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Modern electronic devices are usually subjected to thermo-mechanical loads and prone to buckle during their operation. Thermo-mechanical stability is a crucial standard for their reliable applications. This paper explores the size effect on the thermo-mechanical behavior of the organic solar cells. An effective isogeometric analysis method combined with modified couple stress theory is presented. The thermo-mechanical buckling load-bearing capacities of the organic solar cells subjected to various in-plane loadings, temperatures, and geometrical parameters are discussed. Numerical results show that the size effect has significant effect on the thermo-mechanical load-bearing capacity. The stability region changes minimally when the material length scale parameter $$l$$ to cell thickness $$h$$ ratio is less than 0.2, while the stability region increases remarkably when it is larger than 0.2. Notably, if the material length scale parameter increases to its thickness, the stability region increased almost 25 times than that without size effect. Furthermore, the stability region is narrowest if the temperature is uniform across the thickness direction of the cell.

This paper presents a non-classical refined shear deformation theory model in conjunction with the isogeometric analysis for the static bending, free vibration, and buckling behaviors of multilayered microplates. The modified couple stress theory is used to account for the small-scale effect. Taking a five-layer (Al, P3HT: PCBM, PEDOT: PSS, ITO, and Glass) organic solar cell as an example, it is found that the small-scale effects lead to a decrease in deflection, but an increase in the natural frequency and buckling load. With consideration of the size effect (l/h = 1), the stresses are almost 5 times as much as that without the size effect (l/h = 0). This is why the size effect should be taken into account. Besides, the maximum tensile stress occurs in the ITO layer, which is the dangerous layer. In addition, the normalized deflections increase with increasing aspect ratio, but the normalized natural frequencies and normalized buckling loads decrease with increasing aspect ratio.

The organic solar cell has attracted much interest due to its high power conversion efficiency and low cost. This paper studies the interlaminar stresses between the working layer and the substrate of the organic solar cell. The effects of solar irradiation and wind speed have been considered as well. The multilayered film model and the thin film–substrate model are employed separately in reaction to the different magnitude of the film and substrate thickness. Both models straightforwardly show the dangerous stress areas at the two ends of the working layer. Numerical examples reveal that the interlaminar stress increases as the solar irradiation increases while decreases with the wind speed increasing. A thicker working layer of the organic solar cell results in larger interlaminar stresses. The critical value of sunlight irradiation for varying external environment is predicted. The critical value of sunlight irradiation at the wind speed of Vf = 15 m/s increases by nearly 20%, compared with that of the wind speed Vf = 5 m/s. In addition, the effect of the equivalent thermal expansion coefficient of the working layer on the interlaminar stress is also explored.

A nonlocal strain gradient theory (NSGT) accounts for not only the nongradient nonlocal elastic stress but also the nonlocality of higher-order strain gradients, which makes it benefit from both hardening and softening effects in small-scale structures. In this study, based on the NSGT, an analytical model for the vibration behavior of a piezoelectric sandwich nanobeam is developed with consideration of flexoelectricity. The sandwich nanobeam consists of two piezoelectric sheets and a non-piezoelectric core. The governing equation of vibration of the sandwich beam is obtained by the Hamiltonian principle. The natural vibration frequency of the nanobeam is calculated for the simply supported (SS) boundary, the clamped-clamped (CC) boundary, the clamped-free (CF) boundary, and the clamped-simply supported (CS) boundary. Effects of geometric dimensions, length scale parameters, nonlocal parameters, piezoelectric constants, as well as the flexoelectric constants are discussed. Results demonstrate that both the flexoelectric and piezoelectric constants enhance the vibration frequency of the nanobeam. The nonlocal stress decreases the natural vibration frequency, while the strain gradient increases the natural vibration frequency. The natural vibration frequency based on the NSGT can be increased or decreased, depending on the value of the nonlocal parameter to length scale parameter ratio.

Piezoelectric wind energy harvesters consisting a bluff body and a piezoelectric cantilever beam have great potential for powering small-sized wireless devices. To achieve a higher energy output, the beam is designed for large deformation. This results in the nonlinear nature of the energy harvesters. In this paper, a nonlinear model of a piezoelectric wind harvester with different geometrical parameters is developed. A comparison of the energy harvesting performance of these energy harvesters with different geometrical parameters is provided. Results show that the onset speeds of galloping for trapezoidal and exponential piezoelectric energy harvesters are significantly lower than those of rectangular beam. The average power output density of the beam with exponential shape is larger than trapezoidal and rectangular beams. Therefore, designing a beam with exponentially varying shape can obtain the largest power density and therefore can reduce the cost of piezoelectric wind energy harvester.

