Accepted Manuscripts

A B M Tahidul Haque, Ratiba F. Ghachi, Wael I. Alnahhal, Amjad Aref and Jongmin Shim
J. Appl. Mech   doi: 10.1115/1.4039039
In order to design phononic crystals whose band-gaps are located in low-frequency ranges, researchers commonly adopt low stiffness polymeric materials as a key constituent and exploit the high impedance mismatch between metals and polymers. However, there has been very little research on wave propagation at arbitrary angles in the sagittal plane of viscoelastic-elastic multilayered composites because there exist the intricate wave attenuation characteristics at the layer interfaces. This study analytically investigates wave propagation at oblique angles within alternating viscoelastic-elastic layered composites, where the attenuation of harmonic plane waves is found to occur only in the direction perpendicular to the layers. By using this wave propagation characteristic, we directly apply the semi-analytical approach employed in elastic multilayered composites to calculate the dispersion relation of sagittal plane waves in alternating viscoelastic-elastic multilayered composites. Specifically, we consider a bilayered composite composed of alternating aluminum and polyurethane elastomer, whose complex-valued viscoelastic moduli are experimentally determined by performing dynamic mechanical analysis. The analysis shows that the alternating viscoelastic-elastic layered composite does not possess a phononic band-gap regardless of incident angles. In addition, wave motions at oblique angles are found to travel with a wide range of frequency contents compared to wave motions perpendicular to the layers. The presented analysis demonstrates that wave dispersion relation in viscoelastic-elastic layered composites is distinctively different from the corresponding elastic counterpart, and highlights the importance of the viscoelastic modeling of polymeric materials in wave dispersion analysis.
TOPICS: Solids, Composite materials, Waves, Wave propagation, Energy gap, Dispersion (Optics), Dispersion relations, Design, Modeling, Polymers, Elastomers, Urethane elastomers, Metals, Aluminum, Phononic crystals, Stiffness
Fan Jin, Xu Guo and Qiang Wan
J. Appl. Mech   doi: 10.1115/1.4039040
A systematic study is performed on the plane contact and adhesion of two elastic solids with an interface groove. The non-adhesion and JKR adhesion solutions for a typical groove shape are obtained in closed-form by solving singular integral equations and using energy release rate approaches. It is found that the JKR adhesion solution depends solely on a dimensionless parameter a and the groove is predicted to be unstably flattened with no applied load when a=0.535. Furthermore, the corresponding Maugis-Dugdale adhesion model has been revisited with three possible equilibrium states. By introducing the classical Tabor parameter µ, a complete transition between the non-adhesion and the JKR adhesion contact models is captured, which can be recovered as two limiting cases of the Maugis-Dugdale model. Depending on two non-dimensional parameters a and µ, where a^2 represents the ratio of the surface energy in the groove to the elastic strain energy when the grooved surface is flattened, different transition processes among three equilibrium states are characterized by one or more jumps between partial and full contact. Larger values of a and µ tend to induce more energy loss due to adhesion hysteresis. Combination values of a and µ are also suggested to design self-healing interface grooves due to adhesion.
TOPICS: Solids, Adhesion, Equilibrium (Physics), Surface energy, Design, Integral equations, Shapes, Stress, Energy dissipation
Dani Liu, Bahareh Shakibajahromi, Genevieve Dion, David Breen and Antonios Kontsos
J. Appl. Mech   doi: 10.1115/1.4039046
The mechanical behavior of knitted textiles is simulated using finite element analysis. Given the strong coupling between geometrical and physical aspects that affect the behavior of this type of engineering materials, there are several challenges associated with the development of computa-tional tools capable to enable physics-based predictions, while keeping the associated computa-tional cost appropriate for use within design optimization processes. In this context, this article investigates the relative contribution of a number of computational factors to both local and global mechanical behavior of knitted textiles. Specifically, different yarn-to-yarn interaction definitions in three-dimensional finite element models are compared to explore their relative in-fluence on kinematic features of knitted textiles mechanical behavior. The relative motion be-tween yarns identified by direct numerical simulations is then used to construct reduced order models, which are shown to be computationally more efficient and providing comparable predic-tions of the mechanical performance of knitted textiles that include interfacial effects between yarns.
