Abstract As a smart material thermal shape memory alloys (SMAs) feature actuator behavior combined with self-sensing capabilities. With their high energy density and design flexibility they are predestined to be used in soft robotics and the emerging field of morphing surfaces. Such shape changing surfaces can be used for novel human-machine interaction (HMI) elements based on mode-/situation-dependent interfaces that may be applied to all kind of machines, appliances and smart home devices as well as automotive interiors. Since many of those contain textile surfaces, it is of special interest to place SMA-based actuator-sensor-elements beneath a textile cover or integrated them in the textile itself. In this study, the unique features of SMAs are used to design a system which represents an active “morphing” button. It can lower into the surface it is integrated in, pops up to be used and shows a proportional signal output depending on the pushing stroke. The system is characterized concerning haptics and sensor technology. The button consists of a TPU structure, to which two NiTi wires are attached. When activated, the SMAs contract and the structure curves upwards. The user can now push on the device to use it as a button. In the future, the use of SMA wires and for example TPU fibers enables direct integration in the production process of a possible smart and functional textile.

Abstract Shape memory polymers (SMPs) are extensively studied for self-folding origami due to their large strain recovery, low cost, and low activation energy. SMPs utilize viscoelastic material behavior to change shape in response to an applied stimulus, for instance light or electricity. Electrical actuation is desirable due to its higher energy density and shorter response time. Previous studies reported empirical results on shape recovery of conductive polymer composites actuated by specific applied voltage or current conditions, which required rigorous experimentation. Here, we introduce a finite element framework capable of predicting the coupled electro-thermo-mechanical response of electrically actuated SMPs. As inputs, this framework requires material properties, such as electrical conductivity and viscoelastic parameters. The viscoelastic response is implemented using a Prony series model that is fit to experimental dynamic mechanical analysis (DMA) data. Using this framework, we predict the shape recovery behavior of electrically actuated SMPs subject to various thermal, electrical, and mechanical loads and evaluate the sensitivity of the response to the material properties. Additionally, we show the effects of material pre-straining conditions and localized conductive pathways on shape recovery and self-folding. This computational framework provides a fundamental understanding of the electro-thermo-mechanical response of electrically actuated SMPs and can be used to design electrically actuated self-folding origami for aerospace applications.

This study aims to investigate the influence of temperature on the linear and nonlinear rheological behavior of a MR fluid, MRF 132DG, using a rotational rheometer. The experiments were designed to obtain properties of the fluid under oscillatory shear strain in the amplitude and frequency sweep modes, while maintaining different constant temperatures (−5, 0, 20 and 50 °C). The data were used to evaluate the storage and loss moduli under different levels of magnetic flux density considering the linear as well as nonlinear viscoelastic regions. The critical strain amplitudes were further obtained. Results showed enhanced linear viscoelastic region with increasing magnetic field density. Moreover, the effects of temperature and magnetic field on the frequency dependency of the fluid properties are illustrated for small and large amplitudes of shear strains.