Thermoelectric (TE) materials have a broad range of application in engineering such as cooling for thermal protection. Due to the brittle nature, TE semiconductors are prone to crack/voids under thermal shock. The investigation of the transient problem in cracked thermoelectric materials is essential for engineering applications. This paper describes a thermal-mechanical coupling method to analyze the transient response of the TE medium of finite size with an arbitrarily located inner crack. Based on the Fourier and Laplace transform, the crack problem is simplified into a system of singularity integral equations which can be solved by simple allocation. Besides, the results of this paper are verified through the finite element method (FEM). Furthermore, the effects of the crack position, crack's thermal and electrical permeability are discussed. Also, the effect of crack on the thermoelectric energy conversion efficiency is studied. Results show that the field concentrations at the crack tip become more significant when the crack is centrally located in the vertical direction. The electrical permeability of the crack has a limited influence on the energy conversion efficiency. However, as thermal permeability of the crack goes up, the efficiency falls significantly.

Thermoelectric (TE) materials as energy functional semiconductors can directly convert heat into electrical power. Due to the brittle nature of semiconductors, voids or inclusions are easy to be produced in the TE materials. This paper studies the three-dimensional ellipsoidal inclusion problem in thermoelectric materials. By introducing two auxiliary functions, we successfully simplify the non-linear coupled governing equations into linear un-coupled equations and the linearization is validated by two practical cases. Based on the Green's function method, the analytical solutions of this problem are derived. We find that the thermoelectric field inside the ellipsoidal inclusion is always uniform when subjected to far-field uniform loads. Furthermore, we derive the effective material properties of the matrix-inclusion system in closed-form. We find that it is possible to enhance the thermoelectric properties as well as the figure of merit by inserting specific inclusions. Moreover, among the different shapes of inclusions, the elliptical cylinder fiber that lies along the loading direction has the most significant improvements to the material properties. This paper is the first that derives the analytical solutions of three-dimensional inclusion problems in TE materials.

This paper analyses a two-dimensional problem in thermoelectric materials with an inclined elliptic inclusion. We have obtained the closed-form solutions of electric current density and temperature considering the inclusion's electrical and thermal permeability. Based on the derived thermoelectric field, the thermal stresses are given in the explicit form and the effect of inclusion on effective thermoelectric properties is investigated. The electrically impermeable and thermally impermeable inclusions will respectively cause maximum electric current concentration and heat concentration. The thermally impermeable and rigid inclusion will cause maximum stress concentration around the inclusion. Furthermore, we find that the effective electric conductivity (effective thermal conductivity) of the matrix-inclusion system is increased when the inclusion have higher electric conductivity (thermal conductivity) than the matrix. It is possible to enhance the effective figure of merit by inserting inclusions with specific electric conductivity and heat conductivity. It predicts a new way for the design of high-performance thermoelectric devices. The results in this paper can be directly used for reliability consideration in design and optimization of thermoelectric devices in engineering.

A novel bended wrinkle structure is proposed for layout design in flexible electronics, which is formed by compressive local buckling of the thin film bonded onto a pre-strained, finite-thickness substrate upon release of the pre-strain. The excellent performance of stretchability of this structure, which could be as high as 309%, is shown according to theoretical analyses and validated by finite element method (FEM). Furthermore, the maximum strain of the proposed design is examined to ensure reliability of application devices. Except for the approach to compressibility based on maximum strain analyses, the bended wrinkle structure is taken as a laminate with geometrical imperfections and buckling analyses are conducted to obtain the critical buckling loads, consequently another evaluation criterion for compressibility is established. It is also revealed that the stretchability can be further enhanced by bonding the two ends of the structure to another pre-strained compliant basal substrate, though the pre-strain for the basal substrate is restricted by the compressibility. In the current work, an alternative to existing planar wavelike layout designs is presented and the results obtained offer important design guidelines for future applications.

