Showing papers in "Journal of Applied Mechanics in 2019"

Machine Learning-Driven Real-Time Topology Optimization Under Moving Morphable Component-Based Framework

Abstract: In the present work, it is intended to discuss how to achieve real-time structural topology optimization (i.e., obtaining the optimized distribution of a certain amount of material in a prescribed design domain almost instantaneously once the objective/constraint functions and external stimuli/boundary conditions are specified), an ultimate dream pursued by engineers in various disciplines, using machine learning (ML) techniques. To this end, the so-called moving morphable component (MMC)-based explicit framework for topology optimization is adopted for generating training set and supported vector regression (SVR) as well as K-nearest-neighbors (KNN) ML models are employed to establish the mapping between the design parameters characterizing the layout/topology of an optimized structure and the external load. Compared with existing approaches, the proposed approach can not only reduce the training data and the dimension of parameter space substantially, but also has the potential of establishing engineering intuitions on optimized structures corresponding to various external loads through the learning process. Numerical examples provided demonstrate the effectiveness and advantages of the proposed approach.

Metamaterial With Local Resonators Coupled by Negative Stiffness Springs for Enhanced Vibration Suppression

Abstract: In recent years, metamaterials for the applications in low-frequency vibration suppression and noise reduction have attracted numerous research interests. This paper proposes a metamaterial system with local resonators from adjunct unit cells coupled by negative stiffness springs. Frist, a lumped parameter model of the system is developed, and a stability criterion is derived. The band structure of the infinite lattice model is calculated. The result reveals the appearance of extra band gaps in the proposed metamaterial. A parametric study shows that the first extra band gap can be tuned to ultralow frequency by controlling the negative stiffness of the coupling springs. A transmittance analysis of the finite lattice model verifies the predictions obtained from the band structure analysis. Subsequently, the work is extended to a distributed parameter metamaterial beam model with the proposed configuration of coupled local resonators. The stability analysis shows that the infinitely long metamaterial beam becomes unstable as long as the stiffness of the coupling spring becomes negative. For the finitely long metamaterial beam, the stability could be achieved for negative coupling springs of given stiffnesses. The effects of the number of cells and the lattice constant on the system stability are investigated. The transmittance of the finitely long metamaterial beam is calculated. The result shows that due to the restriction on the tunability of negative stiffness for the proposed metamaterial beam, a quasistatic vibration suppression region can only be achieved when the number of cells is small.

Viscoelastic Snapping Metamaterials

Abstract: Mechanical metamaterials are artificial composites with tunable advanced mechanical properties. Particularly, interesting types of mechanical metamaterials are flexible metamaterials, which harness internal rotations and instabilities to exhibit programable deformations. However, to date, such materials have mostly been considered using nearly purely elastic constituents such as neo-Hookean rubbers. Here, we experimentally explore the mechanical snap-through response of metamaterials that are made of constituents that exhibit large viscoelastic relaxation effects, encountered in the vast majority of rubbers, in particular, in 3D printed rubbers. We show that they exhibit a very strong sensitivity to the loading rate. In particular, the mechanical instability is strongly affected beyond a certain loading rate. We rationalize our findings with a compliant mechanism model augmented with viscoelastic interactions, which qualitatively captures well the reported behavior, suggesting that the sensitivity to the loading rate stems from the nonlinear and inhomogeneous deformation rate, provoked by internal rotations. Our findings bring a novel understanding of metamaterials in the dynamical regime and open up avenues for the use of metamaterials for dynamical shape-changing as well as vibration and impact damping applications.

Multistable Cylindrical Mechanical Metastructures: Theoretical and Experimental Studies

Abstract: An innovative bistable energy-absorbing cylindrical shell structure composed of multiple unit cells is presented in this paper. The structural parameters of the single-layer cylindrical shell structure that produces bistable characteristics are expounded both analytically and numerically. The influence of the number of circumferential cells and the size parameters of the cell ligament on the structure’s macroscopic mechanical response was analyzed. A series of cylindrical shell structures with various size parameters were fabricated using a stereolithography apparatus (SLA). Uniaxial loading and unloading experiments were conducted to achieve force–displacement relationships. Deformation of the structural multistable phase transition response was discussed based on experimental and finite element simulation results. The results show that the proposed innovative single-layer cylindrical shell structure will stabilize at two different positions under certain parameters. The multilayer cylindrical shell exhibits different force–displacement response curves under loading and unloading, and these curves enclose a closed area. In addition, this structure can be cyclically loaded and unloaded, thanks to its good stability and reproducibility, making it attractive in applications requiring repetitive energy absorption.

