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Electrical computers have revolutionized society over the past several decades, but questions have remained about their ability to perform in extreme environments, such as their stability at high-temperature conditions. This has motivated the recent surge of interest in developing mechanical computing platforms at all length scales, including the nanoscale, in which traditional electrical computers are augmented with mechanical ones. However, the most proposed nanomechanical bits are volatile memory bits based on the dynamic response of nanomechanical resonators, and as such, there is a need to develop robust and reprogrammable entirely non-volatile nanomechanical bits. Here, we exploit the multiple quasi-stable configurations of the graphene/fullerene/graphene (GFG) van der Waals heterostructure to work as a novel nonvolatile nanomechanical bit. The GFG heterostructure is unique and robust in that it can return to its initial state without further mechanical input, it can be used for logic functions at relevant operating temperatures through simple application of uniaxial strain, it can exhibit reprogrammability between five basic logic gates (NOT, AND, NAND, OR, NOR) by varying the magnitude or direction of applied strain, and it can be used to represent combinatorial logic through full and half adders. These findings provide a new opportunity to develop mechanical computers based on the large class of nanomaterials. [ABSTRACT FROM AUTHOR]

Soft matter mechanics generally involve finite deformations and instabilities of structures in response to a wide range of mechanical and non-mechanical stimuli. Modeling plates and shells is generally a challenge due to their geometrically nonlinear response to loads; however, non-mechanical loads further complicate matters as it is often not clear how they modify the shell's energy functional. In this work, we demonstrate how to form a mechanical interpretation of these non-mechanical stimuli, in which the standard shell strain energy can be augmented with potentials corresponding to how a non-mechanical stimulus acts to change the shell's area and curvature via the natural stretch and curvature. As a result, the effect of non-mechanical stimuli to deform shells is transformed into effective external loadings, and this framework allows for the application of analytical and computational tools that are standard within the mechanics community. Furthermore, we generalize the effect of mass change during biological growth to account for its effect on the stress constitution. The theory is formulated based on a standard, stress-free reference configuration which is known a priori, meaning it can be physically observed, and only requires the solution of a single-field equation, the standard mechanical momentum or equilibrium equation, despite capturing the effects of non-mechanical stimuli. We validate the performance of this model by several benchmark problems, and finally, we apply it to complex examples, including the snapping of the Venus flytrap, leaf growth, and the buckling of electrically active polymer plates. Overall, we expect that mechanicians and non-mechanicians alike can use the approach presented here to quickly modify existing computational tools with effective external loadings calculated in this novel theory to study how various types of non-mechanical stimuli impact the mechanics and physics of thin shell structures. [ABSTRACT FROM AUTHOR]

The field of topological mechanics has recently emerged due to the interest in robustly transporting various types of energy in a flaw and defect-insensitive fashion. While there have been a significant number of studies based on discovering and proposing topological materials and structures, very few have focused on tuning the resulting topological bandgaps, which is critical because the bandgap frequency is fixed once the structure has been fabricated. Here, we perform both lattice dynamical calculations and molecular dynamical simulations to investigate strain effects on the phononic topological bandgaps in two-dimensional monolayer hexagonal boron nitride. Our studies demonstrate that while the topologically protected phononic bandgaps are not closed even for severely deformed hexagonal boron nitride and are relatively insensitive to uniaxial tension and shear strains, the position of the frequency gap can be efficiently tuned in a wide range through the application of biaxial strains. Overall, this work thus demonstrates that topological phonons are robust against the effects of mechanical strain engineering and shed light on the tunability of the topological bandgaps in nanomaterials. [ABSTRACT FROM AUTHOR]

The Lennard-Jones potential is widely used to describe the interlayer interactions within layered materials like graphene. However, it is also widely known that this potential strongly underestimates the frictional properties for layered materials. Here, we propose to supplement the Lennard-Jones potential by a Gaussian-type potential, which enables more accurate calculations of the frictional properties of two-dimensional layered materials. Furthermore, the Gaussian potential is computationally simple as it introduces only one additional potential parameter that is determined by the interlayer shear mode in the layered structure. The resulting Lennard-Jones-Gaussian potential is applied to compute the interlayer cohesive energy and frictional energy for graphene, MoS2, black phosphorus, and their heterostructures. [ABSTRACT FROM AUTHOR]

We present a parameterization of the Stillinger-Weber potential to describe the interatomic interactions within single-layer MoS2 (SLMoS2). The potential parameters are fitted to an experimentally obtained phonon spectrum, and the resulting empirical potential provides a good description for the energy gap and the crossover in the phonon spectrum. Using this potential, we perform classical molecular dynamics simulations to study chirality, size, and strain effects on the Young's modulus and the thermal conductivity of SLMoS2. We demonstrate the importance of the free edges on the mechanical and thermal properties of SLMoS2 nanoribbons. Specifically, while edge effects are found to reduce the Young's modulus of SLMoS2 nanoribbons, the free edges also reduce the thermal stability of SLMoS2 nanoribbons, which may induce melting well below the bulk melt temperature. Finally, uniaxial strain is found to efficiently manipulate the thermal conductivity of infinite, periodic SLMoS2. [ABSTRACT FROM AUTHOR]