Recently, open cellular substrates instead of traditional solid substrates have been used in flexible electronics, catering to the need for high permeability of bio-fluids through the device. The Poisson ratio of the existing open cellular designs, however, remains positive, which is inappropriate for the cellular substrates mounting on some biological auxetic materials, as the resulting mismatch in deformation may cause irritation. In the current work, a type of triangular lattice networks is presented with satisfactory negative Poisson ratio effect over large strains. A finite deformation model is developed for the deformed angles, constitutive relation and maximum strain of the building block, with nonlinear finite element method (FEM) validations. Results demonstrate desired negative Poisson ratios and mechanical properties can be achieved in an isotropic manner by tailoring three geometric parameters (arc angle θ0, length/radius ratio L/R and width/radius ratio w/R). Thereinto, longer arm lengths not only yield lower equivalent modulus and maximum strain, but also enable wider range of isotropic negative Poisson ratios (from -0.35 to 0) and applied strains (from 0% to 80%), providing more flexibility in network designs and new possibilities to emerging biomedical applications.

Dynamic performance of sandwich beam with shear thickening fluid (STF) core subjected to a periodic excitation is investigated. The addition of STF enables the sandwich beam to have a tuning stiffness and damping capacity under dynamic deformation. Here, the constitutive model of STF is described by a complex shear modulus related to the shear rate. The transverse moving beam is modeled based on Newtonian law and derived nonlinear equations are solved by finite difference method. It is found that the resonant frequency of the beam increases with the amplitude of the external excitation by a power law. In addition, the initial damping ratio decreases first and then increases with the increase of the amplitude of the initial excitation for the STF with shear thinning zone. The minimum value of the initial damping ratio should be avoided, which is caused by initial shear thinning. This work can be used to guide the designing of structures with enhanced damping and the preparation of STF materials for application to such structures.

A fracture mechanics analysis is conducted for a delamination problem of a multilayered thermoelectric material (TEM) that consists of an n-type layer and a p-type layer sandwiched by an insulating layer. A time-varying energy release rate is presented when the n-type layer delaminates from the insulating layer. Effects of the temperature difference across the system and the applied electric current on the energy release rate are identified. The influence of the thickness ratio of the insulating layer to the thermoelectric (TE) layer is also examined. Based on the energy release rate criterion, the critical temperature difference for delamination propagation is obtained. Some useful conclusions are given.

Different from piezoelectric effect, the flexoelectric effect is size dependent and becomes more significant at nanoscale. A nonlinear dynamic model of nanoscale flexoelectric shells is developed based on modified couples stress theory. The governing equations for nonlinear vibration of a flexoelectric cylindrical nanoshell are obtained. The natural frequency and generated voltage of the flexoelectric cylindrical nanoshell is achieved. Effects of geometric dimension, character material length, and vibration amplitude on the natural frequency and the generated voltage are discussed in detail. Results demonstrate that modified couple stress theory and large deformation theory are coupled together and interact with each other in the analyses of natural frequency and electromechanical behavior. Simultaneously taking nonlinearity and couple stress theory into account is necessary.

Unimorph piezoelectric energy harvesters are typically a unimorph cantilever beam located on a vibrating host structure. Delamination is one of the major failure modes of such unimorph cantilevers and therefore is studied in this article. The delaminated cantilever unimorph is modeled with one through-width crack using four Euler beams connected at delamination edges. The governing equations, the corresponding boundary conditions, and the kinematic continuity conditions are derived based on the Hamiltonian principle. The solutions of the voltage and power output for the present model are derived. The influence of the position and the length of the delamination, frequency of input base excitation, and load resistance on the voltage and power output are discussed in detail. The results show that delamination in the unimorph of the energy harvester will impressively decrease the voltage and power outputs. Influences of the delamination located at the free end of the cantilever are more obvious. For a given active length of the delaminated cantilever energy harvester, it is useful to increase the overall length of the cantilever to obtain a higher voltage and power outputs.