Bone is a highly adaptive biological structure. Following Wolff’s law, bone realigns and grows to adapt to its mechanical environment. This leads to structural heterogeneity of trabecular bone and orthotropic symmetry of the elastic properties. Determining the bone alignment and material properties for living patients is difficult and involves implantation of force and displacement sensors on the bone to determine the compliance and stiffness properties. Micro-computed tomography along with finite element modeling have been limited to the vertebrae of donor cadavers to evaluate trabecular architecture, material properties, and density. Here, an adaptive structure topology optimization algorithm is presented and used to predict trabecular architecture. The algorithm predicts the optimal structure by minimizing the global compliance. The lumbar 1 (L1) vertebra is used as an example. Loads common to L1 vertebrae are applied and bone volume fraction measurements that can be taken easily from living patients through bone mineral density scans are used as the only inputs. The mathematical model is an adaptation of “99 Line Topology Optimization Code Written in Matlab” developed by Sigmund (2001). Bone is locally assumed to be isotropic with an elastic modulus of 13 GPa and the Poisson ratio of 0.3 applied to each element. The resulting structural heterogeneity results in global orthotropic relations. The model uses bone volume fraction and the loading orientation as inputs and gives the corresponding ideal bone structure geometry as an output. The trabecular structure can be predicted solely from the results of a bone mineral density scan. Finite element analysis of the optimized structure is then conducted and the global material properties are determined. While this model is for two-dimensional examples representing planes within the vertebral bone, it is extended to three-dimensional modeling to develop the cortical bone geometry and define the total volume. Matlab is then used to run the topology optimization simulation. The ideal structure is defined by optimizing for a prescribed displacement field of the system following the implementation of a gradient descent optimization method. The results are compared to published values from a combined experimental and numerical procedure. The procedure on sectioned vertebrae reported average ratios between elastic moduli of E 1 / E 2 = 5.2, E 1 / E 3 = 8.8, and E 2 / E 3 = 1.4. Results between the models and the previously published data yield similar transversely isotropic symmetry in the elastic moduli of trabecular bone. However, the elastic moduli ratios are not quite in agreement. Improving the accuracy of the boundary conditions and loading of the finite element model may improve the correlation between the optimization models and published data.

In many structural applications the use of composite material systems in both retrofit and new design modes has expanded greatly. The performance benefits from composites such as weight reduction with increased strength, corrosion resistance, and improved thermal and acoustic properties, are balanced by a host of failure modes whose genesis and progression are not yet well understood. As such, structural health monitoring (SHM) plays a key role for in-situ assessment for the purposes of performance/operations optimization, maintenance planning, and overall life cycle cost reduction. In this work, arrays of fiber Bragg grating optical strain sensors are attached to glass-epoxy solid laminate composite specimens that were subsequently subjected to specific levels of fully reversed cyclic loading. The fatigue loading was designed to impose strain levels in the panel that would induce damage to the laminate at varying numbers of cycles. The objectives of this test series were to assess the ability of the fiber Bragg grating sensors to detect fatigue damage (using previously developed SHM algorithms) and to establish a dataset for the development of a prognostic model to be applied to a random magnitude of fully reversed strain loading. The prognostic approach is rooted in the Failure Forecast Method, whereby the periodic feature rate-of-change was regressed against time to arrive at a failure estimate. An uncertainty model for the predictor was built so that a probability density function could be computed around the time-of-failure estimate, from which mean, median, and mode predictors were compared for robustness.

Shape memory alloys (SMAs) have tremendous potential use as actuators in mechanical systems due to their high specific energy density. Large recovery stresses can be generated when Nickel Titanium (NiTi), the most widely used SMA, undergoes constrained recovery where it is held in a deformed geometry and heated from a detwinned martensite phase to austenite phase. Recent experimental results have found that residual stresses can also be generated in NiTi after returning to a low temperature geometrically constrained state. This paper presents experimental results performed on NiTi wire samples where wire was: 1) deformed from a low temperature twinned martensite state to produce a strain that would be recoverable in an unloaded state 2) held at that strain state and heated above the austenite finish transition temperature and then cooled back below the martensite transition finish temperature while recording the forces generated. It was found that a residual load was produced in the low temperature state. Results from further testing beyond this point showed repeatability with application of small and large strains. Post constrained recovery stresses have the potential to be used to generate residual stresses in structures in a low energy, un-actuated state with a remaining potential for thermal actuation.

