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There has been significant recent interest in the mechanics community to design structures that can either violate reciprocity, or exhibit elastic asymmetry or odd elasticity. While these properties are highly desirable to enable mechanical metamaterials to exhibit novel wave propagation phenomena, it remains an open question as to how to design passive structures that exhibit both significant non-reciprocity and elastic asymmetry. In this paper, we first define several design spaces for chiral metamaterials leveraging specific design parameters, including the ligament contact angles, the ligament shape, and circle radius. Having defined the design spaces, we then leverage machine learning approaches, and specifically Bayesian optimization, to determine optimally performing designs within each design space satisfying maximal non-reciprocity or stiffness asymmetry. Finally, we perform multi-objective optimization by determining the Pareto optimum and find chiral metamaterials that simultaneously exhibit high non-reciprocity and stiffness asymmetry. Our analysis of the underlying mechanisms reveals that chiral metamaterials that can display multiple different contact states under loading in different directions are able to simultaneously exhibit both high non-reciprocity and stiffness asymmetry. Overall, this work demonstrates the effectiveness of employing ML to bring insights to a novel domain with limited prior information, and more generally will pave the way for metamaterials with unique properties and functionality in directing and guiding mechanical wave energy.

Fullerene-based sandwiches have emerged as new candidates for potential applications of two-dimensional nanomaterials in electronics or energy storage. Recently, experimentalists have observed the evolution of boundaries for fullerene clusters sandwiched by two graphene layers, while vacuum space with typical dimension of 30 {\AA} was found within the fullerene layer. Because the pattern of the fullerene cluster impacts the physical properties of the sandwiches, it is important to understand the mechanisms for their structural transformations. In the present work, we find that the graphene/fullerene/graphene sandwich structure transforms among three configurations, depending on the fullerene to graphene area ratio. Molecular dynamics simulations show that there are two critical values for the area ratio. The fullerene pattern transforms from circular to rectangular at the first critical area ratio of 1/{\pi}. The critical value of 1/{\pi} is successfully derived by comparing the geometrical perimeter of the circular and rectangular shapes for the fullerene cluster without any physical parameters. At the second critical area ratio, the graphene layers surrounding the fullerene cluster become separated due to the competition between the bending energy and the cohesive energy. Based on the analytic model, the vacuum space is predicted to be 34 {\AA}, which agrees quite well with the experimental result. These findings provide fundamental insights into the mechanisms driving structural transformation of fullerene-based sandwiches, which will enable the selection of appropriate structures and materials to guide the design of future electronic and energy storage applications.

Flexoelectricity is a form of electromechanical coupling that has recently emerged because, unlike piezoelectricity, it is theoretically possible in any dielectric material. Two-dimensional (2D) materials have also garnered significant interest because of their unusual electromechanical properties and high flexibility, but the intrinsic flexoelectric properties of these materials remain unresolved. In this work, using atomistic modeling accounting for charge-dipole interactions, we report the intrinsic flexoelectric constants for a range of two-dimensional materials, including graphene allotropes, nitrides, graphene analogs of group-IV elements, and the transition metal dichalcogenides (TMDCs). We accomplish this through a proposed mechanical bending scheme that eliminates the piezoelectric contribution to the total polarization, which enables us to directly measure the flexoelectric constants. While flat 2D materials like graphene have low flexoelectric constants due to weak $\pi-\sigma$ interactions, buckling is found to increase the flexoelectric constants in monolayer group-IV elements. Finally, due to significantly enhanced charge transfer coupled with structural asymmetry due to bending, the TMDCs are found to have the largest flexoelectric constants, including MoS$_{2}$ having a flexoelectric constant ten times larger than graphene.