Magnetically actuated robots are attracting much interest due to the advantages of fast response, remote manipulation and enabling operations in enclosed spaces. Recent advances in fabricating ferromagnetic polymeric matrices embedded with hard magnetic fillers provide routes to multimodal locomotion for soft-bodied robots. One limitation of these matrix-based robot designs is that it requires low volume fraction of hard magnetic fillers to achieve soft and compliant robot body such that moderate magnetic fields are sufficient for actuation. However, low volume fraction of functional magnetic fillers leads to magnetically weak soft robots that are difficult to actuate. Here, we propose a compliant and high-performance robot design operating at magnetic fields down to 1 mT by utilizing a high-quality ferromagnetic film and mechanics-guided three-dimensional (3D) assembly technique. A parylene coating is deposited to keep the assembled arch shape, allowing releasing and actuating the structure as a freestanding robot. The robot would unfold and fold periodically under cyclic magnetic fields, driving the robot in a desired direction. To illustrate the versatile applicability of this approach, robots in two different representative geometries are presented, one in traditional straight configuration and the other in serpentine configuration. Through theoretical analysis and finite element analysis, fundamental results are offered for the proposed robot design, including concise solutions to the unfolding deformation, the effects of coating thickness on spring back, the maximum strain in the hard ferromagnetic film and a comparison of unfolding deformation of both designs. The results clearly show the effect of geometry/material parameters, external magnetic field and prestrain in assembly process, providing essential design guidelines to compliant and fast-moving magnetic robots via the proposed method.

Serpentine-shaped interconnects are widely employed to achieve high level of stretchability in stretchable electronic devices. In the current work, an analytical model for the mechanical response of planar serpentine interconnects with thermal effect is developed and verified by finite element method (FEM). Specifically, the closed-formed expressions to compliance and stretchability are derived based on curved beam theory and energy method. The numerical results indicate that a considerable error (e.g., >10% relatively) could be induced for many representative configurations using the model with thermal loads absent. The present work provides more accurate predictions for the structural response of serpentine interconnects in practical working conditions, which help in optimal design in future applications.

With the improvement on materials performance gradually reaching its bottleneck, more and more works focus on optimizing the device structures to seek further performance enhancement of thermoelectric (TE) devices. This paper proposed an analytical model to calculate the performance of thermoelectric generators (TEGs) with varied leg cross-sections considering temperature-dependent material properties. The explicit expressions of output power and efficiency are derived and the model is verified by finite element method (FEM). Furthermore, the optimization of leg geometry for higher device performance is performed based on the presented model, the results show that the key to maximum output power is to minimize the leg resistance; and increasing the leg volume may simultaneously raise the output power and efficiency. In addition, we apply the presented model to optimize the leg shape of a commercial TEG module and find that the optimized geometry can simultaneously achieve an enhancement up to 43.1% for output power and 9.67% for efficiency. The presented model thus may be useful in designing high-performance TEGs and shed considerable light on the principles of TEG design.

In this paper, large amplitude free vibration of electrically actuated nanobeams with consideration of surface energy, temperature change and Casimir force is studied. Results show that neglecting of surface energy and intermolecular Casimir force will result in a lower prediction and a higher prediction of fundamental frequency, respectively. Thermal effect may change the relationship between fundamental frequency and applied voltage. In addition, the effect of geometric nonlinear deformation on the fundamental frequency is more significant for large applied voltage. The influence of surface energy and geometric nonlinear deformation on the fundamental frequency depends on the length and height of the nanobeams.

Efficiently converting vibration energy from surrounding environment to electric energy for powering micro/nano-electromechanical systems (MEMS/NEMS), without using batteries, is an interesting research subject. One of the most important applications of flexoelectricity is in the field of transducers in energy harvesters where flexoelectric effect is significant at micro/nano-scale. In this paper, a theoretical model incorporating flexoelectricity and piezoelectricity for energy harvesting is developed. The model includes geometric nonlinearity deformation and damping effect so that it can more accurately predict the electromechanical behavior of energy harvesters. A special case study for a cantilever beam (which is the most common configuration of vibration energy harvesters) is carried out. Two types of commonly-used cantilevered energy harvesters, a single layer and a unimorph energy harvester, are derived. It is found that, in some cases, voltage output contributed by flexoelectric effect is extremely (e.g., five times) higher than that solely contributed by piezoelectric effect.