TOPICS: Textiles, Mechanical behavior, Yarns, Equipment performance, Fluence (Radiation measurement), Design, Finite element analysis, Computer simulation, Physics, Kinematics, Optimization, Finite element model
Refael Fadida, Amnon Shirizly and Daniel Rittel
J. Appl. Mech   doi: 10.1115/1.4039048
The dynamic tensile response of additively manufactured (AM) dense and porous Ti6Al4V specimens was investigated under quasi-static and dynamic tension. The porous specimens contained single embedded spherical pores of different diameters. Such artificial spherical pores can mimic the behavior of realistic flaws in the material. It was found that beyond a certain pore diameter (Ø600 µm) the failure is determined according to the pore location, characterized by an abrupt failure and a significant decrease of ductility, while below that diameter, necking and fracture do not occur at the pore. The dynamic tensile mechanical behavior of the additively manufactured dense material was found to be similar to that of the conventional equivalent material, but the ductility to failure of the latter is observed to be higher.
TOPICS: Ductility, Fracture (Materials), Fracture (Process), Mechanical behavior, Failure, Necking, Tension
Hasan B. Al Ba'ba'a, Mohammad Ali Attarzadeh and Mostafa Nouh
J. Appl. Mech   doi: 10.1115/1.4039042
Elastic metamaterials utilize locally resonant mechanical elements to onset band gap characteristics that are typically exploited in vibration suppression and isolation applications. The present work employs a comprehensive structural intensity analysis (SIA) to depict the structural power distribution and variations associated with band gap frequency ranges, as well as outside them along both dimensions of a 2D metamaterial. Following a brief theoretical dispersion analysis, the actual mechanics of a finite metamaterial plate undergoing flexural loading and consisting of a square array of 100 cells are examined experimentally using a fabricated prototype. Scanning Laser Doppler Vibrometer (SLDV) tests are carried out to experimentally measure the deformations of the metamaterial in response to base excitations within a broad frequency range. In addition to confirming the attenuation and blocked propagation of elastic waves throughout the elastic medium via graphical visualizations of power flow maps, the SIA reveals interesting observations which give additional insights into energy flow and transmission in elastic metamaterials as a result of the local resonance effects. A drastic reduction in power flow magnitudes to the bulk regions of the plate within a band gap is noticeably met with a large amplification of structural intensity around and in the neighborhood of the excitation source as a compensatory effect. Finally, the theoretical and experimentally measured streamlines of power flow are presented as an alternative tool to predict the structural power patterns and track vortices and confined regions of energy concentrations in a manner that is analogous to potential flow in fluid mechanics.
TOPICS: Resonance, Metamaterials, Flow (Dynamics), Energy gap, Excitation, Laser Doppler vibrometers, Fluid mechanics, Deformation, Dimensions, Elastic waves, Engineering prototypes, Vibration suppression, Visualization, Vortices
Tengfei Shi, Yang Liu, Nannan Wang and Caishan Liu
J. Appl. Mech   doi: 10.1115/1.4039047
This paper studies a new comprehensive model for toppling dynamics of regularly spaced dominoes in an array. The model has unlocked the hypotheses introduced by Stronge and Shu [1], which can provide us some essential insights into the mechanism of domino wave. Extensive comparisons are made between the proposed model and the experimental results studied in existing literature. Our numerical studies show that the existing theoretical models are special cases of the proposed model, and the fluctuation in the waveform of propagation speed observed from experiments was caused by the irregular multiple impacts between colliding dominoes. Influence of physical parameters of domino on the natural speed of toppling dominoes is also considered, and it is found that the coefficients of friction and restitution between colliding dominoes have more effects due to the energy dissipation during impact.
TOPICS: Dynamics (Mechanics), Friction, Waves, Energy dissipation
Zhi-Qiao Wang and Emmanuel Detournay
J. Appl. Mech   doi: 10.1115/1.4039044
This paper investigates the tip region of a hydraulic fracture propagating near a free-surface via the related problem of the steady fluid-driven peeling of a thin elastic layer from a rigid substrate. The solution of this problem requires accounting for the existence of a fluid lag, as the pressure singularity that would otherwise exist? at the crack tip is incompatible with the underlying linear beam theory governing the deflection of the thin layer. These considerations lead to the formulation of a nonlinear traveling wave problem with a free boundary, which is solved numerically. The scaled solution depends only on one number K, which has the meaning of a dimensionless toughness. The asymptotic viscosity- and toughness-dominated regimes, respectively corresponding to small and large K, represent the end members of a family of solutions. It is shown that the far-field curvature can be interpreted as an apparent toughness, which is a universal function of K. In the viscosity regime, the apparent toughness is amplified compared to the toughness as it is inversely proportional to K, while in the toughness regime it is equal to K. By noting that the apparent toughness represents an intermediate asymptote under certain conditions, the obtention of time-dependent solutions for propagating near-surface hydraulic fractures can be greatly simplified. Indeed, any such solutions can be constructed by a matched asymptotics approach, with the outer solution corresponding to a uniformly pressurized fracture and the inner solution to the tip solution derived in this paper.