Irregular Hexagonal Cellular Substrate for Stretchable Electronics

Abstract: The existing regular hexagonal cellular substrate for stretchable electronics minimizes the disruptions to the natural diffusive or convective flow of bio-fluids. Its anisotropy is insignificant, which is not ideal for mounting on skins that involve directional stretching. This paper proposes an irregular hexagonal cellular substrate with large anisotropy to minimize the constraints on the natural motion of the skin, and establishes an analytic model to study its stress–strain relation under finite stretching.

Ron Resch Origami Pattern Inspired Energy Absorption Structures

Abstract: Energy absorption structures are widely used in many scenarios. Thin-walled members have been heavily employed to absorb impact energy. This paper presents a novel, Ron Resch origami pattern inspired energy absorption structure. Experimental characterization and numerical simulations were conducted to study the energy absorption of this structure. The results show a new collapse mode in terms of energy absorption featuring multiple plastic hinge lines, which lead to the peak force reduction and larger effective stroke, as compared with the classical honeycomb structure. Overall, the Ron Resch origami-inspired structure and the classical honeycomb structure are quite complementary as energy absorption structures.

Electromechanical Instability of Dielectric Elastomer Actuators With Active and Inactive Electric Regions

Abstract: Electrically driven dielectric elastomers (DEs) suffer from an electromechanical instability (EMI) when the applied potential difference reaches a critical value. A majority of the past investigations address the mechanics of this operational instability by restricting the kinematics to homogeneous deformations. However, a DE membrane comprising both active and inactive electric regions undergoes inhomogeneous deformation, thus necessitating the solution of a complex boundary value problem. This paper reports the numerical and experimental investigation of such DE actuators with a particular emphasis on the EMI in quasistatic mode of actuation. The numerical simulations are performed using an in-house finite element framework developed based on the field theory of deformable dielectrics. Experiments are performed on the commercially available acrylic elastomer (VHB 4910) at varying levels of prestretch and proportions of the active to inactive areas. In particular, two salient features associated with the electromechanical response are addressed: the effect of the flexible boundary constraint and the locus of the dielectric breakdown point. To highlight the influence of the flexible boundary constraint, the estimates of the threshold value of potential difference on the onset of electromechanical instability are compared with the experimental observations and with those obtained using the lumped parameter models reported previously. Additionally, a locus of localized thinning, near the boundary of the active electric region, is identified using the numerical simulations and ascertained through the experimental observations. Finally, an approach based on the Airy stress function is suggested to justify the phenomenon of localized thinning leading to the dielectric breakdown.

Stiffness and Strength of Hexachiral Honeycomb-Like Metamaterials

Abstract: Two-dimensional hexachiral lattices belong to the family of honeycomb-like mechanical metamaterials such as triangular, hexagonal, and kagome lattices. The common feature of this family of beam-based metamaterials is their six-fold rotational symmetry which guarantees their (transversely-) isotropic elastic response. In the case of hexachiral lattices, a single geometric parameter may be introduced to control the degree of chirality such that the elastic Poisson's ratio can be adjusted between 0.33 and −0.8. Detailed finite element simulations are performed to establish the structure–property relationships for hexachiral lattices for relative densities ranging from 1% to 45%. It is shown that both the Young's and shear moduli are always lower for hexachiral structures than for optimal lattices (triangular and kagome). This result is in line with the general understanding that stretching-dominated architectures outperform bending-dominated architectures. The same conclusions may be drawn from the comparison of the tensile yield strength. However, hexachiral structures provide a lower degree of plastic anisotropy than stretching-dominated lattices. Furthermore, special hexachiral configurations have been identified that exhibit a slightly higher shear yield strength than triangular and kagome lattices, thereby presenting an example of bending-dominated architectures outperforming stretching-dominated architectures of equal mass. Tensile specimens have been additively manufactured from a tough PLA polymer and tested to partially validate the simulation results.