We utilize classical molecular dynamics to study flexural, or transverse wave propagation in monolayer graphene sheets and compare the resulting dispersion relationships to those expected from continuum thin plate theory. In doing so, we determine that regardless of the chirality for monolayer graphene, transverse waves exhibit a dispersion relationship that corresponds to the lowest order antisymmetric (A0) mode of wave propagation in a thin plate with plate thickness of h=0.104 nm. Finally, we find that the achievable wave speeds in monolayer graphene are found to exceed those reported previously for single walled carbon nanotubes, while the frequency of wave propagation in the graphene monolayer is found to reach the terahertz range, similar to that of carbon nanotubes. [ABSTRACT FROM AUTHOR]

In a previous publication [P. A. T. Olsson, J. Appl. Phys. 108, 034318 (2010)], molecular dynamics (MD) simulations have been performed to study the resonant properties of gold nanowires. It has been documented in the aforementioned publication that the eigenfrequencies of the fundamental mode follows the continuum mechanically predicted behavior when Bernoulli-Euler beam theory is used, whereas the higher order modes tend to be low in comparison to Bernoulli-Euler beam theory predictions. In this work, we have studied the resonant properties of unstressed and prestressed nanowires to explain why the eigenfrequencies of the fundamental mode follows the behavior predicted by Bernoulli-Euler beam theory while those of higher order modes are low in comparison. This is done by employing Timoshenko beam theory and studying the nanowire deformations for different modes. We find good agreement between the MD results and Timoshenko predictions due to the increasing importance of shearing and rotary inertia for higher order resonant modes. Furthermore, we argue that this type of behavior is merely a geometric effect stemming from low aspect ratio for the considered structures as a converging type of behavior is found when the aspect ratios fall between 15 and 20. Finally, we have found that classical Timoshenko beam theory that neglects nanoscale surface effects is able to, simply through utilization of the size dependent Young's modulus, capture the dynamic properties of the gold nanowires as calculated through MD. [ABSTRACT FROM AUTHOR]

In this article, we study the potential of gold nanowires as resonant nanoscale strain sensors. The sensing ability of the nanowires is determined by calculating the variations in resonant frequency that occur due to applied uniaxial tensile and compressive strain. The resonant frequencies are obtained using the surface Cauchy–Born model, which captures surface stress effects on the nanowires through a nonlinear continuum mechanics framework; due to the continuum formulation, the strain-dependent nanowire resonant frequencies are calculated through the solution of a standard finite element eigenvalue problem, where the coupled effects of the applied uniaxial strain and surface stress are naturally included through the finite element stiffness matrix. The nanowires are found to be more sensitive to compressive than tensile strain, with resonant frequency shifts around 200–400 MHz with the application of 1% tensile and compressive strain. In general, the strain sensitivity of the nanowires is found to increase with decreasing cross-sectional size, with additional dependencies on their aspect ratio. [ABSTRACT FROM AUTHOR]

The purpose of the present work is to quantify the coupled effects of surface stresses and boundary conditions on the resonant properties of silicon nanowires. We accomplish this by using the surface Cauchy–Born model, which is a nonlinear, finite deformation continuum mechanics model that enables the determination of the nanowire resonant frequencies including surface stress effects through solution of a standard finite element eigenvalue problem. By calculating the resonant frequencies of both fixed/fixed and fixed/free <100> silicon nanowires with unreconstructed {100} surfaces using two formulations, one that accounts for surface stresses and one that does not, it is quantified how surface stresses cause variations in nanowire resonant frequencies from those expected from continuum beam theory. We find that surface stresses significantly reduce the resonant frequencies of fixed/fixed nanowires as compared to continuum beam theory predictions, while small increases in resonant frequency with respect to continuum beam theory are found for fixed/free nanowires. It is also found that the nanowire aspect ratio, and not the surface area to volume ratio, is the key parameter that correlates deviations in nanowire resonant frequencies due to surface stresses from continuum beam theory. [ABSTRACT FROM AUTHOR]

• The interfacial thermal resistance shows a switchable, step-like enhancement by varying the number of fullerene, where the magnitude can be enhanced by a factor of two. • The switchable phenomenon can be analyzed using analytic expressions based on the thermal transport theory. • The switchable phenomenon can be realized by applying mechanical strain or by varying the temperature of the sandwich structure. • The temperature range can be increased using mechanical strain, demonstrating the robust environmental sensitivity of the proposed thermal switch structure. [Display omitted] Switchable thermal devices are attracting significant research interest as a basic thermal management component. In this work, taking graphene/fullerene/graphene sandwiches as an example, we demonstrate that the interfacial thermal resistance can show a switchable, step-like change by varying the number of fullerenes in the sandwich structure. Changing the number of fullerenes causes a structural transition between the graphene layers from adhered to separated, resulting in an enhancement of about a factor of two in the interfacial thermal resistance during this on/off switchable phenomenon, which we analyze using analytic expressions based on the thermal transport theory. We further illustrate that the switchable phenomenon can also be realized by applying mechanical strain or by varying the temperature of the sandwich structure. This work demonstrates that the sandwich-liked nanoscale heterostructures can exhibit hysteretic changes in heat transport, and thus have promise for potential applications in switchable thermal devices. [ABSTRACT FROM AUTHOR]