TOPICS: Fracture (Materials), Fracture (Process), Fracture toughness, Fluids, Viscosity, Deflection, Euler-Bernoulli beam theory, Traveling waves, Accounting, Pressure
Chen Huang, Zuguang Bian, Chengfeng Fang, Xiaoliang Zhou and Jizhou Song
J. Appl. Mech   doi: 10.1115/1.4039041
Polydimethylsiloxane (PDMS) is extensively used in clinical flexible electronics, due to its biocompatibility and stability. When it is employed in a stretchable epidermal sensor for long-term monitoring, PDMS must have open pores within it to assure the sweat penetration. In present paper, we focus on the mechanical properties of porous PDMS with different volume porosities at different temperatures. The emulsion polymerization technique is applied to fabricate porous PDMS. By controlling the ratio of water to PDMS prepolymer, different porosities of PDMS were obtained, and elastic moduli of such porous PDMS were measured in experiment. Results indicate that the elastic modulus increases non-linearly as its temperature rises from 0? to 40? (a temperature range frequently encountered in clinical applications). Meanwhile, an asymptotic homogenization method is employed to theoretically predict the elastic modulus and Poisson's ratio of porous PDMS, whose reliability is testified by comparing the results with experimentally measured data. Further theoretical discussions on mechanical properties are carried out, and results show that the pore size of porous PDMS has almost no effect on the elastic modulus and Poisson's ratio for certain porosities. Porosity of porous PDMS, however, has significant effect on both of these two mechanical parameters. Two fitted nonlinear formulas are then proposed to estimate the elastic modulus and Poisson's ratio of porous PDMS for any volume porosity less than 50%. All the results in present paper are essential for mechanical design and optimization of clinical flexible electronics based on porous PDMS.
TOPICS: Plasma desorption mass spectrometry, Mechanical properties, Elastic moduli, Poisson ratio, Temperature, Flexible electronics, Porosity, Water, Biocompatibility, Polymerization, Stability, Sensors, Reliability, Emulsions, Design engineering, Optimization
Technical Brief  
Bijoy Pal and Syed Nizamuddin Khaderi
J. Appl. Mech   doi: 10.1115/1.4038965
The idealized inverse-opal lattice is a network of slender struts that has cubic symmetry. We analytically investigate the elasto-plastic properties of the idealized inverse-opal lattice. The analysis reveals that the inverse-opal lattice is bending-dominated under all loadings, except under pure hydrostatic compression or tension. Under hydrostatic loading, the lattice exhibits a stretching dominated behavior. Interestingly, for this lattice Young's modulus and shear modulus are equal in magnitude. The analytical estimates for the elastic constants and yield behavior are validated by performing unit-cell finite element simulations. The hydrostatic buckling response of the idealized inverse-opal lattice is also investigated using the Floquet-Bloch wave method.
TOPICS: Hydrostatics, Simulation, Waves, Mechanical properties, Engineering simulation, Finite element analysis, Buckling, Compression, Elastic constants, Shear modulus, Tension, Young's modulus
Amir Nasrollahi, Piervincenzo Rizzo and Mehmet Sefa Orak
J. Appl. Mech   doi: 10.1115/1.4038990
This paper discusses the dynamic interaction between a monoatomic chain of solid spheres and a thin-walled spherical pressure vessel. The objective is to find a relationship between the highly nonlinear solitary waves (HNSWs) propagating within the chain and the internal pressure of the vessel. The study introduces first a general finite element model to predict the abovementioned interaction, and then a specific application to tennis balls. The scope is to demonstrate a new nondestructive testing method to infer the internal pressure of the balls. The overarching idea is that a mechanically induced solitary pulse propagating within the chain interacts with the thin-walled ball to be probed. At the chain-ball interface, the acoustic pulse is partially reflected back to the chain and partially deforms the rubber giving rise to secondary pulses. The research hypothesis is that one or more features of the reflected waves are monotonically dependent on the internal pressure. The model is validated experimentally by testing commercial balls of different characteristics. Both numerical and experimental results demonstrate a monotonic relationship between the time-of-flight of the solitary waves and the internal pressure of the tennis balls. In addition, the pressure inferred nondestructively with the HNSWs matches very well the pressure measured destructively with an ad-hoc pressure gauge needle. In the future, the results presented in this study could be used to develop a portable device to infer anytime anywhere the internal pressure of deformable systems for which conventional pressure gages cannot be used noninvasively.
