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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 $\ensuremath{\pi}\ensuremath{-}\ensuremath{\sigma}$ 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 ${\mathrm{MoS}}_{2}$ having a flexoelectric constant ten times larger than graphene.

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.

Flexoelectricity is an electromechanical coupling occurring in dielectric materials that has recently attracted significant attention. The flexoelectric effect is described by a coupled, higher-order electromechanical set of equations that have typically been solved using a computationally expensive monolithic formulation. In the present work, we propose a staggered, explicit-implicit formulation that both significantly reduces the computational expense, while enabling the capturing of electromechanical instabilities through the usage of inertia. The higher order equations are discretized using an isogeometric formulation, and we demonstrate via two numerical examples the combination of increased computational efficiency with comparable accuracy that is gained from the proposed formulation as compared to the standard monolithic approaches.

The coefficient of thermal expansion, which measures the change in length, area, or volume of a material upon heating, is a fundamental parameter with great relevance for many applications. Although there are various routes to design materials with targeted coefficient of thermal expansion at the macroscale, no approaches exist to achieve a wide range of values in graphene-based structures. Here, we use molecular dynamics simulations to show that graphene origami structures obtained through pattern-based surface functionalization provide tunable coefficients of thermal expansion from large negative to large positive. We show that the mechanisms giving rise to this property are exclusive to graphene origami structures, emerging from a combination of surface functionalization, large out-of-plane thermal fluctuations, and the three-dimensional geometry of origami structures.

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.

This year marks the eightieth anniversary of the invention of the finite element method (FEM). FEM has become the computational workhorse for engineering design analysis and scientific modeling of a wide range of physical processes, including material and structural mechanics, fluid flow and heat conduction, various biological processes for medical diagnosis and surgery planning, electromagnetics and semi-conductor circuit and chip design and analysis, additive manufacturing, i.e. virtually every conceivable problem that can be described by partial differential equations (PDEs). FEM has fundamentally revolutionized the way we do scientific modeling and engineering design, ranging from automobiles, aircraft, marine structures, bridges, highways, and high-rise buildings. Associated with the development of finite element methods has been the concurrent development of an engineering science discipline called computational mechanics, or computational science and engineering. In this paper, we present a historical perspective on the developments of finite element methods mainly focusing on its applications and related developments in solid and structural mechanics, with limited discussions to other fields in which it has made significant impact, such as fluid mechanics, heat transfer, and fluid-structure interaction. To have a complete storyline, we divide the development of the finite element method into four time periods: I. (1941-1965) Early years of FEM; II. (1966-1991) Golden age of FEM; III. (1992-2017) Large scale, industrial applications of FEM and development of material modeling, and IV (2018-) the state-of-the-art FEM technology for the current and future eras of FEM research. Note that this paper may not strictly follow the chronological order of FEM developments, because often time these developments were interwoven across different time periods.

Soft, active materials have been widely studied due to their ability to undergo large, complex shape changes in response to both mechanical and non-mechanical external stimuli. However, the vast majority of such studies has focused on investigating the forward problem, i.e. determining the shape changes that result from the applied stimuli. In contrast, very little work has been done to solve the inverse problem, i.e. that of identifying the external loads and stimuli that are needed to generate desired shapes and morphological changes. In this work, we present a new inverse methodology to study residual thermal expansion induced morphological changes in geometric composites made of soft, thin shells. In particular, the method presented in this work aims to determine the prescribed external stimuli needed to reconstruct a specific target shape, with a specific focus and interest in morphological changes from two-dimensional (2D) to three-dimensional (3D) shapes by considering the external stimuli within a thermohyperelastic framework. To do so, we utilize a geometrically exact, rotation-free Kirchhoff–Love shell formulation discretized by NURBS-based shape functions. We show that the proposed method is capable of identifying the stimuli, including cases where thermal expansion induced shape changes involving elastic softening occur in morphing from the initially flat 2D to non-planar 3D shapes. Validation indicates that the reconstructed shapes are in good agreement with the target shape.