Electroactive polymers such as dielectric elastomers (DEs) have attracted significant attention in recent years. Computational techniques to solve the coupled electromechanical system of equations for this class of materials have universally centered around fully coupled monolithic formulations, which while generating good accuracy requires significant computational expense. However, this has significantly hindered the ability to solve large scale, fully three-dimensional problems involving complex deformations and electromechanical instabilities of DEs. In this work, we provide theoretical basis for the effectiveness and accuracy of staggered explicit–implicit finite element formulations for this class of electromechanically coupled materials, and elicit the simplicity of the resulting staggered formulation. We demonstrate the stability and accuracy of the staggered approach by solving complex electromechanically coupled problems involving electroactive polymers, where we focus on problems involving electromechanical instabilities such as creasing, wrinkling, and bursting drops. In all examples, essentially identical results to the fully monolithic solution are obtained, showing the accuracy of the staggered approach at a significantly reduced computational cost. [ABSTRACT FROM AUTHOR]

We present a computational method that can be applied to capture surface stress and surface tension-driven effects in both stiff, crystalline nanostructures, like size-dependent mechanical properties, and soft solids, like elastocapillary effects. We show that the method is equivalent to the classical Young-Laplace model. The method is based on converting surface tension and surface elasticity on a zero-thickness surface to an initial stress and corresponding elastic properties on a finite thickness shell, where the consideration of geometric nonlinearity enables capturing the out-of-plane component of the surface tension that results for curved surfaces through evaluation of the surface stress in the deformed configuration. In doing so, we are able to use commercially available finite element technology, and thus do not require consideration and implementation of the classical Young-Laplace equation. Several examples are presented to demonstrate the capability of the methodology for modeling surface stress in both soft solids and crystalline nanostructures. [ABSTRACT FROM AUTHOR]

We present a computational design methodology for topology optimization of multi-material-based flexoelectric composites. The methodology extends our recently proposed design methodology for a single flexoelectric material. We adopt the multi-phase vector level set (LS) model which easily copes with various numbers of phases, efficiently satisfies multiple constraints and intrinsically avoids overlap or vacuum among different phases. We extend the point wise density mapping technique for multi-material design and use the B-spline elements to discretize the partial differential equations (PDEs) of flexoelectricity. The dependence of the objective function on the design variables is incorporated using the adjoint technique. The obtained design sensitivities are used in the Hamilton–Jacobi (H–J) equation to update the LS function. We provide numerical examples for two, three and four phase flexoelectric composites to demonstrate the flexibility of the model as well as the significant enhancement in electromechanical coupling coefficient that can be obtained using multi-material topology optimization for flexoelectric composites. [ABSTRACT FROM AUTHOR]

This paper presents a design methodology based on a combination of isogeometric analysis (IGA), level set and point wise density mapping techniques for topology optimization of piezoelectric/flexoelectric materials. The fourth order partial differential equations (PDEs) of flexoelectricity, which require at least C 1 continuous approximations, are discretized using Non-Uniform Rational B-spline (NURBS). The point wise density mapping technique with consistent derivatives is directly used in the weak form of the governing equations. The boundary of the design domain is implicitly represented by a level set function. The accuracy of the IGA model is confirmed through numerical examples including a cantilever beam under a point load and a truncated pyramid under compression with different electrical boundary conditions. Finally, we provide numerical examples demonstrating the significant enhancement in electromechanical coupling coefficient that can be obtained using topology optimization. [ABSTRACT FROM AUTHOR]

There has been a massive increase in research interest towards applying data driven methods to problems in mechanics, with a particular emphasis on using data driven methods for predictive modeling and design of materials with novel functionality. While traditional machine learning (ML) methods have enabled many breakthroughs, they rely on the assumption that the training (observed) data and testing (unseen) data are independent and identically distributed (i.i.d). However, when these standard ML approaches are applied to real world mechanics problems with unknown test environments, they can be very sensitive to data distribution shifts, and can break down when evaluated on test datasets that violate the i.i.d. assumption. In contrast, out-of-distribution (OOD) generalization approaches assume that the data contained in test environments are allowed to shift (i.e., violate the i.i.d. assumption). To date, multiple methods have been proposed to improve the OOD generalization of ML methods. However, most of these OOD generalization methods have been focused on classification problems, driven in part by the lack of benchmark datasets available for OOD regression problems. Thus, the efficiency of these OOD generalization methods on regression problems, which are typically more relevant to mechanics research than classification problems, is unknown. To address this, we perform a fundamental study of OOD generalization methods for regression problems in mechanics. Specifically, we identify three OOD generalization problems: covariate shift, mechanism shift, and sampling bias. For each problem, we create two benchmark examples that extend the Mechanical MNIST dataset collection, and we investigate the performance of popular OOD generalization methods on these mechanics-specific regression problems. Our numerical experiments show that in most cases, while the OOD algorithms perform better compared to traditional ML methods on these OOD generalization problems, there is a compelling need to develop more robust OOD methods that can generalize the notion of invariance across multiple OOD scenarios. Overall, we expect that this study, as well as the associated open access benchmark datasets, will enable further development of OOD methods for mechanics specific regression problems. [ABSTRACT FROM AUTHOR]