Knitted Textiles made from Nickel-Titanium (NiTi) shape memory alloy wires are a new structural element with enhanced properties for a variety of applications. Potential advantages of this structural form include enhanced bending flexibility, tailorable in-plane, and through-thickness mechanical performance, and energy absorption and damping. Inspection of the knit pattern reveals a repeating cell structure of interlocking loops. Because of this repeating structure, knits can be evaluated as cellular structures that leverage their loop-based architecture for mechanical robustness and flexibility. The flexibility and robustness of the structure can be further enhanced by manufacturing with superelastic NiTi. The stiffness of superelastic NiTi, however, makes traditional knit manufacturing techniques inadequate, so knit manufacturing in this research is aided by shape setting the superelastic wire to a predefined pattern mimicking the natural curve of a strand within a knit fabric. This predefined shape-set geometry determines the outcome of the knit’s mechanical performance and tunes the mechanical properties. In this research, the impact of the shape setting process on the material itself is explored through axial loading tests to quantify the effect that heat treatment has on a knit sample. A means of continuously shape setting and feeding the wire into traditional knitting machines is described. These processes lend themselves to mass production and build upon previous textile manufacturing technologies. This research also proposes an empirical exploration of superelastic NiTi knit mechanical performance and several new techniques for manufacturing such knits with adjustable knit parameters. Displacement-controlled axial loading tests in the vertical (wale) direction determined the recoverability of each knit sample in the research and were iteratively increased until failure resulted. Knit samples showed recoverable axial strains of 65–140%, which could be moderately altered based on knit pattern and loop parameters. Furthermore, this research demonstrates that improving the density of the knit increases the stiffness of the knit without any loss in recoverable strains. These results highlight the potential of this unique structural architecture that could be used to design fabrics with adjustable mechanical properties, expanding the design space for aerospace structures, medical devices, and consumer products.

Shape Memory Alloys (SMAs), known as an intermetallic alloys with the ability to recover its predefined shape under specific thermomechanical loading, has been widely aware of working as actuators for active/smart morphing structures in engineering industry. Because of the high actuation energy density of SMAs, compared to other active materials, structures integrated with SMA-based actuators has high advantage in terms of tradeoffs between overall structure weight, integrity and functionality. The majority of available constitutive models for SMAs are developed within infinitesimal strain regime. However, it was reported that particular SMAs can generate transformation strains nearly up to 8%–10%, for which the adopted infinitesimal strain assumption is no longer appropriate. Furthermore, industry applications may require SMA actuators, such as a SMA torque tube, undergo large rotation deformation at work. Combining the above two facts, a constitutive model for SMAs developed on a finite deformation framework is required to predict accurate response for these SMA-based actuators under large deformations. A three-dimensional constitutive model for SMAs considering large strains with large rotations is proposed in this work. This model utilizes the logarithmic strain as a finite strain measure for large deformation analysis so that its rate form hypoelastic constitutive relation can be consistently integrated to deliver a free energy based hyper-elastic constitutive relation. The martensitic volume fraction and the second-order transformation strain tensor are chosen as the internal state variables to characterize the inelastic response exhibited by polycrystalline SMAs. Numerical experiments for basic SMA geometries, such as a bar under tension and a torque tube under torsion are performed to test the capabilities of the newly proposed model. The presented formulation and its numerical implementation scheme can be extended in future work for the incorporation of other inelastic phenomenas such as transformation-induced plasticity, viscoplasticity and creep under large deformations.

The thermal shape memory effect describes the ability of a deformed material to return to its original shape when heated. This effect is found in shape memory alloys (SMAs) such as nickel-titanium (NiTi). SMA actuator wire is known for its high energy density and allows for the construction of compact systems. An additional advantage is the so-called “self-sensing” effect, which can be used for sensor tasks within an actuator-sensor-system. In most applications, a current is used to heat the SMA wires through joule heating. Usually a current between zero and four ampere is recommended by the SMA wire manufacturers depending on the wire diameter. Therefore, supply voltage is adjusted to the SMA wire’s electrical resistance to reach the recommended current. The focus of this work is to use supply voltages of magnitudes higher than the recommended supply voltages on SMA actuator wires. This actuation method has the advantage of being able to use industry standard voltage supplies for SMA actuators. Additionally, depending on the application, faster actuation and higher strokes can be achieved. The high voltage results in a high current in the SMA wire. To prevent the wire from being destroyed by the high current, short pulses in the micro- and millisecond range are used. As part of the presented work, a test setup has been constructed to examine the effects of the crucial parameters such as supply voltage amplitude, pulse duration, wire diameter and wire pre-tension. The monitored parameters in this setup are the wire displacement, wire current and force generated by the SMA wire. All sensors in this setup and their timing is validated through several experiments. Additionally, a highspeed optical camera system is used to record qualitative videos of the SMA wire’s behavior under there extreme conditions. This optical feedback is necessary to fully understand and interpret the measured force and displacement signals.