TOPICS: Waves, Pressure, Chain, Testing, Finite element model, needles, Vessels, Flight, Pressure gages, Acoustics, Rubber, Pressure vessels, Nondestructive evaluation, Vacuum gages
Yue Mei and Sevan Goenezen
J. Appl. Mech   doi: 10.1115/1.4038966
We present a non-destructive approach to map the heterogeneous viscoelastic moduli from time harmonic motion via a constrained optimization strategy under the framework of finite element techniques. The adjoint equations are carefully derived to determine the gradient of the objective function with respect to the viscoelastic moduli. The feasibility of this inverse scheme is tested with simulated experiments under various driving frequencies. We observe that the overall strategy results in well reconstructed moduli, however for low frequencies, the mapped loss modulus is of inferior quality. To explain this observation, we analyze two simple one dimensional models theoretically. The analysis reveals that the known displacement amplitude is insensitive to the loss modulus value at low frequencies. Thus, we conclude that the inverse algorithm is incapable of finding a well reconstructed loss modulus distribution for low driving frequencies in the presence of noisy data. Overall, the inverse algorithms presented in this work are highly robust to map the storage and loss modulus with high accuracy given that the right range of frequencies are utilized.
TOPICS: Solids, Viscoelasticity, Harmonic motion, Algorithms, Finite element analysis, Optimization, Displacement, Storage
Chiara Ceccato, Xinwei Zhou, Daniele Pelessone and Gianluca Cusatis
J. Appl. Mech   doi: 10.1115/1.4038967
The application of explicit dynamics to simulate quasi-static events often becomes impractical in terms of computational cost. Different solutions have been investigated in the literature to decrease the simulation time and a family of interesting, increasingly adopted approaches, are the ones based on the Proper Orthogonal Decomposition (POD) as a model reduction technique. In this study, the algorithmic framework for the integration of the equation of motions through POD is proposed for discrete linear and nonlinear systems: a low dimensional approximation of the full order system is generated by the so called Proper Orthogonal Modes (POM), computed with snapshots from the full order simulation. Aiming to a predictive tool, the POMs are updated \emph{in itinere} alternating the integration in the complete system, for the snapshots collection, with the integration in the reduced system. The paper discusses details of the transition between the two systems and issues related to the application of essential and natural boundary conditions. Results show that, for one dimensional cases, just few modes are capable of excellent approximation of the solution, even in the case stress-strain softening behavior, allowing to conveniently increase the critical time step of the simulation without significant loss in accuracy. For more general three dimensional situations, the paper discusses the application of the developed algorithm to a discrete model formulated to simulate quasi-brittle materials characterized by a softening response. Efficiency and accuracy of the reduced order LDPM response are discussed with reference to both tensile and compressive loading conditions.
TOPICS: Discrete systems, Principal component analysis, Simulation, Approximation, Boundary-value problems, Dynamics (Mechanics), Brittleness, Stress, Algorithms, Nonlinear systems
Feng Deng, Qian Deng and Shengping Shen
J. Appl. Mech   doi: 10.1115/1.4038919
Flexoelectric effect is a universal and size dependent electromechanical coupling between the strain gradient and electric field. The mathematical framework for flexoelectricity, which involves higher order gradients of field quantities, is difficult to handle using traditional finite element method. Thus, it is important to develop an effective numerical method for flexoelectricity. In this paper, we develop a 3D mixed finite element considering both flexoelectricity and strain gradient elasticity. To validate the developed element, we simulate the electromechanical behavior of a flexoelectric spherical shell subjected to inner pressure and compare the numerical results to analytical results. Their excellent agreement shows the reliability of the proposed finite element method. The developed finite element is also used to simulate the electromechanical behavior of a nanometer sized flexoelectric truncated pyramid. By decreasing the sample size, we observed the increase of its effective piezoelectricity. However, due to the effects of strain gradient elasticity and the influence of flexoelectricity on stiffness, the dependency of effective piezoelectricity on the sample size is not trivial. Numerical results indicate that, when the sample size is smaller than a certain value, the increase of effective piezoelectricity slows down. This finding also shows the importance of a numerical tool for the study of flexoelectric problems.