We present a new finite deformation, dynamic finite element model that incorporates surface tension to capture elastocapillary effects on the electromechanical deformation of dielectric elastomers. We demonstrate the significant effect that surface tension can have on the deformation of dielectric elastomers through three numerical examples: (1) surface tension effects on the deformation of single finite elements with homogeneous boundary conditions; (2) surface tension effects on instabilities in constrained dielectric elastomer films, and (3) surface tension effects on bursting drops in solid dielectrics. Generally, we find that surface tension creates a barrier to instability nucleation. Specifically, we find in agreement with recent experimental studies of constrained dielectric elastomer films a transition in the surface instability mechanism depending on the elastocapillary length. The present results indicate that the proposed methodology may be beneficial in studying the electromechanical deformation and instabilities for dielectric elastomers in the presence of surface tension. [ABSTRACT FROM AUTHOR]

The J-integral is recognized as a fundamental parameter in fracture mechanics that characterizes the inherent resistance of materials to crack growth. However, the conventional methods to calculate the J-integral, which require knowledge of the exact position of a crack tip and the continuum fields around it, are unable to precisely measure the J-integral of polymer composites at the nanoscale. This work aims to propose an effective calculation method based on coarse-grained (CG) simulations for predicting the J-integral of carbon nanotube (CNT)/polymer composites. In the proposed approach, the J-integral is determined from the load displacement curve of a single specimen. The distinguishing feature of the method is the calculation of J-integral without need of information about the crack tip, which makes it applicable to complex polymer systems. The effects of the CNT weight fraction and covalent cross-links between the polymer matrix and nanotubes, and polymer chains on the fracture behavior of the composites are studied in detail. The dependence of the J-integral on the crack length and the size of representative volume element (RVE) is also explored. [ABSTRACT FROM AUTHOR]

Short-fiber-reinforced polymer composites are increasingly used in engineering applications and industrial products owing to their unique combination of superior mechanical properties, and relatively easy and low-cost manufacturing process. The mechanical behavior of short carbon nanotube (CNT) polymer composites, however, remains poorly understood due to size and time limitations of experiments and atomistic simulations. To address this issue, the tensile fracture behavior of short CNT reinforced poly (methyl methacrylate) (PMMA) matrix composites is investigated using a coarse-grained (CG) model. The reliability of the CG model is demonstrated by reproducing experimental results on the strain–stress behavior of the polymer material. The effect of the nanotube weight fraction on the mechanical properties, i.e. the Young’s modulus, yield strength, tensile strength and critical strain, of the CNT/polymer composites is studied in detail. The dependence of the mechanical properties of the composites on the orientation and length-to-diameter aspect ratio of nanotube reinforcements is also examined. [ABSTRACT FROM AUTHOR]

In this work, a coarse-grained (CG) model of carbon nanotube (CNT) reinforced polymer matrix composites is developed. A distinguishing feature of the CG model is the ability to capture interactions between polymer chains and nanotubes. The CG potentials for nanotubes and polymer chains are calibrated using the strain energy conservation between CG models and full atomistic systems. The applicability and efficiency of the CG model in predicting the elastic properties of CNT/polymer composites are evaluated through verification processes with molecular simulations. The simulation results reveal that the CG model is able to estimate the mechanical properties of the nanocomposites with high accuracy and low computational cost. The effect of the volume fraction of CNT reinforcements on the Young's modulus of the nanocomposites is investigated. The application of the method in the modeling of large unit cells with randomly distributed CNT reinforcements is examined. The established CG model will enable the simulation of reinforced polymer matrix composites across a wide range of length scales from nano to mesoscale. [ABSTRACT FROM AUTHOR]

We present an analytic study, based on the tight-binding approximation, of strain effects on the electronic bandgap in single-layer black phosphorus. We obtain an expression for the variation of the bandgap induced by a general strain type that includes both tension in and out of the plane and shear, and use this to determine the most efficient strain direction for different strain types, along which the strongest bandgap manipulation can be achieved. We find that the strain direction that enables the maximum manipulation of the bandgap is not necessarily in the armchair or zigzag direction. Instead, to achieve the strongest bandgap modulation, the direction of the applied mechanical strain is dependent on the type of applied strain. [ABSTRACT FROM AUTHOR]

We perform classic molecular dynamics simulations to comparatively investigate the mechanical properties of single-layer MoS2 and a graphene/MoS2/graphene heterostructure under uniaxial tension. We show that the lattice mismatch between MoS2 and graphene will lead to an spontaneous strain energy in the interface. The Young's modulus of the heterostructure is much larger than that of MoS2. While the stiffness is enhanced, the yield strain of the heterostructure is considerably smaller than the MoS2 due to lateral buckling of the outer graphene layers owning to the applied mechanical tension. [ABSTRACT FROM AUTHOR]