The sensitivity of piezoelectric/polymer composite materials is inversely proportional to their dielectric permittivity. Introducing a cellular structure into these composites can decrease the permittivity while enhancing their mechanical flexibility. Foaming of highly filled polymer composites is however challenging. Polymers filled with high content of dense additives such as lead zirconate titanate (PZT) exhibit significantly decreased physical foaming ability. This can be attributed to difficulty in gas diffusion, decreased fraction of the matrix available, the reduced number of nucleated cells and the difficulty in cell growth. Here, both CO 2 foaming and Expancel foaming were examined as potential methods to fabricate low-density thermoplastic polyurethane (TPU)/ PZT composite foams. While composites containing up to only 10vol.% PZT could be foamed using CO 2 , Expancel foaming could successfully yield highly-expanded composite foams containing up to 40vol.% (80wt.%) PZT. Dispersed Expancel particles in TPU/PZT composites acted as the blowing agent, activated by subjecting the samples to high temperatures using a hot press. Using Expancel, foams with expansion ratios of up to 9 were achieved. However, expansion ratios of greater than 4 were not of interest due to their poor structural integrity. The density of solid samples ranged from 1.8 to 3.3 g.cm −3 and dropped by a maximum of 80%, even for the highest PZT content, at an expansion ratio of 4. As the expansion increased, the dielectric permittivity of both CO 2 -foamed and Expancel-foamed TPU/PZT composites decreased significantly (up to 7.5 times), while the dielectric loss and electrical conductivity were affected only slightly. This combination of properties is suitable for high-sensitivity and flexible piezoelectric applications.

In this article, it is proposed that a membrane with tunable ionic conductivity can be used as a separator between the electrodes of a supercapacitor to both allow normal charge/discharge operation and minimize self-discharge when not in use. It is shown that the redox active conducting polymer PPy(DBS), when polymerized on a porous substrate, will span across the pores of the membrane. PPy(DBS) is also shown to function as an ionic redox transistor, in which the transmembrane ionic conductivity of the polymer membrane is a function of its redox state. The PPy(DBS) ionic redox transistor is applied between the electrodes in a supercapacitor as a smart membrane separator. It is demonstrated that the maximum tunable ionic conductivity of the smart membrane separator is comparable in operation to an industry standard separator at maximum ionic conductivity, with a self-discharge leakage current of ∼0.12mA/cm 2 at 1V. The minimum tunable ionic conductivity of the smart membrane separator is shown to decrease the supercapacitor self-discharge when not in use by a factor of 10, with a leakage current of 0.012mA/cm 2 at 1V. This range of tunable ionic conductivity could lead to the emergence of redox transistor batteries with high energy density and low self-discharge for short and long-term storage applications.

Black box design is a constraint driven design approach that distills essential elements of a physical process into inputs and outputs. This paper details the black box design implementation and validation of shape memory alloy (SMA) coil actuators as active members in a Watt I six bar avian-inspired wearable morphing angel wing mechanism. SMA coil actuators leverage the unique characteristics of high energy density SMA wire by providing a compact structural platform for large actuation displacement applications. The moderate force and displacement performance of low spring index coil actuators paired with their virtually silent actuation performance made them an attractive actuator solution to an avian-inspired wearable morphing wing mechanism for the University of Minnesota Department of Theatre Arts and Dance production of ‘ Marisol ’. The wing design constraints (extended span of 7.5 ft, a closed span of 3 ft) required a tailorable actuator system with capacity to perform at particular target force and strain metrics cyclically. A low spring index parameter study was conducted to facilitate an accelerated phase of design prototyping. The parameter study featured six SMA coil actuator prototypes made with 0.012” diameter Dynalloy Flexinol ® wire of varying spring indexes (C = 2.5–4.9). The coil actuators were manufactured through a CNC winding process, shape set in a furnace at 450 °C for 10 minutes, and water quenched for hardening. A series of thermomechanical actuation tests were conducted to experimentally characterize the low spring index actuation performances. The coil actuation characterizations demonstrated increased force and decreased actuator displacement corresponding to decreased spring indexes. Scaling these results aided an accelerated design of an actuator system. The actuator system consisted of four C = 3.05 coil actuators wound with 0.02” diameter SMA that were integrated into each Watt I mechanism. The characterization of the force-displacement profiles for low index SMA coil actuators provides an effective empirical design strategy for scaling actuator performance to mechanical systems requiring moderate force, moderate displacement actuators.