Due to their combination of mechanical stiffness and flexibility, two-dimensional (2D) materials have received significant interest as potential electromechanical materials. Flexoelectricity is an electromechanical coupling between strain gradient and polarization. Unlike piezoelectricity, which exists only in non-centrosymmetric materials, flexoelectricity theoretically exists in all dielectric materials. However, most work on the electromechanical energy conversion potential of 2D materials has focused on their piezoelectric, and not flexoelectric behavior and properties. In the present work, we demonstrate that the intrinsic structural asymmetry present in monolayer Janus transition metal dichalcogenides (TMDCs) enables significant flexoelectric properties. We report these flexoelectric properties using a recently developed charge-dipole model that couples with classical molecular dynamics simulations. By employing a prescribed bending deformation, we directly calculate the flexoelectric constants while eliminating the piezoelectric contribution to the polarization. We find that the flexoelectric response of a Janus TMDC is positively correlated to its initial degree of asymmetry, which contributes to stronger $\sigma-\sigma$ interactions as the initial degree of asymmetry rises. In addition, the high transfer of charge across atoms in Janus TMDCs leads to larger electric fields due to $\pi-\sigma$ coupling. These enhanced $\sigma-\sigma$ and $\pi-\sigma$ interactions are found to cause the flexoelectric coefficients of the Janus TMDCs to be several times higher than traditional TMDCs such as MoS$_{2}$, whose flexoelectric constant is already ten times larger than graphene.

There has been a massive increase in research interest towards applying data driven methods to problems in mechanics. 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). Thus, traditional ML approaches often break down when applied to real world mechanics problems with unknown test environments and data distribution shifts. In contrast, out-of-distribution (OOD) generalization assumes that the test data may 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, because of the lack of benchmark datasets for OOD regression problems, the efficiency of these OOD methods on regression problems, which dominate the mechanics field, remains unknown. To address this, we investigate the performance of OOD generalization methods for regression problems in mechanics. Specifically, we identify three OOD 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 generalization algorithms perform better compared to traditional ML methods on these OOD problems, there is a compelling need to develop more robust OOD generalization methods that are effective 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 generalization methods for mechanics specific regression problems.

In bistable actuators and other engineered devices, a homogeneous stimulus (e.g. mechanical, chemical, thermal, or magnetic) is often applied to an entire shell to initiate a snap-through instability. In this work, we demonstrate that restricting the active area to the shell boundary allows for a large reduction in its size, thereby decreasing the energy input required to actuate the shell. To do so, we combine theory with 1D finite element simulations of spherical caps with a non-homogeneous distribution of stimulus-responsive material. We rely on the effective curvature stimulus, i.e. the natural curvature induced by the non-mechanical stimulus, which ensures that our results are entirely stimulus-agnostic. To validate our numerics and demonstrate this generality, we also perform two sets of experiments, wherein we use residual swelling of bilayer silicone elastomers--a process that mimics differential growth--as well as a magneto-elastomer to induce curvatures that cause snap-through. Our results elucidate the underlying mechanics, offering an intuitive route to optimal design for efficient snap-through., Comment: 12 pages, 7 figures

We demonstrate a general route to making active, odd elastic solids from passive chiral elements that can act as sources of mechanical work by violating static equilibrium without internal sources of energy or momentum. We further demonstrate that by starting from a discrete, Newtonian mechanics viewpoint of the chiral unit cell, we can develop the continuum field equations for isotropic 2D chiral metamaterials that reveal odd elasticity, while elucidating the structure-property relationships underpinning the chiral, elastic moduli that enable the mechanical activity of the chiral metamaterials. By demonstrating the energy gain of chiral metamaterials as they undergo quasistatic deformation cycles, we show a new route to designing active, non-reciprocal mechanical metamaterials that can operate at zero frequency., Comment: 6 pages, 2 figures

Because phononic topological insulators have primarily been studied in discrete, graphene-like structures with C$_{6}$ or C$_{3}$ hexagonal symmetry, an open question is how to systematically achieve double Dirac cones and topologically non-trivial structures using continuous, non-hexagonal unit cells. Here, we address this challenge by presenting a novel computational methodology for the inverse design of continuous two-dimensional square phononic metamaterials exhibiting C$_{4v}$ and C$_{2v}$ symmetry. This leads to the systematic design of square unit cell topologies exhibiting a double Dirac degeneracy, which enables topologically-protected interface propagation based on the quantum spin Hall effect (QSHE). Numerical simulations prove that helical edge states emerge at the interface between two topologically distinct square phononic metamaterials, which opens the possibility of QSHE-based pseudospin-dependent transport beyond hexagonal lattices.