Researchers have recently discoveredultrastrong and ductile behaviorof Au nanowires (NWs) through long-ranged coherent-twin-propagation.An elusive but fundamentally important question arises whether thesize and surface effects impact the twin propagation behavior witha decreasing diameter. In this work, we demonstrate size-dependentstrength behavior of ultrastrong and ductile metallic NWs. For Au,Pd, and AuPd NWs, high ductility of about 50% is observed throughcoherent twin propagation, which occurs by a concurrent reorientationof the bounding surfaces from {111} to {100}. Importantly, the ductilityis not reduced with an increase in strength, while the twin propagationstress dramatically increases with decreasing NW diameter from 250to 40 nm. Furthermore, we find that the power-law exponent describingthe twin propagation stress is fundamentally different from the exponentdescribing the size-dependence of the yield strength. Specifically,the inverse diameter-dependence of the twin propagation stress isdirectly attributed to surface reorientation, which can be capturedby a surface energy differential model. Our work further highlightsthe fundamental role that surface reorientations play in enhancingthe size-dependent mechanical behavior and properties of metal NWsthat imply the feasibility of high efficiency mechanical energy storagedevices suggested before. [ABSTRACT FROM AUTHOR]

We perform molecular dynamics simulations to investigate the effect of polar surfaces on the quality (Q)-factors of zinc oxide (ZnO) nanowire-based nanoresonators. We find that the Q-factors in ZnO nanoresonators with free polar (0001) surfaces are about one order of magnitude higher than in nanoresonators that have been stabilized with reduced charges on the polar (0001) surfaces. From normal mode analysis, we show that the higher Q-factor is due to a shell-like reconstruction that occurs for the free polar surfaces. This shell-like reconstruction suppresses twisting motion in the nanowires such that the mixing of other modes with the resonant mode of oscillation is minimized, and leads to substantially higher Q-factors in ZnO nanoresonators with free polar surfaces. [ABSTRACT FROM AUTHOR]

We couple the recently developed self-learning metabasin escape algorithm, which enables efficient exploration of the potential energy surface (PES), with shear deformation to elucidate strain-rate and temperature effects on the shear transformation zone (STZ) characteristics in two-dimensional amorphous solids. In doing so, we report a transition in the STZ characteristics that can be obtained through either increasing the temperature or decreasing the strain rate. The transition separates regions having two distinct STZ characteristics. Specifically, at high temperatures and high strain rates, we show that the STZs have characteristics identical to those that emerge from purely strain-driven, athermal quasistatic atomistic calculations. At lower temperatures and experimentally relevant strain rates, we use the newly coupled PES + shear deformation method to show that the STZs have characteristics identical to those that emerge from a purely thermally activated state. The specific changes in STZ characteristics that occur in moving from the strain-driven to thermally activated STZ regime include a 33% increase in STZ size, faster spatial decay of the displacement field, a change in the deformation mechanism inside the STZ from shear to tension, a reduction in the stress needed to nucleate the first STZ, and finally a notable loss in characteristic quadrupolar symmetry of the surrounding elastic matrix that has previously been seen in athermal, quasistatic shear studies of STZs. [ABSTRACT FROM AUTHOR]

Highlights: [•] New finite element formulation for dielectric elastomers. [•] Q1P0 model alleviates locking. [•] Creasing to cratering instability captured, with experimental comparison. [Copyright &y& Elsevier]

Abstract: We present a three-dimensional nonlinear finite element formulation for dielectric elastomers. The mechanical and electrical governing equations are solved monolithically using an implicit time integrator, where the governing finite element equations are given for both static and dynamic cases. By accounting for inertial terms in conjunction with the Arruda–Boyce rubber hyperelastic constitutive model, we demonstrate the ability to capture the various modes of inhomogeneous deformation, including pull-in instability and wrinkling, that may result in dielectric elastomers that are subject to various forms of electrostatic loading. The formulation presented here forms the basis for needed computational tools that can elucidate the electromechanical behavior and properties of dielectric elastomers that are used for engineering applications. [Copyright &y& Elsevier]

Abstract: In the present work, we have applied recently developed nonlinear multiscale finite element techniques which account for nanoscale surface stress and surface elastic effects to investigate the elastic properties of silicon nanowires as obtained through bending deformation. The numerical results are used to clarify the factors underlying the current disconnect between atomistic simulations and experiments as to the nanowire sizes at which deviation from bulk elastic properties due to surface effects are observed. In particular, we demonstrate that when nanowires with aspect ratios (defined as the axial length divided by the square cross sectional length) larger than about 15 are considered, the elastic softening that has been observed experimentally for larger (i.e. diameter) nanowires is observed. In contrast, when smaller aspect ratios are considered, very little deviation from the bulk elastic properties are observed, in agreement with existing atomistic calculations. Furthermore, we demonstrate that the elastic softening is strongly boundary condition dependent, where fixed/fixed silicon nanowires exhibit a strong aspect ratio-dependent softening, while little variation in the elastic properties of fixed/free nanowires are observed. Comparisons are made with existing surface elastic theories and experiments to bring further insights into the boundary condition dependence in elastic properties. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to quantify how nanoscale surface stresses impact the critical buckling strains of silicon nanowires. These insights are gained by using nonlinear finite element calculations based upon a multiscale, finite deformation constitutive model that incorporates nanoscale surface stress and surface elastic effects to study the buckling behavior of silicon nanowires that have cross sectional dimensions between 10 and 25nm under axial compressive loading. The key finding is that, in contrast to existing surface elasticity solutions, the critical buckling strains are found to show little deviation from the classical bulk Euler solution. The present results suggest that accounting for axial strain relaxation due to surface stresses may be necessary to improve the accuracy and predictive capability of analytic linear surface elastic theories. [Copyright &y& Elsevier]