In this paper, we discuss the development and implementation of a 3-D electromechanically coupled homogenized energy model (HEM) for ferroelectric materials. A stochastic-based methodology is introduced and applied to problems involving large scale switching of ferroelectric and ferroelastic materials. Switching criteria for polarization variants are developed using density distributions in three dimensions to accommodate both electrical and mechanical loading and their coupled response. The theory accommodates non-proportional loading and major/minor loop hysteresis. Such formulations are known to accelerate computations for real-time control of nonlinear and hysteretic actuators. The proposed formulation maintains superior computational efficiency in the three dimensional case through the application of density formulations that are based on internal distributions of stress and electric field to produce a distribution of polarization switching events over a range of applied fields and stresses.

Shape memory alloy (SMA) knitted actuators are a type of functional fabric that uses shape memory alloy wire as an active fiber within a knitted textile. Through intentional design of the SMA knitted actuator geometry, various two- and three-dimensional actuation motions, such as scrolling and contraction [1], can be accomplished. Contractile SMA knitted actuators leverage the unique thermo-mechanical properties of SMA wires by integrating them within the hierarchical knitted structure to achieve large distributed uniaxial contractions and variable stiffness behavior upon thermal actuation. During the knit manufacturing process, the SMA wire is bent into a network of interlacing adjacent loops, storing potential energy within the contractile SMA knitted actuator. Thermal actuation above the wire-specific austenite finish temperature leads to a partial recovery of the bending deformations, resulting in large distributed uniaxial contraction (15–40% actuation contraction observed) of the SMA knitted actuator. The achievable load capacity and %-actuation contraction are dependent on the geometric loop parameters of the contractile SMA knitted actuator. While exact descriptions of the geometric loop parameters exist, a reduction of the geometric complexity is advantageous for high-level contractile SMA knitted actuator design procedures. This paper defines a simple geometric measure, the non-dimensional knit density, and experimentally correlates the contractile SMA knitted actuator performance to this measure. The experimentally demonstrated dependency of relevant actuator metrics on the knit density and the wire diameter, suggests the usability of the simplified geometry definition for a high-level contractile SMA knitted actuator design.

Origami — the Japanese art of folding — has inspired various engineering applications for several decades due to its ability to manipulate complex shapes. In our study, multi-field actuated self-folding Origami structures are developed with the implementation of two classes of smart materials: relaxor ferroelectric polymers and magneto-active elastomers (MAEs). The chosen relaxor ferroelectric is P(VDF-TrFE-CTFE), a P(VDF)-based terpolymer and the MAE is a PDMS substrate with embedded barium hexaferrite particles. At the macroscale, this study involves the modeling of the large deformation of a bimorph comprising the aforementioned magnetically and electrically actuated materials using a 1D analytical model derived from the equilibrium of a differential element. The large deformation is extracted from curvatures solved at each point for the resulting differential equation of the equilibrium state. On the microscale, this study also considers the nonlinear behavior of the smart materials. The nonlinear dielectric response of the relaxor ferroelectric polymer is captured by an electric field-dependent electrostrictive coefficient derived from a microstructure-based energy balance for the electrostriction of the terpolymer. The energy density function is postulated to be composed of an elastic contribution described by the Arruda-Boyce hyperelastic model and an electric contribution based on dipole-dipole interactions. On the other hand, a magnetic field-dependent torque drives the actuation of the MAEs, which is also dependent on the orientation of the material to the field. The integration of the micro and macro components results in an analytical model of a 1D, multi-layered flat structure that can be numerically solved for displacements under combined fields. The model is compared with well-matching experimental results of a unimorph and a bimorph structure as validation. The experiments measured the tip displacement of the beam under combined fields for a quantitative analysis. The study takes the analysis further by optimizing parameters such as geometry, field strengths, and the combination of active layers for relevant target shapes.