Machine learning (ML) methods have recently been used as forward solvers to predict the mechanical properties of composite materials. Here, we use a supervised-autoencoder (sAE) to perform inverse design of graphene kirigami, where predicting the ultimate stress or strain under tensile loading is known to be difficult due to nonlinear effects arising from the out-of-plane buckling. Unlike the standard autoencoder, our sAE is able not only to reconstruct cut configurations but also to predict mechanical properties of graphene kirigami and classify the kirigami witheither parallel or orthogonal cuts. By interpolating in the latent space of kirigami structures, the sAE is able to generate novel designs that mix parallel and orthogonal cuts, despite being trained independently on parallel or orthogonal cuts. Our method allows us to both identify novel designs and predict, with reasonable accuracy, their mechanical properties, which is crucial for expanding the search space for materials design.

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 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.

In this work, we consider the stability of a spherical shell under combined loading from a uniform external pressure and a homogenous natural curvature. Non-mechanical stimuli, such as one that tends to modify the rest curvature of an elastic body, are prevalent in a wide range of natural and engineered systems, and may occur due to thermal expansion, changes in pH, differential swelling, and differential growth. Here, we investigate how the presence of both an evolving natural curvature and an external pressure modifies the stability of a complete spherical shell. We show that due to a mechanical analogy between pressure and curvature, positive natural curvatures can severely destabilize a thin shell, while negative natural curvatures can strengthen the shell against buckling, providing the possibility to design shells that buckle at or above the theoretical limit for pressure alone, i.e. a knock-up factor. These results extend directly from the classical analysis of the stability of shells under pressure, and highlight the important role that non-mechanical stimuli can have on modifying the the membrane state of stress in a thin shell.

Making kirigami-inspired cuts into a sheet has been shown to be an effective way of designing stretchable materials with metamorphic properties where the 2D shape can transform into complex 3D shapes. However, finding the optimal solutions is not straightforward as the number of possible cutting patterns grows exponentially with system size. Here, we report on how machine learning (ML) can be used to approximate the target properties, such as yield stress and yield strain, as a function of cutting pattern. Our approach enables the rapid discovery of kirigami designs that yield extreme stretchability as verified by molecular dynamics (MD) simulations. We find that convolutional neural networks (CNN), commonly used for classification in vision tasks, can be applied for regression to achieve an accuracy close to the precision of the MD simulations. This approach can then be used to search for optimal designs that maximize elastic stretchability with only 1000 training samples in a large design space of $\sim 4\times10^6$ candidate designs. This example demonstrates the power and potential of ML in finding optimal kirigami designs at a fraction of iterations that would be required of a purely MD or experiment-based approach, where no prior knowledge of the governing physics is known or available.

One of the exciting features of two-dimensional (2D) materials is their electronic and optical tunability through strain engineering. Previously, we found a class of 2D ferroelectric Rashba semiconductors PbX (X = S, Se, Te) with tunable spin-orbital properties. In this work, based on our previous tight-binding (TB) results, we derive an effective low-energy Hamiltonian around the symmetry points that captures the effects of strain on the electronic properties of PbX. We find that strains induce gauge fields which shift the Rashba point and modify the Rashba parameter. This effect is equivalent to the application of in-plane magnetic fields. The out-of-plane strain, which is proportional to the electric polarization, is also shown to modify the Rashba parameter. Overall, our theory connects strain and spin splitting in ferroelectric Rashba materials, which will be important to understand the strain-induced variations in local Rashba parameters that will occur in practical applications.

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.

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 sheds light on the tunability of the topological bandgaps in nanomaterials., Comment: Journal of Applied Physics, accepted

We perform both lattice dynamics analysis and molecular dynamics simulations to demonstrate the existence of topologically protected phonon modes in a two-dimensional, monolayer hexagonal boron nitride sheet. The topological phonon modes are found to be localized at an in-plane interface that divides the system into two regions of distinct valley Chern numbers. The dispersion of this topological phonon mode crosses over the frequency gap [1123, 1278] cm^{-1}, which is opened through analogy with the quantum valley Hall effect by breaking inversion symmetry of the boron and nitride atoms in the primitive unit cell. Consequently, vibrational energy with frequency within this gap is topologically protected, resulting in wave propagation that exhibits minimal backscattering, is robust with regards to structural defects such as sharp corners, and exhibits excellent temporal stability. Our findings open up the possibility of realizing topological phonons and mechanics in two-dimensional nanomaterials., Comment: Nanoscale, accepted