Because phononic topological insulators have primarily been studied in discrete, graphenelike structures with ${C}_{6(v)}$ or ${C}_{3(v)}$ hexagonal symmetry, an open question is how to systematically achieve double Dirac cones and topologically nontrivial structures using continuous, nonhexagonal unit cells. Here, we address this challenge by presenting a computational methodology for the inverse design of continuous two-dimensional square phononic metamaterials exhibiting ${C}_{4(v)}$ and ${C}_{2(v)}$ 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.

International audience; We present a topology optimization framework to design periodic composites comprised of piezoelectric constituents that exhibit large flexoelectric constants. The novelty of the approach is that it leverages a representative volume element (RVE)-based computational homogenization approach that enables the analysis of periodic composites where the characteristic dimensions of the microstructure are significantly smaller than those of the structure, and as such requires only the optimization of a single RVE rather than that of the entire structure. We utilize this approach to analyze the enhancement in flexoelectric constants that can be achieved in different types of PZT-based composites, including hard-hard (PZT-PZT), and hard-soft (PZT-polymer composite, and porous PZT) structures. In all cases, significant enhancements are observed, with improvements between 2 and 15 times those of a naive guess, with some designs reaching a factor of one order of magnitude larger than BTO. We identify different mechanisms governing the enhanced electromechanical couplings, which can arise either from an enhancement of effective piezoelectricity in the RVE for PZT-PZT composites, or from a more subtle interplay involving the enhancement of effective piezoelectric and dielectric properties coupled with a reduction in mechanical compliance for PZT-polymer and porous PZT RVEs.

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.

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.

The successful discovery and isolation of graphene in 2004, and the subsequent synthesis of layered semiconductors and heterostructures beyond graphene have led to the exploding field of two-dimensional (2D) materials that explore their growth, new atomic-scale physics, and potential device applications. This review aims to provide an overview of theoretical, computational, and machine learning methods and tools at multiple length and time scales, and discuss how they can be utilized to assist/guide the design and synthesis of 2D materials beyond graphene. We focus on three methods at different length and time scales as follows: (i) nanoscale atomistic simulations including density functional theory (DFT) calculations and molecular dynamics simulations employing empirical and reactive interatomic potentials; (ii) mesoscale methods such as phase-field method; and (iii) macroscale continuum approaches by coupling thermal and chemical transport equations. We discuss how machine learning can be combined with computation and experiments to understand the correlations between structures and properties of 2D materials, and to guide the discovery of new 2D materials. We will also provide an outlook for the applications of computational approaches to 2D materials synthesis and growth in general.

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.

Understanding the time-dependent mechanical behavior of nanomaterials such as nanowires is essential to predict their reliability in nanomechanical devices. This understanding is typically obtained using creep tests, which are the most fundamental loading mechanism by which the time-dependent deformation of materials is characterized. However, due to existing challenges facing both experimentalists and theorists, the time-dependent mechanical response of nanowires is not well-understood. Here, we use atomistic simulations that can access experimental time scales to examine the creep of single-crystal face-centered cubic metal (Cu, Ag, Pt) nanowires. We report that both Cu and Ag nanowires show significantly increased ductility and superplasticity under low creep stresses, where the superplasticity is driven by a rate-dependent transition in defect nucleation from twinning to trailing partial dislocations at the micro- or millisecond time scale. The transition in the deformation mechanism also governs a corresponding transition in the stress-dependent creep time at the microsecond (Ag) and millisecond (Cu) time scales. Overall, this work demonstrates the necessity of accessing time scales that far exceed those seen in conventional atomistic modeling for accurate insights into the time-dependent mechanical behavior and properties of nanomaterials.

This article presents original work combining a NURBS-based inverse analysis with both kinematic and constitutive nonlinearities to recover the applied loads and deformations of thin shell structures. The inverse formulation is tackled by gradient-based optimization algorithms based on computed and measured displacements at a number of discrete locations. The proposed method allows accurately recovering the target shape of shell structures such that instabilities due to snapping and buckling are captured. The results obtained show good performance and applicability of the proposed algorithms to computer-aided manufacturing of shell structures.

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.

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.

Nanomaterials have recently been found to exhibit auxetic behavior, or a negative Poisson’s ratio, whereby the lateral dimensions of the material expand, rather than shrink, in response to applied tensile loading. In this brief review, we use the form of question–answer to highlight key points and outstanding issues related to the field of auxetic nanomaterials.