Traditionally, sensors to be integrated into a structural component are attached to or mounted on the component after the component has been fabricated. This tends to result in unsecured sensor attachment and/or serious offset between the sensor reading and the actual status of the structure, leading to performance degradation of the host structure. This paper describes a novel extrusion-based additive manufacturing process that has been developed to enable embedment of sensors in ceramic components during the part fabrication. In this process, an aqueous paste of ceramic particles with a very low amount of binder content (< 1 vol%) is extruded through a moving nozzle to build the part layer-by-layer. In the case of sensor embedment, the fabrication process is halted after a certain number of layers have been deposited. The sensors are placed in their predetermined locations, and the remaining layers are deposited until the part fabrication is completed. Because the sensors are embedded during the fabrication process, they are fully integrated with the part and the aforementioned problems of traditional sensor embedment can be eliminated. The sensors used in this study were made of sapphire optical fibers of 125 and 250 micro-meters diameter and can withstand temperatures up to 1600 °C. After the parts were built, two different drying processes (freeze drying and humid drying) were investigated to dry the parts. The dried parts were then sintered to achieve near theoretical density. Scanning electron microscopy was used to observe the embedded sensors and to detect any possible flaws in the part or embedded sensor. Attenuation of the sensors was measured in near-infrared region (1500–1600 nm wavelength) with a tunable laser source. Raman spectroscopy was performed on the samples to measure the residual stresses caused by shrinkage of the part and its slippage on the fibers during sintering and mismatch between the coefficients of thermal expansion of the fiber and host material. Standard test methods were employed to examine the effect of embedded fibers on the strength and hardness of the parts. The result indicated that the sapphire fiber sensors with diameters smaller than 250 micrometers are able to endure the freeform extrusion fabrication process and also the post-processing without compromising the part properties.

State-of-the-art actuators that produce rotatory motion and torsional moment are based on either combustion engines, electro-motors, hydraulic or pneumatic machines. Each of these actuation methods has several drawbacks. All of these systems often come with high initial costs, big weight and need a lot of construction space because of their dimensions. Shape memory alloys are known for their superior energy density. That allows for the construction of very compact and light-weight actuator systems. In this paper, the design and construction of a light weight rotational actuator based on SMA wires is presented. The design is based on a modular concept, with each module contributing to the total rotational radius. This way, the actuator can be custom fitted to specific application needs.