TOPICS: Finite element analysis, Piezoelectricity, Strain gradient, Electromechanical effects, Elasticity, Finite element methods, Pressure, Numerical analysis, Electric fields, Reliability, Spherical shells, Stiffness
Ming Hu, Yrjo Huang, Fei Wang and Martin Foss
J. Appl. Mech   doi: 10.1115/1.4038920
Coefficients of restitution (CoR) is used to scale the kinetic energy dissipation, which is a necessary parameter for discrete element modelling (DEM) simulations of granular flow. Different from the collision of spherical particles, CoR of spheroid particle is not only affected by materials, particle size and impacting velocity, but the contact inclination angle of the particle, as well. This article presents our experimental investigation to measure the velocities of translation and rotation using high-speed camera and calculate the CoR of prolate spheroid particles impacting on flat targets. The results show that the CoR of a prolate spheroid particle is composed of two parts, translation and rotation. The effect from the contact inclination angle is not obvious for a given velocity. When the contact point is close to a pole, the first part plays a major role. On the contrary, the second part dominates the CoR, when the contact point is close to the equator. A dimensionless number, e*, is defined to scale the proportion of velocity due to rotation in the total reflect velocity at the contact point. The relationship between the contact inclination angle, \phi, and e* for 25^o< \phi < 90^o is given in this article.
TOPICS: Particulate matter, Rotation, Flow (Dynamics), Kinetic energy, Simulation, Poles (Building), Collisions (Physics), Energy dissipation, Engineering simulation, Modeling, Discrete element methods, Particle size, Dimensionless numbers
Wei Wang and Xinming Qiu
J. Appl. Mech   doi: 10.1115/1.4038921
In this study, the plastic deformation mechanism of a fully clamped beam under oblique loading at its free end is analyzed. Supposing the cross-sections are variable along the beam length, a characteristic length L*=Mp/ Np, defined as the ratio of fully plastic bending moment Mp divide fully compression force Np, is employed to estimate the load carrying capacity of each cross-section of the beam. By FE simulations of the conical tubes, it is validated that if the initial failure positon locates in the middle of the beam, it will not change with the total beam length. Then, based on the analytical analysis and FE simulation, a progressive deformation mechanism triggered by bending, notated as progressive bending, is proposed for the first time. From the optimization result of maximum loading force that the unit mass can withstand, the tubes with constant thickness are found to be better than tubes with graded thickness, when they are using as supporting structures. The multi-objective optimization for tubes with varying cross-sections under oblique loading with different angles. Then, two methods to improve the load carrying capacity of tubes are given: 1) to strengthen the weakest point of the tube, which is corresponding to the minimum load withstood; 2) to optimize the initial failure point, so as to produce repeated failure modes. Besides, it is found that the loading capacity of a tube will be best, if the critical loading force of all the cross-sections are equal.
TOPICS: Deformation, Simulation, Stress, Cross section (Physics), Load bearing capacity, Failure mechanisms, Optimization, Compression, Failure, Pareto optimization
Konik Kothari, yuhang hu, Sahil Gupta and Ahmed Elbanna
J. Appl. Mech   doi: 10.1115/1.4038883
The skeleton of many natural and artificial soft materials can be abstracted as networks of fibers/ polymers interacting in a non-linear fashion. Here, we present a numerical model for networks of nonlinear, elastic polymer chains with rate-dependent crosslinkers similar to what is found in gels. The model combines the worm-like chain at the polymer level with the transition state theory for crosslinker bond dynamics. We study the damage evolution and the force-displacement response of these networks under uniaxial stretching for different loading rates, network topology, and crosslinking density. Our results suggest a complex non-monotonic response as the loading rate or the crosslinking density increases. We discuss this in terms of the microscopic deformation mechanisms and suggest a novel framework for increasing toughness and ductility of polymer networks using a bio-inspired Sacrificial Bonds and Hidden Length (SBHL) mechanism. This work highlights the role of local network characteristics on macroscopic mechanical observables and opens new pathways for designing tough polymer networks.
TOPICS: Polymers, Topology, Damage, Fracture toughness, Chain, Density, Dynamics (Mechanics), Deformation, Fibers, Computer simulation, Elastomers, Ductility, Design, Biomimetics, Displacement

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