Mode I and II Interlaminar Fracture in Laminated Composites: A Size Effect Study

Abstract: This work investigates the mode I and II interlaminar fracturing behavior of laminated composites and the related size effects. Fracture tests on geometrically scaled Double Cantilever Beam (DCB) and End Notch Flexure (ENF) specimens were conducted to understand the nonlinear effects of the cohesive stresses in the Fracture Process Zone (FPZ). The results show a significant difference between the mode I and mode II fracturing behaviors. It is shown that, while the strength of the DCB specimens scales according to the Linear Elastic Fracture Mechanics (LEFM), this is not the case for the ENF specimens. Small specimens exhibit a pronounced pseudo-ductility with limited size effect and a significant deviation from LEFM, whereas larger specimens behave in a more brittle way, with the size effect on nominal strength closer to that predicted by LEFM. This behavior, due to the significant size of the Fracture Process Zone (FPZ) compared to the specimen size, needs to be taken into serious consideration. It is shown that, for the specimen sizes investigated in this work, neglecting the non-linear effects of the FPZ can lead to an underestimation of the fracture energy by as much as 55%, with an error decreasing for increasing specimen sizes. Both the mode I and II test data can be captured very accurately by Bažant's type II Size Effect Law (SEL).

A Simultaneous Multiscale and Multiphysics Model and Numerical Implementation of A Core-Shell Model for Lithium-Ion Full-Cell Batteries

Abstract: The increasing significance on the development of high-performance lithium-ion (Li-ion) batteries is calling for new battery materials, theoretical models, and simulation tools. Lithiation-induced deformation in electrodes calls attention to study the multiphysics coupling between mechanics and electrochemistry. In this paper, a simultaneous multiscale and multiphysics model to study the coupled electrochemistry and mechanics in the continuum battery cell level and the microscale particle level was developed and implemented in comsolmultiphysics. In the continuum scale, the porous electrode theory and the classical mechanics model were applied. In the microscale, the specific particle structure has been incorporated into the model. This model was demonstrated to study the effects of mechanical constraints, charging rate, and silicon/C ratio, on the electrochemical performance. This model provides a powerful tool to perform simultaneous multiscale and multiphysics design on Li-ion batteries, from the particle level to full-cell level.

Tunable Two-Way Unidirectional Acoustic Diodes: Design and Simulation

Abstract: Predeformation simultaneously changes the effective material stiffness as well as the geometric configuration and therefore may be utilized to tune wave propagation in soft phononic crystals (PCs). Moreover, the band gaps of soft PCs, as compared with those of the hard ones, are more sensitive to the external mechanical stimuli. A one-dimensional tunable soft acoustic diode based on soft functionally graded (FG) PCs is proposed. The two-way asymmetric propagation behavior is studied at the resonant frequency within the band gap. Numerical results show that the operating frequency (i.e., the resonant peak) of the soft graded acoustic diode can be altered by adjusting the mechanical biasing fields (including the longitudinal prestress and the lateral equibiaxial tension). The adjustment becomes significant when the strain-stiffening effect of the Gent hyperelastic material is properly harnessed. Furthermore, the prestress or equibiaxial tension can affect the two-way filtering of the soft FG PC in a separate and different manner. In addition, it is much easier to realize the tunable acoustic diode by exploiting soft FG materials with stronger compressibility. It is shown that the introduction of acoustic impedance is beneficial for predicting the tunable effects. The simulations and conclusions should provide a solid guidance for the design of tunable two-way unidirectional acoustic diodes made from soft hyperelastic materials.

Soft Magnetoactive Laminates: Large Deformations, Transverse Elastic Waves and Band Gaps Tunability by a Magnetic Field

Abstract: We investigate the behavior of soft magnetoactive periodic laminates under remotely applied magnetic field. We derive explicit formulae for the induced deformation due to magnetic excitation of the laminates with hyperelastic magnetoactive phases. Next, we obtain the closed-form formulas for the velocities of long transverse waves. We show the dependence of the wave velocity on the applied magnetic intensity and induced strains, as well as on the wave propagation direction. Based on the long wave analysis, we derive closed form formulae for the critical magnetic field corresponding to loss of macroscopic stability. Finally, we analyze the transverse wave band gaps appearing in magnetoactive laminates in direction normal to the layers. We illustrate the band gap tunability – width and position – by magnetically induced deformation.