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.

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.

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.

We characterize the force-dependent unfolding pathways and intermediate configurations of the green fluorescence protein (GFP) using novel atomistic simulations based on potential energy surface exploration. By using this approach, we are able to unfold GFP to significantly longer end-to-end distances, i.e. 40 nm, as compared to that seen in previous atomistic simulation studies. We find that there are four intermediate states between 5 and 40 nm end-to-end distance, where the intermediate configurations and unfolding pathways are strongly force-dependent. We additionally calculate the force-dependent lifetime of the 14 nm α β 1 intermediate, and demonstrate that it obeys Bell’s formula.

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

Oligomeric and fibrillar amyloids, which cause neurodegenerative diseases, are typically formed through repetitive fracture and elongation processes involving single homogeneous amyloid monomers. However, experimental and computational methods have shown that the amyloid proteins could be composed of heterogeneous amyloid segments. Specifically, owing to the polymorphism of amyloids under physiological conditions, it is crucial to understand the structural characteristics of heterogeneous amyloids in detail by considering their specific mutations and polymorphic nature. Therefore, in this study we used atomistic simulations to reveal the various structural characteristics of heterogeneous amyloids, which are amyloids composed of amyloid beta (Aβ) and mutated tau proteins. Furthermore, we showed that the different characteristics and conformations of Aβ–tau mixtures are the cause of the different types of tau proteins based on Aβ segments. Interestingly, we found that valine and lysine residues have a significant impact on the structural conformation and stability of the heterogeneous Aβ–tau mixtures. We also showed that two types of binding are key to understanding the different binding features and mechanical reactions to tensile load. This study sheds light on the assembly features of heterogeneous Aβ–tau mixtures as neurodegenerative disease factors.

Inspired by macroscale self-assembly using the higher order resonant modes of Chladni plates, we use classical molecular dynamics to investigate the self-assembly of water molecules using graphene nanoresonators. We find that water molecules can assemble into water chains and that the location of the assembled water chain can be controlled through the resonant frequency. More specifically, water molecules assemble at the location of maximum amplitude if the resonant frequency is lower than a critical value. Otherwise, the assembly occurs near the nodes of the resonator provided the resonant frequency is higher than the critical value. We provide an analytic formula for the critical resonant frequency based on the interaction between water molecules and graphene. Furthermore, we demonstrate that the water chains assembled by the graphene nanoresonators have some universal properties including a stable value for the number of hydrogen bonds.

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

P.Z.H. developed the theory, wrote the paper, and performed the DFT calculations. A.S.R. contributed to the analytical work. H.S.P., D.K.C., and A.C.H.N. supervised the research. We thank Vitor M. Pereira for useful comments and discussions. P.Z.H., H.S.P., and D.K.C. acknowledge support by the Boston University Materials Science and Engineering Innovation Grants. P.Z.H, H.S.P., and D.K.C are grateful for computing resources provided by the Boston University Shared Computing Cluster. (Boston University Materials Science and Engineering Innovation Grants)

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., Soft Matter, 2017

In mechanical systems, Maxwell-Betti reciprocity means that the displacement at point B in response to a force at point A is the same as the displacement at point A in response to the same force applied at point B. Because the notion of reciprocity is general, fundamental, and is operant for other physical systems like electromagnetics, acoustics, and optics, there is significant interest in understanding systems that are not reciprocal, or exhibit non-reciprocity. However, most studies on non-reciprocity have occurred in bulk-scale structures for dynamic problems involving time reversal symmetry. As a result, little is known about the mechanisms governing static non-reciprocal responses, particularly in atomically-thin two-dimensional materials like graphene. Here, we use classical atomistic simulations to demonstrate that out-of-plane ripples, which are intrinsic to graphene, enable significant, multiple orders of magnitude enhancements in the statically non-reciprocal response of graphene metamaterials. Specifically, we find that a striking interplay between the ripples and the stress fields that are induced in the metamaterials due to their geometry impacts the displacements that are transmitted by the metamaterial, thus leading to a significantly enhanced static non-reciprocal response. This study thus demonstrates the potential of two-dimensional mechanical metamaterials for symmetry-breaking applications.