Abstract: We present a new multiscale, finite deformation, electromechanical formulation to capture the response of surface-dominated nanomaterials to externally applied electric fields. To do so, we develop and discretize a total energy that combines both mechanical and electrostatic terms, where the mechanical potential energy is derived from any standard interatomic atomistic potential, and where the electrostatic potential energy is derived using a Gaussian-dipole approach. By utilizing Cauchy–Born kinematics, we derive both the bulk and surface electrostatic Piola–Kirchhoff stresses that are required to evaluate the resulting electromechanical finite element equilibrium equations, where the surface Piola–Kirchhoff stress enables us to capture the non-bulk electric field-driven polarization of atoms near the surfaces of nanomaterials. Because we minimize a total energy, the present formulation has distinct advantages as compared to previous approaches, where in particular, only one governing equation is required to be solved. This is in contrast to previous approaches which require either the staggered or monolithic solution of both the mechanical and electrostatic equations, along with coupling terms that link the two domains. The present approach thus leads to a significant reduction in computational expense both in terms of fewer equations to solve and also in eliminating the need to remesh either the mechanical or electrostatic domains due to being based on a total Lagrangian formulation. Though the approach can apply to three-dimensional cases, we concentrate in this paper on the one-dimensional case. We first derive the necessary formulas, then give numerical examples to validate the proposed approach in comparison to fully atomistic electromechanical calculations. [Copyright &y& Elsevier]

Abstract: Recent advances in nanotechnology have led to the development of nano-electro-mechanical systems (NEMS) such as nanomechanical resonators, which have recently received significant attention from the scientific community. This is not only due to their capability of label-free detection of bio/chemical molecules at single-molecule (or atomic) resolution for future applications such as the early diagnosis of diseases like cancer, but also due to their unprecedented ability to detect physical quantities such as molecular weight, elastic stiffness, surface stress, and surface elastic stiffness for adsorbed molecules on the surface. Most experimental works on resonator-based molecular detection have been based on the principle that molecular adsorption onto a resonator surface increases the effective mass, and consequently decreases the resonant frequencies of the nanomechanical resonator. However, this principle is insufficient to provide fundamental insights into resonator-based molecular detection at the nanoscale; this is due to recently proposed novel nanoscale detection principles including various effects such as surface effects, nonlinear oscillations, coupled resonance, and stiffness effects. Furthermore, these effects have only recently been incorporated into existing physical models for resonators, and therefore the universal physical principles governing nanoresonator-based detection have not been completely described. Therefore, our objective in this review is to overview the current attempts to understand the underlying mechanisms in nanoresonator-based detection using physical models coupled to computational simulations and/or experiments. Specifically, we will focus on issues of special relevance to the dynamic behavior of nanoresonators and their applications in biological/chemical detection: the resonance behavior of micro/nanoresonators; resonator-based chemical/biological detection; physical models of various nanoresonators such as nanowires, carbon nanotubes, and graphene. We pay particular attention to experimental and computational approaches that have been useful in elucidating the mechanisms underlying the dynamic behavior of resonators across multiple and disparate spatial/length scales, and the resulting insight into resonator-based detection that has been obtained. We additionally provide extensive discussion regarding potentially fruitful future research directions coupling experiments and simulations in order to develop a fundamental understanding of the basic physical principles that govern NEMS and NEMS-based sensing and detection applications. [Copyright &y& Elsevier]

Abstract: In this work, we present results from atomistic simulations of gold nanowires under axial compression, with a focus on examining the effects of both axial and surface orientation effects on the buckling behavior. This was accomplished by using molecular statics simulations while considering three different crystallographic systems: 〈100〉/{100}, 〈100〉/{110} and 〈110〉/{110}{100}, with aspect ratios spanning from 20 to 50 and cross-sectional dimensions ranging from 2.45 to 5.91nm. The simulations indicate that there is a deviation from the inverse square length dependence of critical forces predicted from traditional linear elastic Bernoulli–Euler and Timoshenko beam theories, where the nature of the deviation from the perfect inverse square length behavior differs for different crystallographic systems. This variation is found to be strongly correlated to either stiffening or increased compliance of the tangential stiffness due to the influence of nonlinear elasticity, which leads to normalized critical forces that decrease with decreasing aspect ratio for the 〈100〉/{100} and 〈100〉/{110} systems, but increase with decreasing aspect ratio for the 〈110〉/{110}{100} system. In contrast, it was found that the critical strains are all lower than their bulk counterparts, and that the critical strains decrease with decreasing cross-sectional dimensions; the lower strains may be an effect emanating from the presence of the surfaces, which are all more elastically compliant than the bulk and thus give rise to a more compliant flexural rigidity. [Copyright &y& Elsevier]