We propose the lead sulphide (PbS) monolayer as a 2D semiconductor with a large Rashba-like spin-orbit effect controlled by the out-of-plane buckling. The buckled PbS conduction band is found to possess Rashba-like dispersion and spin texture at the $M$ and $\Gamma$ points, with large effective Rashba parameters of $\lambda\sim5~$eV$\AA~$ and $\lambda\sim1~$eV$~\AA$, respectively. Using a tight-binding formalism, we show that the Rashba effect originates from the very large spin-orbit interaction and the hopping term that mixes the in-plane and out-of-plane $p$ orbitals of Pb and S atoms. The latter, which depends on the buckling angle, can be controlled by applying strain to vary the spin texture as well as the Rashba parameter at $\Gamma$ and $M$. Our density functional theory results together with tight-binding formalism provide a unifying framework for designing Rashba monolayers and for manipulating their spin properties.

Thin elastic sheets bend easily and, if they are patterned with cuts, can deform in sophisticated ways. Here we show that carefully tuning the location and arrangement of cuts within thin sheets enables the design of mechanical actuators that scale down to atomically-thin 2D materials. We first show that by understanding the mechanics of a single, non-propagating crack in a sheet we can generate four fundamental forms of linear actuation: roll, pitch, yaw, and lift. Our analytical model shows that these deformations are only weakly dependent on thickness, which we confirm with experiments at centimeter scale objects and molecular dynamics simulations of graphene and MoS$_{2}$ nanoscale sheets. We show how the interactions between non-propagating cracks can enable either lift or rotation, and we use a combination of experiments, theory, continuum computational analysis, and molecular dynamics simulations to provide mechanistic insights into the geometric and topological design of kirigami actuators., Comment: Soft Matter, 2017

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 stress-stain 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., Comment: arXiv admin note: text overlap with arXiv:1704.01451

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.

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., Comment: arXiv admin note: text overlap with arXiv:1704.01451

We propose a novel model for including spin-orbit interactions in buckled two dimensional systems. Our results show that in such systems, intrinsic spin-orbit coupling leads to a formation of Dirac cones, similar to Rashba model. We explore the microscopic origins of this behaviour and confirm our results using DFT calculations.

Dielectric elastomers have recently been proposed for various biologically-relevant applications, in which they may operate in fluidic environments where surface tension effects may have a significant effect on their stability and reliability. Here, we present a theoretical analysis coupled with computational modeling for a generalized electromechanical analysis of surface stability in dielectric elastomers accounting for surface tension effects. For mechanically deformed elastomers, significant increases in critical strain and instability wavelength are observed for small elastocapillary numbers. When the elastomers are deformed electrostatically, both surface tension and the amount of pre-compression are found to substantially increase the critical electric field while decreasing the instability wavelength.

Since the first successful synthesis of graphene just over a decade ago, a variety of two-dimensional (2D) materials (e.g., transition metal-dichalcogenides, hexagonal boron-nitride, etc.) have been discovered. Among the many unique and attractive properties of 2D materials, mechanical properties play important roles in manufacturing, integration and performance for their potential applications. Mechanics is indispensable in the study of mechanical properties, both experimentally and theoretically. The coupling between the mechanical and other physical properties (thermal, electronic, optical) is also of great interest in exploring novel applications, where mechanics has to be combined with condensed matter physics to establish a scalable theoretical framework. Moreover, mechanical interactions between 2D materials and various substrate materials are essential for integrated device applications of 2D materials, for which the mechanics of interfaces (adhesion and friction) has to be developed for the 2D materials. Here we review recent theoretical and experimental works related to mechanics and mechanical properties of 2D materials. While graphene is the most studied 2D material to date, we expect continual growth of interest in the mechanics of other 2D materials beyond graphene.