Multistable Cosine-Curved Dome System for Elastic Energy Dissipation

Abstract: This paper presents a new energy dissipation system composed of multistable cosine-curved domes (CCD) connected in series. The system exhibits multiple consecutive snap-through and snap-back buckling behavior with a hysteretic response. The response of the CCDs is within the elastic regime and hence the system's original configuration is fully recoverable. Numerical studies and experimental tests were conducted on the geometric properties of the individual CCD units and their number in the system to examine the force–displacement and energy dissipation characteristics. Finite element analysis (FEA) was performed to simulate the response of the system to develop a multilinear analytical model for the hysteretic response that considers the nonlinear behavior of the system. The model was used to study the energy dissipation characteristics of the system. Experimental tests on 3D printed specimens were conducted to analyze the system and validate numerical results. Results show that the energy dissipation mainly depends on the number and the apex height-to-thickness ratio of the CCD units. The developed multilinear analytical model yields conservative yet accurate values for the dissipated energy of the system. The proposed system offered reliable high energy dissipation with a maximum loss factor value of 0.14 for a monostable (self-recoverable) system and higher for a bistable system.

Experimental testing of vibration mitigation in 3D printed architected metastructures

Abstract: Band gaps in metamaterials and phononic crystals provide a way to engineer vibration mitigation into a material’s geometry. Here, we present a comprehensive experimental characterization of band gaps in lattice-resonator metastructures, which have been previously analyzed with finite element simulations, to better understand this phenomenon in 3D-printed materials. We fabricate the metastructures with a new approach to obtain multimaterial structures using stereolithography. We experimentally characterize the material’s frequency-dependent storage and loss modulus over the band gap frequencies to confirm that the measured band gaps are due to geometry and not due to material properties. Experimental results using both frequency sweep and impulse excitations show that band gaps and attenuation efficiencies strongly depend on the lattice geometry as well as loading direction, and a comparison between axial and bending excitation responses reveals frequency ranges of “fluid-like” and “optical-like” behaviors. Comparison between finite element simulations and experimental results demonstrate the robustness of the metastructure design. While the experiments used here are well established, their combination allows us to gain additional insights into band gaps measurements. Specifically, we show that the coherence function, a common concept in signal processing, is a strong predictor of band gaps in linear materials and that the attenuation efficiency inside the measured band gap can be physically limited by fluid–structure interactions.

Micropolar Modeling of Auxetic Chiral Lattices With Tunable Internal Rotation

Abstract: Based on micropolar continuum theory, the closed-form stiffness tensor of auxetic chiral lattices with V-shaped wings and rotational joints were derived. Representative volume element (RVE) of the chiral lattice was decomposed into V-shape wings with fourfold symmetry. A unified V-beam finite element was developed to reduce the nodal degrees of freedoms of the RVE to enable closed-form analytical solutions. The elasticity constants were derived as functions of the angle of the V-shaped wings, nondimensional in-plane thickness of the ribs, and the stiffness of the rotational joints. The influences of these parameters on the coupled chiral and auxetic effects were systematically explored. The results show that the elastic moduli were significantly influenced by all three parameters, while Poisson's ratio was barely influenced by the in-plane thickness of the ribs but is sensitive to the angle of the V-shaped wings and the stiffness of the rotational springs. There is a transition region out of which the spring stiffness does not considerably affect the auxeticity and the overall lattice stiffness.

Piezoelectric Energy Harvesting From Roadways Based on Pavement Compatible Package

Abstract: Scavenging mechanical energy from the deformation of roadways using piezoelectric energy transformers has been intensively explored and exhibits a promising potential for engineering applications. We propose here a new packaging method that exploits MC nylon and epoxy resin as the main protective materials for the piezoelectric energy harvesting (PEH) device. Wheel tracking tests are performed, and an electromechanical model is developed to double evaluate the efficiency of the PEH device. Results indicate that reducing the embedded depth of the piezoelectric chips may enhance the output power of the PEH device. A simple scaling law is established to show that the normalized output power of the energy harvesting system relies on two combined parameters, i.e., the normalized electrical resistive load and normalized embedded depth. It suggests that the output power of the system may be maximized by properly selecting the geometrical, material, and circuit parameters in a combined manner. This strategy might also provide a useful guideline for optimization of piezoelectric energy harvesting system in practical roadway applications.