Three-dimensional (3D) serpentine mesostructures assembled by mechanics-guided, deterministic 3D assembly have potential applications in energy harvesting, mechanical sensing, and soft robotics. One limitation is that the serpentine structures are required to have sufficient bending stiffness such that they can overcome the adhesion with the underlying substrate to fully buckle into the 3D shape (global buckling). This note introduces the use of cellular substrate in place of conventional homogeneous substrate to reduce the adhesion energy and therefore ease the above limitation. A theoretical model based on energetic analysis suggests that cellular substrates significantly enlarge the design space of global buckling. Numerical examples show that the enlarged design space enables 3D serpentine structures with reduced maximum strains and resonant frequencies, which offers more possibilities for their potential applications.

Cracking is a critical issue in the preparation and application of thermoelectric materials. Traditional models for thermoelectric fracture predict infinite electric current and heat flux at the crack tip. However, it is impossible since infinite electric current and heat cannot be sustained at the atomic level. To give a physically reasonable fracture prediction of thermoelectric materials, this paper proposes an analytical model of thermoelectric fracture based on the concept of electrical and thermal field saturation along a strip at the crack front, in which we assume the electric current and heat flux cannot exceed a saturation limit. Firstly, based on the complex variable method, we derive the thermoelectric field solutions with electrical and thermal field saturation at the crack tip. Then, the thermally induced stresses and the fracture criterions are given. The results show that the thermoelectric field predicted by the saturation model exhibits no singularity at the crack tip, which may give better agreement with the experimental observations and thus shows better application potential.

Effects of surface energy on the pull-in instability and free vibration of electrostatically actuated micro/nanoscale plates are analyzed based on the modified couple stress theory. A reduced-order model is derived to consider the geometrically nonlinear strain, surface energy, the Casimir force and the material length scale simultaneously. Results show that the pull-in voltage and fundamental frequency of the plate are considerably enhanced by the material length scale, surface energy and geometrically nonlinear deformation. However, these quantities are weakened with the inclusion of Casimir force. The effects of surface energy and the material length scale become more significant if the thickness decreases. In addition, the effects of surface energy and geometrically nonlinear strain on the pull-in voltage are the largest for a square plate.

The vibration behavior of a bridged single walled carbon nanotube with a bio-mass adsorbed at various positions subjected to temperature change is investigated. The frequency equation of the sensor is derived analytically based on nonlocal Euler–Bernoulli beam theory. The relationship between the vibration frequency, the temperature change, the nonlocal parameter, the attached bio-mass and its location was obtained. Results without temperature change are compared with available results of analytical and molecular mechanics. It is found that the influence of thermal effect on the frequency and sensitivity of the biosensor is significant if its length-to-diameter ratio is large. On the other hand, the effect of nonlocal parameter on the frequency and sensitivity of the biosensor increases if its length-to-diameter ratio decreases.

The governing equation of a nanotube-based mass sensor is derived with consideration of surface energy, transverse shear deformation, and rotary inertia. Dependencies of the frequency shift and the sensitivity of the sensor on the attached mass are obtained in closed form. The results show that the traditional model, which neglects the surface energy, predicts a higher attached mass and lower sensitivity of the sensor. On the other hand, neglecting the transverse shear deformation and rotary inertia of the sensor will result in a lower prediction of attached mass and a higher prediction of sensitivity of the sensor. It is also found that the surface energy has no effect on the mode shape of the sensor. However, the effect of the location of the attached mass on the mode shape is significant. In particular, if the attached mass is close to the midpoint of the sensor, the frequency shift and sensitivity become very significant.

Vibration of nanotubes embedded in an elastic matrix is investigated by using the nonlocal Timoshenko beam model. Both a stress gradient and a strain gradient approach are considered. The Hamilton’s principle is adopted to obtain the frequencies of the nanotubes. The dependencies of frequency on the stiffness and mass density of the surrounding elastic matrix, the nonlocal parameter, the transverse shear stiffness and the rotary inertia of the nanotubes are obtained. The results show a significant dependence of frequencies on the surrounding medium and the nonlocal parameter. The frequencies are over-predicted by using the Euler beam model that neglects the shear stiffness and rotary inertia of the nanotubes. It is also found that the lower bound and the upper bound for the frequencies of nanotubes are, respectively, provided by the strain gradient model provides and the stress gradient theory. Explicit formulas for the frequency are obtained and therefore are easy to use by material scientists and engineers for the design of nanotubes and nanotubes based composites.