Auxetic materials (materials with negative Poisson's ratio) and nanomaterials have independently been for many years two of the most active research fields in material science. Recently, these formerly independent fields have begun to intersect in new and interesting ways due to the recent discovery of auxeticity in nanomaterials like graphene, metal nanoplates, black phosphorus, and others. Here we review the research emerging at the intersection of auxeticity and nanomaterials. We first survey the atomistic mechanisms, both intrinsic and extrinsic, that have been found, primarily through atomistic simulations, to cause auxeticity in nanomaterials. We then outline the available experimental evidence for auxetic nanomaterials. In order to lay the groundwork for future work in this exciting area, we close by discussing several future prospects as well as the current challenges in this field., Comment: Applied Physics Review, accepted

Negative Poisson's ratio (NPR) materials have drawn significant interest because the enhanced toughness, shear resistance and vibration absorption that typically are seen in auxetic materials may enable a range of novel applications. In this work, we report that single-layer graphene exhibits an intrinsic NPR, which is robust and independent of its size and temperature. The NPR arises due to the interplay between two intrinsic deformation pathways (one with positive Poisson's ratio, the other with NPR), which correspond to the bond stretching and angle bending interactions in graphene. We propose an energy-based deformation pathway criteria, which predicts that the pathway with NPR has lower energy and thus becomes the dominant deformation mode when graphene is stretched by a strain above 6%, resulting in the NPR phenomenon., Comment: Nano Letters, published

The quantum transport properties of a graphene kirigami similar to those studied in recent experiments are calculated in the regime of elastic, reversible deformations. Our results show that, at low electronic densities, the conductance profile of such structures replicates that of a system of coupled quantum dots, characterized by a sequence of minibands and stop-gaps. The conductance and I-V curves have different characteristics in the distinct stages of elastic deformation that characterize the elongation of these structures. Notably, the effective coupling between localized states is strongly reduced in the small elongation stage, whereas in the large elongation regime the development of strong, localized pseudomagnetic field barriers can reinforce the coupling and reestablish resonant tunneling across the kirigami. This provides an interesting example of interplay between geometry and pseudomagnetic field-induced confinement. The alternating miniband and stop-gaps in the transmission lead to I-V characteristics with negative differential conductance in well defined energy/doping ranges. These effects should be stable in a realistic scenario that includes edge roughness and Coulomb interactions, as these are expected to further promote localization of states at low energies in narrow segments of graphene nanostructures., Comment: 10 pages, 10 figures

Group-IV monochalcogenides are a family of two-dimensional puckered materials with an orthorhombic structure that is comprised of polar layers. In this article, we use first principles calculations to show the multistability of monolayer SnS and GeSe, two prototype materials where the direction of the puckering can be switched by application of tensile stress or electric field. Furthermore, the two inequivalent valleys in momentum space, which are dictated by the puckering orientation, can be excited selectively using linearly polarized light, and this provides an additional tool to identify the polarization direction. Our findings suggest that SnS and GeSe monolayers may have observable ferroelectricity and multistability, with potential applications in information storage.

The Poisson's ratio characterizes the resultant strain in the lateral direction for a material under longitudinal deformation. Though negative Poisson's ratios (NPR) are theoretically possible within continuum elasticity, they are most frequently observed in engineered materials and structures, as they are not intrinsic to many materials. In this work, we report NPR in single-layer graphene ribbons, which results from the compressive edge stress induced warping of the edges. The effect is robust, as the NPR is observed for graphene ribbons with widths smaller than about 10 nm, and for tensile strains smaller than about 0.5%, with NPR values reaching as large as -1.51. The NPR is explained analytically using an inclined plate model, which is able to predict the Poisson's ratio for graphene sheets of arbitrary size. The inclined plate model demonstrates that the NPR is governed by the interplay between the width (a bulk property), and the warping amplitude of the edge (an edge property), which eventually yields a phase diagram determining the sign of the Poisson's ratio as a function of the graphene geometry., Comment: 4 figures

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 and inhomogeneous 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.

We report the results of classical molecular dynamics simulations focused on studying the mechanical properties of MoS$_{2}$ kirigami. Several different kirigami structures were studied based upon two simple non-dimensional parameters, which are related to the density of cuts, as well as the ratio of the overlapping cut length to the nanoribbon length. Our key finding is significant enhancements in tensile yield (by a factor of four) and fracture strains (by a factor of six) as compared to pristine MoS$_{2}$ nanoribbons. These results in conjunction with recent results on graphene suggest that the kirigami approach may be a generally useful one for enhancing the ductility of two-dimensional nanomaterials.