Nonlinear Torsional Vibration Absorber for Flexible Structures

Abstract: A new kind of nonlinear energy sink (NES) is proposed to control the vibration of a flexible structure with simply supported boundaries in the present work. The new kind of absorber is assembled at the end of structures and absorbs energy through the rotation angle at the end of the structure. It is easy to design and attached to the support of flexible structures. The structure and the absorber are coupled just with a nonlinear restoring moment and the damper in the absorber acts on the structure indirectly. In this way, all the linear characters of the flexible structure will not be changed. The system is investigated by a special perturbation method and verified by simulation. Parameters of the absorber are fully discussed to optimize the efficiency of it. For the resonance, the maximum motion is restrained up to 90% by the optimized absorber. For the impulse, the vibration of the structure could attenuate rapidly. In addition to the high efficiency, energy transmits to the absorber uniaxially. For the high efficiency, convenience of installation and the immutability of linear characters, the new kind of rotating absorber provides a very good strategy for the vibration control.

Piezotronic Effect of a Thin Film With Elastic and Piezoelectric Semiconductor Layers Under a Static Flexural Loading

Abstract: We theoretically study the electromechanical behaviors of a laminated thin-film piezoelectric semiconductor (PS) composite plate with flexural deformation. The nonlinear equations for drift currents of electrons and holes are linearized for a small carrier concentration perturbation. Following the structural theory systemized by R. D. Mindlin, a system of two-dimensional (2D) equations for the laminated thin-film PS plate, including the lowest order coupled extensional and flexural motion, are presented by expanding the displacement, potential, and the incremental concentration of electrons and holes as power series of the plate thickness. Based on the derived 2D equations, the analytical expressions of the electromechanical fields and distribution of electrons in the thin-film PS plate with an n-type ZnO layer subjected to a static bending are presented. The numerical results show that the electromechanical behaviors and piezotronic effects can be effectively controlled by the external applied force and initial concentration of carriers. The derived 2D equations and numerical results in this paper are helpful for developing piezotronic devices.

Newmark-Beta Method in Discrete Elastic Rods Algorithm to Avoid Energy Dissipation

Abstract: Discrete elastic rods (DER) algorithm presents a computationally efficient means of simulating the geometrically nonlinear dynamics of elastic rods. However, it can suffer from artificial energy loss during the time integration step. Our approach extends the existing DER technique by using a different time integration scheme—we consider a second-order, implicit Newmark-beta method to avoid energy dissipation. This treatment shows better convergence with time step size, specially when the damping forces are negligible and the structure undergoes vibratory motion. Two demonstrations—a cantilever beam and a helical rod hanging under gravity—are used to show the effectiveness of the modified discrete elastic rods simulator.

Formulation of Statistical Linearization for M-D-O-F Systems Subject to Combined Periodic and Stochastic Excitations

Abstract: A formulation of statistical linearization for multi-degree-of-freedom (M-D-O-F) systems subject to combined mono-frequency periodic and stochastic excitations is presented. The proposed technique is based on coupling the statistical linearization and the harmonic balance concepts. The steady-state system response is expressed as the sum of a periodic (deterministic) component and of a zero-mean stochastic component. Next, the equation of motion leads to a nonlinear vector stochastic ordinary differential equation (ODE) for the zero-mean component of the response. The nonlinear term contains both the zero-mean component and the periodic component, and they are further equivalent to linear elements. Furthermore, due to the presence of the periodic component, these linear elements are approximated by averaging over one period of the excitation. This procedure leads to an equivalent system whose elements depend both on the statistical moments of the zero-mean stochastic component and on the amplitudes of the periodic component of the response. Next, input–output random vibration analysis leads to a set of nonlinear equations involving the preceded amplitudes and statistical moments. This set of equations is supplemented by another set of equations derived by ensuring, in a harmonic balance sense, that the equation of motion of the M-D-O-F system is satisfied after ensemble averaging. Numerical examples of a 2-D-O-F nonlinear system are considered to demonstrate the reliability of the proposed technique by juxtaposing the semi-analytical results with pertinent Monte Carlo simulation data.

