with the advantages of easy implementation, large design freedom, and high printing resolution of shape memory polymer components. The results in this paper provide a method for precisely controlling the shape recovery profile and enabling the manufacture of devices with complicated geometries and unprecedented multifunctional performance.

It has been observed that coexistence of multiple ruga (wrinkle, crease, fold or ridge) phases hinders advancement of nano and soft materials technology to control and manufacture uniform ruga phases in bilayer material systems. In this paper, we construct the primary bilayer (PB) ruga-phase diagram which can guide manipulation of various ruga configurations in bilayer systems. The PB ruga-phase diagram is a generic phase diagram of a bilayer system composed of a thin film on a half-space substrate, both of which are represented as incompressible neo-Hookean solids. On the PB ruga-phase diagram, various phase boundaries represent bifurcation sites of ruga structures caused by lateral compression of the bilayer. We have identified eleven different ruga phases and five triple points of ruga phases on the PB ruga-phase diagram. All the ruga phases eventually evolve to a limit phase of either global crease or global fold localization, depending on the stiffness ratio of the bilayer, when compressed up to the Biot critical strain of 0.456. Another global localization–ridge localization which is principally caused by large substrate pre-stretch (or mismatch strain)–is treated in a sequel paper.

Adhesion is a fundamental phenomenon that plays a role in many engineering and biological applications. This paper concerns the use of machine learning to characterize the effective adhesive properties when a thin film is peeled from a heterogeneous substrate. There has been recent interest in the use of machine learning in multiscale modeling where macroscale constitutive relations are learnt from data gathered from repeated solution of the microscale problem. We extend this approach to peeling; this is challenging because peeling from heterogeneous substrates is characterized by pinning where the peel front gets stuck at a heterogeneity followed by an abrupt depinning. This results in a heterogeneity dependent critical force and a singular peel force vs. overall peel rate relationship. We propose a neural architecture that is able to accurately predict both the critical peel force and the singular nature of the peel force vs. overall peel rate relationship from the heterogeneous adhesive pattern. Similar issues arise in other free boundary and free discontinuity problems, and the methods we develop are applicable in those contexts.

High strain rate loading of materials with spatially heterogeneous properties produces non-homogeneous and transient stress-strain states. Such stress-strain states are atypical of classical split Hopkinson pressure bar (SHPB) analysis that assumes homogeneous deformation and dynamic force equilibrium. To determine spatio-temporal stress fields in heterogeneous materials, a novel concept combining digital image correlation (DIC) full-field deformation measurements and explicit dynamic finite element method (EFEM) is described in this paper. The concept utilizes measured boundary forces and DIC measurements including both displacements and accelerations as input. The measured input is used to calculate internal forces, and hence the stress fields, within each continuum finite element by solving the governing equations of motion using the framework of EFEM. The DIC+EFEM concept procedure is verified using simulated synthetic data considering one-dimensional stress wave propagation in a bar. The reconstructed axial stress fields match identically with the exact EFEM solution for both homogeneous and heterogeneous materials that are elastic or elastic-plastic. The influence of DIC measurement noise on the reconstructed stresses is also studied.

Magneto-elastic materials have unique mechanical properties arising from the coupling between the magnetic and elastic components, which can be used in many engineering applications, such as waveguide systems, impact mitigation, and soft robotics. Traditional designs of magneto-elastic materials embed magnets or magnetic particles in a monolithic body. Under extreme conditions, the elastic matrices are prone to permanent damage and loss of functionality. An alternative framework was previously proposed by the authors in which 2D magneto-elastic networks were created through vibration-driven self-assembly from a dilute system of elastic bars with sticky magnetic ends. While these networks were demonstrated to fail gracefully under extreme loading and re-assemble under random excitation, how their emergent elasticity depends on magnet and elastic member characteristics remains to be fully understood. In this paper, to calculate the 2D bulk modulus of a given magneto-elastic network, particle dynamics simulations are first performed. An analytical framework is then developed to predict the bulk modulus of derived networks with varying design parameters, such as bar length and magnetic strength, based on the Cauchy–Born approximation. Through dimensional analysis, we demonstrate that 2D bulk modulus is linearly proportional to a composite variable that combines magnet strength, elastic member length, and wall thickness of the magnet holder, as evidenced by the collapse of 120 systems onto a single line. The numerical and analytical investigation of the bulk modulus of this architected magneto-elastic material demonstrates the broad tunability of its emergent elasticity, thereby enabling a myriad of promising applications of these systems.

Computational analysis of composites is well established; however, the process is time-consuming, owing to the disparate length scales and nonlinearities involved. Therefore, the use of machine learning models to predict the mechanical properties of short fiber-reinforced composites (SFRCs) is promising when large amounts of data are lacking. However, predicting data for an unseen design space remains challenging. The use of existing theoretical models for training is a viable solution to address this issue. This paper proposes a theory-guided machine learning (TGML) framework through training deep neural networks, based on the finite element analysis dataset that considers the cohesive effect of the interface, to predict the nonlinear mechanical responses of SFRCs. Our results demonstrate that incorporating the Halpin-Tsai theory with machine learning improves the predictive performance of the model in an unseen design space. Moreover, inspired by this theory, we propose a theory-inspired two-phase machine learning (TPML) approach to further improve predictive performance. Our results indicate that TGML and TPML capture more information from the data and thus enhance predictive performance. The proposed method can be adapted to the analyses of other composites with nonlinear mechanical behaviors.

Mechanical metamaterials with negative stiffness and negative Poisson’s ratio are exciting prospects for advanced material design. A plastic column with a series of periodically-spaced holes exhibits both of these properties when buckled under compression. In this paper, the behaviour of such a column under compression is measured experimentally and described with a simple mathematical model. This model predicts the compression, buckling and post-buckling behaviour of the entire column from the mechanical response of the thin ligaments of material that form the column’s microarchitecture to compression, rotation and shear forces, which are characterised experimentally, The softening behaviour in holey columns beyond the critical level of compression for pattern transformation is shown to be due to material constitutive nonlinearities in the rotation and shear response of the microarchitecture. Geometric perturbations to the columns can cause the observed pattern to change, but result in approximately the same force–displacement measurements as for the column with perfect geometry. This approach provides a useful framework to study systems where both geometric and material nonlinearities underpin observed phenomena.