Because the normal operation of the eye depends on sensitive morphogenetic processes for its eventual shape, developmental flaws can lead to wide-ranging ocular defects. However, the physical processes and mechanisms governing ocular morphogenesis are not well understood. Here, using analytical theory and nonlinear shell finite-element simulations, we show, for optic vesicles experiencing matrix-constrained growth, that elastic instabilities govern the optic cup morphogenesis. By capturing the stress amplification owing to mass increase during growth, we show that the morphogenesis is driven by two elastic instabilities analogous to the snap through in spherical shells, where the second instability is sensitive to the optic cup geometry. In particular, if the optic vesicle is too slender, it will buckle and break axisymmetry, thus, preventing normal development. Our results shed light on the morphogenetic mechanisms governing the formation of a functional biological system and the role of elastic instabilities in the shape selection of soft biological structures. [ABSTRACT FROM AUTHOR]

Abstract: We present a Surface Cauchy-Born approach to modeling non-centrosymmetric, semiconducting nanostructures such as silicon that exist in a diamond cubic lattice structure. The model is based on an extension to the standard Cauchy-Born theory in which a surface energy term that is obtained from the underlying crystal structure and governing interatomic potential is used to augment the bulk energy. The incorporation of the surface energy leads naturally to the existence of surface stresses, which are key to capturing the size-dependent mechanical behavior and properties of nanomaterials. We present the approach in detail, then demonstrate its capabilities by calculating the minimum energy configurations of silicon nanowires due to surface stresses as compared to full scale atomistic calculations. [Copyright &y& Elsevier]

Abstract: We present a multiscale, finite deformation formulation that accounts for surface stress effects on the coupled thermomechanical behavior and properties of nanomaterials. The foundation of the work lies in the development of a multiscale surface Helmholtz free energy, which is constructed through utilization of the surface Cauchy–Born hypothesis. By doing so, temperature-dependent surface stress measures as well as a novel form of the heat equation are obtained directly from the surface free energy. The development of temperature-dependent surface stresses distinguishes the present approach, as the method can be utilized to study the behavior of nanomaterials by capturing the size-dependent variations in the thermoelastic properties with decreasing nanostructure size. The coupled heat and momentum equations are solved in 1D using a fully implicit, monolithic scheme, and show the importance of capturing surface stress effects in accurately modeling the thermomechanical behavior of nanoscale materials. [Copyright &y& Elsevier]

Abstract: The purpose of this work is to develop the theoretical basis needed to study nanoscale resonant mass sensing with finite elements using the surface Cauchy–Born (SCB) model. The theory is developed in 1D, where it is identified that the primary modeling issue lies in capturing inhomogeneous surface stresses arising from adsorbate/substrate interactions. By utilizing internal degrees of freedom within the SCB framework, we show that the SCB model can represent the bonding energies, and thus the inhomogeneous surface stress that arises due to interactions by atoms of dissimilar materials. A key outcome of this is that it is shown that a finite element solution using the SCB model is able to simultaneously capture both mass and stiffness variations due to adsorbate/substrate interactions, and their effects on the nanostructure resonant properties. We first verify that the SCB model accurately captures the resonant properties of monatomic 1D atomic chains, then demonstrate the approach by studying the resonant properties of 1D atomic chains that interact with adsorbates. Importantly, we demonstrate that a finite element solution using the SCB model can predict the distinct shifts in resonant frequency that occur due to the adsorption of different materials on the 1D monatomic chain. [Copyright &y& Elsevier]

Abstract: We present an analysis of the uniaxial thermomechanical deformation of single-crystal silver shape memory nanowires using atomistic simulations. We first demonstrate that silver nanowires can show both shape memory and pseudoelastic behavior, then perform uniaxial tensile loading of the shape memory nanowires at various deformation temperatures, strain rates and heat transfer conditions. The simulations show that the resulting mechanical response of the shape memory nanowires depends strongly upon the temperature during deformation, and can be fundamentally different from that observed in bulk polycrystalline shape memory alloys. The energy and temperature signatures of uniaxially loaded silver shape memory nanowires are correlated to the observed nanowire deformation, and are further discussed in comparison to bulk polycrystalline shape memory alloy behavior. [Copyright &y& Elsevier]

Abstract: We present atomistic simulations of 〈110〉 oriented gold nanowires under tensile deformation. We find that 〈110〉 gold nanowires tend to form elongated, stable nanobridges upon necking, which is in agreement with previous experimental observations. In addition, the simulations reveal that the formation of a high strength multishell lattice structure during the plastic deformation of the 〈110〉 wires may account for the stability of the elongated nanobridges observed experimentally. [Copyright &y& Elsevier]

Abstract: Inspired by the pioneering work of Professor T.J.R. Hughes on the variational multi-scale method, this document summarizes recent developments in multiple-scale modeling using a newly developed technique called the bridging scale. The bridging scale consists of a two-scale decomposition in which the coarse scale is simulated using continuum methods, while the fine scale is simulated using atomistic approaches. The bridging scale offers unique advantages in that the coarse and fine scales evolve on separate time scales, while the high frequency waves emitted from the fine scale are eliminated using lattice impedance techniques. Recent advances in extending the bridging scale to quantum mechanical/continuum coupling are briefly described. The method capabilities are demonstrated via quasistatic nanotube bending, dynamic crack propagation and dynamic shear banding. [Copyright &y& Elsevier]