Symplectic Analysis of Wrinkles in Elastic Layers with Graded Stiffnesses

Abstract: Wrinkles in layered neo-Hookean structures were recently formulated as a Hamiltonian system by taking the thickness direction as a pseudo-time variable. This enabled an efficient and accurate numerical method to solve the eigenvalue problem for onset wrinkles. Here, we show that wrinkles in graded elastic layers can also be described as a time-varying Hamiltonian system. The connection between wrinkles and the Hamiltonian system is established through an energy method. Within the Hamiltonian framework, the eigenvalue problem of predicting wrinkles is defined by a series of ordinary differential equations with varying coefficients. By modifying the boundary conditions at the top surface, the eigenvalue problem can be efficiently and accurately solved with numerical solvers of boundary value problems. We demonstrated the accuracy of the symplectic analysis by comparing the theoretically predicted displacement eigenfunctions, critical strains, and wavelengths of wrinkles in two typical graded structures with finite element simulations.

Modeling the Large Deformation and Microstructure Evolution of Nonwoven Polymer Fiber Networks

Abstract: The electrospinning process enables the fabrication of randomly distributed nonwoven polymer fiber networks with high surface area and high porosity, making them ideal candidates for multifunctional materials. The mechanics of nonwoven networks has been well established for elastic deformations. However, the mechanical properties of the polymer fibrous networks with large deformation are largely unexplored, while understanding their elastic and plastic mechanical properties at different fiber volume fractions, fiber aspect ratio, and constituent material properties is essential in the design of various polymer fibrous networks. In this paper, a representative volume element (RVE) based finite element model with long fibers is developed to emulate the randomly distributed nonwoven fibrous network microstructure, enabling us to systematically investigate the mechanics and large deformation behavior of random nonwoven networks. The results show that the network volume fraction, the fiber aspect ratio, and the fiber curliness have significant influences on the effective stiffness, effective yield strength, and the postyield behavior of the resulting fiber mats under both tension and shear loads. This study reveals the relation between the macroscopic mechanical behavior and the local randomly distributed network microstructure deformation mechanism of the nonwoven fiber network. The model presented here can also be applied to capture the mechanical behavior of other complex nonwoven network systems, like carbon nanotube networks, biological tissues, and artificial engineering networks.

Mechanics Design for Compatible Deformation of Fractal Serpentine Interconnects in High-Density Stretchable Electronics

Abstract: Inorganic stretchable electronics based on the island-bridge layout have attracted great attention in recent years due to their excellent electrical performance under the extreme condition of large deformations. During the mechanics design of interconnects in such devices, the major task is not only to maximize the elastic stretchability of device but also to smoothen the whole deformation process of interconnects. In this work, a novel design strategy is proposed for free-standing fractal serpentine interconnects to improve their elastic performance comprehensively without reducing the areal coverage of functional/active components of device. By modifying the classical design slightly, the new strategy can achieve a larger elastic stretchability, a smaller maximum out-of-plane displacement, and most strikingly, a smoother post-buckling deformation. This study will provide helpful guidance to the mechanics design of stretchable electronics with free-standing interconnects.

Development of damage-tolerant and fracture-resistant materials by utilizing the material inhomogeneity effect

Abstract: The improvement of fracture strength by insertion of thin, soft interlayers is a strategy observed in biological materials such as deep-see sponges. The basic mechanism is a reduction of the crack driving force due to the spatial variation of yield strength and/or Young's modulus. The application of this “material inhomogeneity effect” is demonstrated in this paper. The effectiveness of various interlayer configurations is investigated by numerical simulations under application of the configurational force concept. Laminated composites, made of high-strength tool steels as matrix materials and low-strength deep-drawing steel as interlayer material, were manufactured by hot press bonding. The number of interlayers and the interlayer thickness were varied. Fracture mechanics experiments show crack arrest in the first interlayer and significant improvements in fracture toughness, even without the occurrence of other toughening mechanisms, such as interface delamination. The application of the material inhomogeneity effect for different types of matrix materials is discussed.