Additive manufacturing ( i.e. 3D printing) has only recently be shown as a well-established technology to create complex shapes and porous structures from different biocompatible metal powder such as titanium, nitinol, and stainless steel alloys. This allows for manufacturing bone fixation hardware with patient-specific geometry and properties (e.g. density and mechanical properties) directly from CAD files. Superelastic NiTi is one of the most biocompatible alloys with high shock absorption and biomimetic hysteresis behavior. More importantly, NiTi has the lowest stiffness (36–68 GPa) among all biocompatible alloys [1]. The stiffness of NiTi can further be reduced, to the level of the cortical bone (10–31.2 GPa), by introducing engineered porosity using additive manufacturing [2–4]. The low level of fixation stiffness allows for bone to receive a stress profile close to that of healthy bone during the healing period. This enhances the bone remodeling process (Wolf’s Law) which primarily driven by the pattern of stress. Also, this match in the stiffness of bone and fixation mitigates the problem of stress shielding and detrimental stress concentrations. Stress shielding is a known problem for the currently in-use Ti-6Al-4V fixation hardware. The high stiffness of Ti-6Al-4V (112 GPa) compared to bone results in the absence of mechanical loading on the adjacent bone that causes loss of bone mass and density and subsequently bone/implant failure. We have proposed additively manufactured porous NiTi fixation hardware with a patient-specific stiffness to be used for the mandibular reconstructive surgery (MRS). In MRS, the use of metallic fixation hardware and double barrel fibula graft is the standard methodology to restore the mandible functionality and aesthetic. A validated finite element model was developed from a dried cadaveric mandible using CT scan data. The model simulated a patient’s mandible after mandibular reconstructive surgery to compare the performance of the conventional Ti-6Al-4V fixation hardware with the proposed one (porous superelastic NiTi fixation plates). An optimized level of porosity was determined to match the NiTi equivalent stiffness to that of a resected bone, then it was imposed to the simulated fixation plates. Moreover, the material property of superelastic NiTi was simulated by using a validated customized code. The code was calibrated by using DSC analysis and mechanical tests on several prepared bulk samples of Ni-rich NiTi. The model was run under common activities such as chewing by considering different levels of the applied fastening torques on screws. The results show a higher level of stress distribution on mandible cortical bone in the case of using NiTi fixation plates. Based on wolf’s law it can lead to a lower level of stress shielding on the grafted bone and over time bone can remodel itself. Moreover, the results suggest an optimum fastening torque for fastening the screws for the superelastic fixations causes more normal distribution of stress on the bone similar to that for the healthy mandible. Finally, we successfully fabricated the stiffness-matched porous NiTi fixation plates using selective laser melting technique, and they were mounted on the dried cadaveric mandible used to create the finite element model.

A two-dimensional phononic crystal (PC) can exhibit longitudinal-mode negative energy refraction on its lowest (acoustical) frequency pass band. The effective elastodynamic properties of a typical PC are calculated and it is observed that the components of the effective density tensor can achieve negative values at certain low frequencies on the acoustical branches for the longitudinal-mode pass-band, and that negative refraction may be accompanied by either positive or negative effective density. Furthermore, such a PC has a high anisotropy ratio at certain low frequencies, offering potential for application to acoustic cloaking where effective material anisotropy is essential.

Energy harvesting using a triboelectric nanogenerator (TENG) has been a major area of research in the recent years in order to harvest mechanical energy in different scales. High energy conversion efficiency, broad range of application in different systems and relatively easy fabrication process are among the factors demonstrating essential needs for TENG technology development. Performance of a TENG could be affected by many factors such as the frequency of vibration and the surface charge density. As a key factor in improving the power output of TENGs, surface charge density could be modified by the selection of proper charging materials and by increasing the contact area between the tribo-pairs. Although there have been numerous studies analyzing the performance of different tribo-pairs and different interfacial structures for a TENG, a systematical analysis of the contact phenomena between the interfacial structures in order to investigate the effects of different surface properties and structures such as, surface roughness, dielectric properties or the presence of nanostructures is still not available. In the current study, systematical numerical simulations have been performed on the adhesive contact behavior of the macro/nanostructures at the TENG interface. An interaction potential has been used to represent the adhesive interactions while surface deformations are coupled using half-space Green’s function. Furthermore, effects of the deformation of the interfacial structure on the performance and output of the TENG has been investigated by developing a theoretical model for a vertical-contact-mode TENG using a mass-spring system to represent the motion of the moving electrode. Coupling the theoretical model to the instantaneous deformation of the interfacial structure, real-time output of the TENG in terms of short-circuit voltage and open-circuit current has been studied in response to a predefined pressure input. The results of the current study demonstrate the effects of the deformation of the interfacial structure on the output characteristics of TENGs during the transition between partial-contact to full-contact modes. Numerical simulation results represent acceptable correlations with previously reported experimental data. The simulation package developed in this study is capable of simulating the contact behavior of the interfacial structure and predicting the deformed geometry.