Abstract: This paper presents a three-dimensional generalization of the bridging scale concurrent method, a finite temperature multiple scale method that couples molecular dynamics (MD) to finite elements (FE). The generalizations include the numerical calculation of the boundary condition acting upon the reduced MD region, as such boundary conditions are analytically intractable for realistic three-dimensional crystal structures. The formulation retains key advantages emphasized in previous papers, particularly the compact size of the resulting time history kernel matrix. The coupled FE and reduced MD equations of motion are used to analyze dynamic fracture in a three-dimensional FCC lattice, where interesting physical phenomena such as crack branching are seen. The multiple scale results are further compared to benchmark MD simulations for verification purposes. [Copyright &y& Elsevier]

In this paper, we present all necessary generalisations to extend the bridging scale, a finite-temperature multiple scale method which couples molecular dynamics (MD) and finite element (FE) simulations, to two dimensions. The crucial development is a numerical treatment of the boundary condition acting upon the reduced atomistic system, as such boundary conditions are analytically intractable beyond simple one-dimension systems. The approach presented in this paper offers distinct advantages compared to previous works, specifically the compact size of the resulting time history kernel, and the fact that the time history kernel can be calculated using an automated numerical procedure for arbitrary multi-dimensional lattice structures and interatomic potentials. We demonstrate the truly two-way nature of the coupled FE and reduced MD equations of motion via two example problems, wave propagation and dynamic crack propagation. Finally, we compare both problems to benchmark full MD simulations to validate the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Concurrent multiple-scale methods can be defined as those which combine information available from distinct length and time scales into a single coherent, coupled simulation. These methods have recently become both popular and necessary for the following reasons. One is the recent discovery of new, nanoscale materials, and the corresponding boom in nanotechnology research. Another factor is that experiments have conclusively shown the connection between microscale physics and macroscale deformation. Finally, the concept of linking disparate length and time scales has become feasible recently due to the ongoing explosion in computational power.We present a detailed introduction to the available technologies in the field of multiple-scale analysis. In particular, our review centers on methods which aim to couple molecular-level simulations (such as molecular dynamics) to continuum level simulations (such as finite element and meshfree methods). Using this definition, we first review existing multiple-scale technology, and explain the pertinent issues in creating an efficient yet accurate multiple-scale method. Following the review, we highlight a new multiple-scale method, the bridging scale, and compare it to existing multiple-scale methods. Next, we show example problems in which the bridging scale is applied to fully non-linear problems. Concluding remarks address the research needs for multiple-scale methods in general, the bridging scale method in particular, and potential applications for the bridging scale. [Copyright &y& Elsevier]

We present a simple method for calculating a continuum temperature field directly from a molecular dynamics (MD) simulation. Using the idea of a projection matrix previously developed for use in the bridging scale, we derive a continuum temperature equation which only requires information that is readily available from MD simulations, namely the MD velocity, atomic masses and Boltzmann constant. As a result, the equation is valid for usage in any coupled finite element (FE)/MD simulation. In order to solve the temperature equation in the continuum where an MD solution is generally unavailable, a method is utilized in which the MD velocities are found at arbitrary coarse scale points by means of an evolution function. The evolution function is derived in closed form for a 1D lattice, and effectively describes the temporal and spatial evolution of the atomic lattice dynamics. It provides an accurate atomistic description of the kinetic energy dissipation in simulations, and its behavior depends solely on the atomic lattice geometry and the form of the MD potential. After validating the accuracy of the evolution function to calculate the MD variables in the coarse scale, two 1D examples are shown, and the temperature equation is shown to give good agreement to MD simulations. [Copyright &y& Elsevier]

We utilize classical molecular dynamics to study the effects of intrinsic, interlayer friction between graphene monolayers, as well as extrinsic attachment or clamping strength between graphene and a model silicon substrate on the energy dissipation (Q-factors) of oscillating graphene nanoresonators. Both interlayer friction and attachment effects are found to significantly degrade the graphene Q-factors, with an increase in energy dissipation with increasing temperature, while both effects are found to be strongly dependent on the strength of the van der Waals interactions, either between adjacent layers of graphene or between graphene and the underlying substrate. [ABSTRACT FROM AUTHOR]

This letter addresses the direct effect that geometry has in controlling the mechanisms of inelastic deformation in metal nanowires. By performing atomistic simulations of the tensile deformation of <100>/{100} hollow copper nanowires (nanoboxes), the authors find that the nanoboxes deform in an unexpected twinning-dominated mode; the nonsquare wall geometries of the nanoboxes bias the deformation by allowing the larger transverse {100} surfaces to reduce their area through twinning by reorienting to a lower energy {111} surface. Additional analyses on solid nanowires with nonsquare cross sections confirm that geometry can be utilized to engineer the mechanical behavior and properties of nanomaterials. [ABSTRACT FROM AUTHOR]