Experimentally and Numerically Validated Analytical Solutions to Nonbuckling Piezoelectric Serpentine Ribbons

Abstract: Emerging stretchable piezoelectric devices have added exciting sensing and energy harvesting capabilities to wearable and implantable soft electronics. As conventional piezoelectric materials are intrinsically stiff and some are even brittle, out-of-plane wrinkled or buckled structures and in-plane serpentine ribbons have been introduced to enhance their compliance and stretchability. Among those stretchable structures, in-plane piezoelectric serpentine ribbons (PSRs) are preferred on account of their manufacturability and low profiles. To elucidate the trade-off between compliance and sensitivity of PSRs of various shapes, we herein report a theoretical framework by combining the piezoelectric plate theory with our previously developed elasticity solutions for passive serpentine ribbons without piezoelectric property. The electric displacement field and the output voltage of a freestanding but nonbuckling PSR under uniaxial stretch can be analytically solved under linear assumptions. Our analytical solutions were validated by finite element modeling (FEM) and experiments using polyvinylidene fluoride (PVDF)-based PSR. In addition to freestanding PSRs, PSRs sandwiched by polymer layers were also investigated by FEM and experiments. We found that thicker and stiffer polymers reduce the stretchability but enhance the voltage output of PSRs. When the matrix is much softer than the piezoelectric material, our analytical solutions to a freestanding PSR are also applicable to the sandwiched ones.

Tunable Adhesion of a Bio-Inspired Micropillar Arrayed Surface Actuated by a Magnetic Field

Abstract: Bio-inspired functional surfaces attract many research interests due to the promising applications. In this paper, tunable adhesion of a bio-inspired micropillar arrayed surface actuated by a magnetic field is investigated theoretically in order to disclose the mechanical mechanism of changeable adhesion and the influencing factors. Each polydimethylsiloxane (PDMS) micropillar reinforced by uniformly distributed magnetic particles is assumed to be a cantilever beam. The beam's large elastic deformation is obtained under an externally magnetic field. Specially, the rotation angle of the pillar's end is predicted, which shows an essential effect on the changeable adhesion of the micropillar arrayed surface. The larger the strength of the applied magnetic field, the larger the rotation angle of the pillar's end will be, yielding a decreasing adhesion force of the micropillar arrayed surface. The difference of adhesion force tuned by the applied magnetic field can be a few orders of magnitude, which leads to controllable adhesion of such a micropillar arrayed surface. Influences of each pillar's cross section shape, size, intervals between neighboring pillars, and the distribution pattern on the adhesion force are further analyzed. The theoretical predictions are qualitatively well consistent with the experimental measurements. The present theoretical results should be helpful not only for the understanding of mechanical mechanism of tunable adhesion of micropillar arrayed surface under a magnetic field but also for further precise and optimal design of such an adhesion-controllable bio-inspired surface in future practical applications.

Broadband Vibration Isolation for Rods and Beams Using Periodic Structure Theory

Abstract: The alternating stop-band characteristics of periodic structures have been widely used for narrow band vibration control applications. The objective of this work is to extend this idea for broadband excitations. Toward this end, we seek to synthesize a longitudinal and a flexural periodic structure having the largest fraction of the frequencies falling in the attenuation bands of the structure. Such a periodic structure when subjected to broadband excitation has minimal transmission of the response away from the source of excitation. The unit cell of such a periodic structure is constituted of two distinct regions having different inertial and stiffness properties. We derive guidelines for suitable selection of inertial and stiffness properties of the two regions in the unit cell such that the maximal frequency region corresponds to attenuation bands of the periodic structure. It is found that maximal dissimilarity between the neighboring regions of the unit cell leads to maximal attenuating frequencies. In the extreme case, it is found that more than 98% of the frequencies are blocked. For seismic excitations, it is shown that large, finite periodic structures corresponding to the optimal unit cell derived using the infinite periodic structure theory has significant vibration isolation benefits in comparison to a homogeneous structure or an arbitrarily chosen periodic structure.