Edge effects play an important role for many properties of graphene. While most works have focused on the effects from isolated free edges, we present a novel knotting phenomenon induced by the interactions between a pair of free edges in graphene, and investigate its effect on the buckling of monolayer graphene. Upon compression, the buckling of graphene starts gradually in the form of two buckling waves from the warped edges. The collision of these two buckling waves results in the creation of a knot structure in graphene. The knot structure enables the buckled graphene to exhibit two unique post-buckling characteristics. First, it induces a five-fold increase in graphene's mechanical stiffness during the buckling process. Second, the knotted structure enables graphene to exhibit a mechanically stable post-buckling regime over a large (3%) compressive strain regime, which is significantly larger than the critical buckling strain of about 0.5%. The combination of these two effects enables graphene to exhibit an unexpected post-buckling stability that has previously not been reported. We predict that numerical simulations or experiments should observe two distinct stress strain relations for the buckling of identical graphene samples, due to the characteristic randomness in the formation process of the knot structure., Comment: 16 figures

We perform classical molecular dynamics to investigate the effects of mechanical strain on single-layer black phosphorus nanoresonators at different temperatures. We find that the resonant frequency is highly anisotropic in black phosphorus due to its intrinsic puckered configuration, and that the quality factor in the armchair direction is higher than in the zigzag direction at room temperature. The quality factors are also found to be intrinsically larger than graphene and MoS2 nanoresonators. The quality factors can be increased by more than a factor of two by applying tensile strain, with uniaxial strain in the armchair direction being most effective. However, there is an upper bound for the quality factor increase due to nonlinear effects at large strains, after which the quality factor decreases. The tension induced nonlinear effect is stronger along the zigzag direction, resulting in a smaller maximum strain for quality factor enhancement.

We investigate the impact of strained nanobubbles on the conductance characteristics of graphene nanoribbons using a combined molecular dynamics - tight-binding simulation scheme. We describe in detail how the conductance, density of states, and current density of zigzag or armchair graphene nanoribbons are modified by the presence of a nanobubble. In particular, we establish that low-energy electrons can be confined in the vicinity or within the nanobubbles by the delicate interplay between the pseudomagnetic field pattern created by the shape of the bubble, mode mixing, and substrate interaction. The coupling between confined evanescent states and propagating modes can be enhanced under different clamping conditions, which translates into Fano resonances in the conductance traces., Comment: 13 pages, 8 figures

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., Comment: Physical Review B, accepted

We report, based on its variation in electronic transport to coupled tension and shear deformation, a highly sensitive graphene-based strain sensor consisting of an armchair graphene nanoribbon (AGNR) between metallic contacts. As the nominal strain at any direction increases from 2.5 to 10%, the conductance decreases, particularly when the system changes from the electrically neutral region. At finite bias voltage, both the raw conductance and the relative proportion of the conductance depends smoothly on the gate voltage with negligible fluctuations, which is in contrast to that of pristine graphene. Specifically, when the nominal strain is 10% and the angle varies from 0 degree to 90 degree, the relative proportion of the conductance changes from 60 to 90%., Comment: 4 pages, 3 figures

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., Comment: 9 figures, 3 tables

The interlayer breathing and shear modes in few-layer black phosphorus are investigated for their symmetry and lattice dynamical properties. The symmetry groups for the even-layer and odd-layer few-layer black phosphorus are utilized to determine the irreducible representation and the infrared and Raman activity for the interlayer modes. The valence force field model is applied to calculate the eigenvectorw and frequencies for the interlayer breathing and shear modes, which are explained using the atomic chain model. The anisotropic puckered configuration for black phosphorus leads to a highly anisotropic frequency for the two interlayer shear modes. More specifically, the frequency for the shear mode in the direction perpendicular to the pucker is less than half of the shear mode in the direction parallel with the pucker. We also report a set of interlayer modes having the same frequency for all few-layer black phosphorus with layer number N=3i with integer i, because of their collective vibrational displacements. The optical activity of the collective modes supports possible experimental identification for these modes., Comment: 10 figures, 7 tables