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., Journal of Applied Physics, accepted

We present a computational method for the optimization of nanostructures, where our specific interest is in capturing and elucidating surface stress and surface elastic effects on the optimal nanodesign. XFEM is used to solve the nanomechanical boundary value problem, which involves a discontinuity in the strain field and the presence of surface effects along the interface. The boundary of the nano-structure is implicitly represented by a level set function, which is considered as the design variable in the optimization process. Two objective functions, minimizing the total potential energy of a nanostructure subjected to a material volume constraint and minimizing the least square error compared to a target displacement, are chosen for the numerical examples. We present results of optimal topologies of a nanobeam subject to cantilever and fixed boundary conditions. The numerical examples demonstrate the importance of size and aspect ratio in determining how surface effects impact the optimized topology of nanobeams.

The distinguishing structural feature of single-layer black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger-Weber potential for single-layer black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the longitudinal direction. As a consequence, single-layer black phosphorus has a negative Poisson's ratio in the direction perpendicular to the atomic plane. As an additional demonstration of the impact of the cross-pucker interaction, we show that it is also the key factor that enables capturing of the edge stress-induced bending of single-layer black phosphorus that has been reported in ab initio calculations., Nanoscale, published

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., 13 pages, 8 figures

The HET-s prion fibril, which is found in the filamentous fungus Podospora anserina, exhibits conformational changes due to variations in pH. Here, we explain the effects of changing pH on the conformational changes of fibrils through the fundamental eigenmodes of the fibrils, in particular the torsional and bending modes, using a parameter free elastic network model. In particular, the motion resulting from these fundamental eigenmodes is found to be very similar to the conformational changes stimulated by pH variations as shown in previous experimental results. Finally, we calculated the mechanical properties of the triplet prion fibrils to elucidate its variations in the infectious state.

The band structure of a general class of buckled square lattice materials is investigated using ab initio calculations along with tight-binding modeling. We show that buckling and spin-orbit interaction give rise to a large Rashba-like splitting in the absence of an external electric field. The generality and the robustness of the effect make this class of materials promising candidates for spintronic applications.

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.

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

We present a dynamic finite element formulation for dielectric elastomers that significantly alleviates the problem of volumetric locking that occurs due to the incompressible nature of the elastomers. We accomplish this by modifying the Q1P0 formulation of Simo et al. [1] , and adapting it to the electromechanical coupling that occurs in dielectric elastomers. We demonstrate that volumetric locking has a significant impact on the critical electric fields that are necessary to induce electromechanical instabilities such as creasing and cratering in dielectric elastomers, and that the locking effects are most severe in problems related to recent experiments that involve significant constraints upon the deformation of the elastomers. We then compare the results using the new Q1P0 formulation to that obtained using standard 8-node linear and 27-node quadratic hexahedral elements to demonstrate the capability of the proposed approach. Finally, direct comparison to the recent experimental work on the creasing instability on dielectric polymer surface by Wang et al. [2] is presented. The present formulation demonstrates good agreement to experiment for not only the critical electric field for the onset of the creasing instability, but also the experimentally observed average spacing between the creases.

We present a new determination of the Ds decay constant, f_{Ds} using 5 million continuum charm events obtained with the CLEO II detector. Our value is derived from our new measured ratio of widths for Ds -> mu nu/Ds -> phi pi of 0.173+/- 0.021 +/- 0.031. Taking the branching ratio for Ds -> phi pi as (3.6 +/- 0.9)% from the PDG, we extract f_{Ds} = (280 +/- 17 +/- 25 +/- 34){MeV}. We compare this result with various model calculations., 23 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLNS

Using the CLEO~II detector, we have measured the differential cross sections for exclusive two-photon production of light pseudoscalar mesons $\pi^0$, $\eta$, and $\eta^{\prime}$. From our measurements we have obtained the form factors associated with the electromagnetic transitions $\gamma^*\gamma$ $\to$ meson. We have measured these form factors in the momentum transfer ranges from 1.5 to 9, 20, and 30 GeV$^2$ for $\pi^0$, $\eta$, and $\eta^{\prime}$, respectively, and have made comparisons to various theoretical predictions., Comment: 30 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLNS

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., 10 pages, 10 figures

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

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.