A refined JKR-model for adhesion of a rigid sphere on a soft elastic substrate

Abstract: Surface energy outside the contact zone, which is ignored in the classical Johnson–Kendall–Roberts (JKR) model, can play an essential role in adhesion mechanics of soft bodies. In this work, based on a simple elastic foundation model for a soft elastic half space with constant surface tension, an explicit expression for the change of surface energy outside the contact zone is proposed for a soft elastic substrate indented by a rigid sphere in terms of two JKR-type variables (δ, a), where a is the radius of the contact zone and δ is the indentation depth of the rigid sphere. The derived expression is added to the classical JKR model to achieve two explicit equations for the determination of the two JKR variables (δ, a). The results given by the present model are demonstrated with detailed comparison with known results reported in recent literature, which verified the validity and robust accuracy of the present method. In particular, the present model confirms that the change of surface energy of the substrate can play an essential role in micro/nanoscale contact of soft materials (defined by W/(E*R)≥0.1, where W is the adhesive energy, E* is the substrate elasticity, and R is the rigid sphere radius). The present model offers a simpler analytical method for adhesion mechanics of a rigid sphere on a soft elastic substrate when compared with several existing methods proposed in recent literature that request more substantial numerical calculations.

Nudging axially compressed cylindrical panels towards imperfection insensitivity

Abstract: Curved shell structures are known for their excellent load-carrying capability and are commonly used in thin-walled constructions. Although theoretically able to withstand greater buckling loads than flat structures, shell structures are notoriously sensitive to imperfections owing to their postbuckling behavior often being governed by subcritical bifurcations. Thus, shell structures often buckle at significantly lower loads than those predicted numerically and the ensuing dynamic snap to another equilibrium can lead to permanent damage. Furthermore, the strong sensitivity to initial imperfections, as well as their stochastic nature, limits the predictive capability of current stability analyses. Our objective here is to convert the subcritical nature of the buckling event to a supercritical one, thereby improving the reliability of numerical predictions and mitigating the possibility of catastrophic failure. We explore the elastically nonlinear postbuckling response of axially compressed cylindrical panels using numerical continuation techniques. These analyses show that axially compressed panels exhibit a highly nonlinear and complex postbuckling behavior with many entangled postbuckled equilibrium curves. We unveil isolated regions of stable equilibria in otherwise unstable postbuckled regimes, which often possess greater load-carrying capacity. By modifying the initial geometry of the panel in a targeted—rather than stochastic—and imperceptible manner, the postbuckling behavior of these shells can be tailored without a significant increase in mass. These findings provide new insight into the buckling and postbuckling behavior of shell structures and opportunities for modifying and controlling their postbuckling response for enhanced efficiency and functionality.

A Bayesian framework to identify random parameter fields based on the copula theorem and Gaussian fields: Application to polycrystalline materials

Abstract: For many models of solids, we frequently assume that the material parameters do not vary in space nor that they vary from one product realization to another. If the length scale of the application approaches the length scale of the microstructure however, spatially fluctuating parameter fields (which vary from one realization of the field to another) can be incorporated to make the model capture the stochasticity of the underlying micro-structure. Randomly fluctuating parameter fields are often described as Gaussian fields. Gaussian fields, however, assume that the probability density function of a material parameter at a given location is a univariate Gaussian distribution. This entails for instance that negative parameter values can be realized, whereas most material parameters have physical bounds (e.g., Young’s modulus cannot be negative). In this contribution, randomly fluctuating parameter fields are therefore described using the copula theorem and Gaussian fields, which allow different types of univariate marginal distributions to be incorporated but with the same correlation structure as Gaussian fields. It is convenient to keep the Gaussian correlation structure, as it allows us to draw samples from Gaussian fields and transform them into the new random fields. The benefit of this approach is that any type of univariate marginal distribution can be incorporated. If the selected univariate marginal distribution has bounds, unphysical material parameter values will never be realized. We then use Bayesian inference to identify the distribution parameters (which govern the random field). Bayesian inference regards the parameters that are to be identified as random variables and requires a user-defined prior distribution of the parameters to which the observations are inferred. For homogenized Young’s modulus of a columnar polycrystalline material of interest in this study, the results show that with a relatively wide prior (i.e., a prior distribution without strong assumptions), a single specimen is sufficient to accurately recover the distribution parameter values.