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We explore dynamic structural superlubricity for the case of a relatively large contact area, where the friction force is proportional to the area (exceeding $\sim 100\,nm^2$) experimentally, numerically, and theoretically. We use a setup comprised of two molecular smooth incommensurate surfaces -- graphene-covered tip and substrate. The experiments and MD simulations demonstrate independence of the friction force on the normal load, for a wide range of normal loads and relative surface velocities. We propose an atomistic mechanism of this phenomenon, associated with synchronic out-of-plane surface fluctuations of thermal origin, and confirm it by numerical experiments. Based on this mechanism, we develop a theory for this type of superlubricity and show that friction force increases linearly with increasing temperature and relative velocity, for velocities, larger than a threshold velocity. The MD results are in a fair agreement with predictions of the theory., Comment: Accepted to Physical Review Letters on November 14, 2023

Discrete particle simulations have become the standard in science and industrial applications exploring the properties of particulate systems. Most of such simulations rely on the concept of interacting spherical particles to describe the properties of particulates, although, the correct representation of the nonspherical particle shape is crucial for a number of applications. In this work we describe the implementation of clumps, i.e. assemblies of rigidly connected spherical particles, which can approximate given nonspherical shapes, within the \textit{MercuryDPM} particle dynamics code. \textit{MercuryDPM} contact detection algorithm is particularly efficient for polydisperse particle systems, which is essential for multilevel clumps approximating complex surfaces. We employ the existing open-source \texttt{CLUMP} library to generate clump particles. We detail the pre-processing tools providing necessary initial data, as well as the necessary adjustments of the algorithms of contact detection, collision/migration and numerical time integration. The capabilities of our implementation are illustrated for a variety of examples.

The paper is concerned with the problem of toppling propagation velocity in elastic, domino-like mechanical systems. We build on the work of Efthimiou and Johnson, who developed the theory of perfectly elastic collisions of thin rigid dominoes on a frictional foundation. This theory has been criticised for the lack of correspondence with the experimental observations, in particular, prediction of infinite propagation velocity for zero spacing between dominoes, as well as the inability to represent the collective nature of collisions in real domino systems. In our work we consider a more realistic scenario of dominoes of finite stiffness and obtain a theory of fast elastic domino waves, taking into account a limit velocity of the perturbation propagation in the system of dominoes. Moreover, finite collision time allows to extract dynamic quantities of collisions and establish upper and lower borders for domino separations where the theory could still be applied. Our discrete element simulations support our theoretical findings and shed light on the nature of collective interactions in the nearly-elastic domino chains.

Fabrication of nanostructured metasurfaces poses a significant technological and fundamental challenge. Despite developing novel systems that support reversible elongation and distortion, their nanoscale patterning and control of optical properties remain an open problem. Herein we report the atomic force microscope lithography (AFML) application for nanoscale patterning of single-walled carbon nanotube films and the associated reflection coefficient tuning. We present models of bundling reorganization, formed-pattern stability, and energy distribution describing mechanical behavior with mesoscopic distinct element method (MDEM). All observed and calculated phenomena support each other and present a platform for developing AFML patterned optical devices using meshy nanostructured matter.

The paper describes a novel methodology of designing granular phononic crystals for acoustic wave manipulations. A discrete element method is utilized to model the dynamics of a pulse wave propagating through the densely packed assembly of elastic spherical particles with an embedded phononic crystal - the region consisting of a certain arrangement of particles with varying densities. We suggest an optimization strategy that extremizes the useful properties of a granular phononic crystal, which are described in terms of a noise-proof functional based on frequency-wavenumber summation of spectral energy density. Few types of efficient phononic crystals are identified. The suggested methodology is of interest for a number of applications, in particular, for seismic shielding and selective sound absorption.

Nanometer thin single-walled carbon nanotube (CNT) films collected from the aerosol chemical deposition reactors have gathered attention for their promising applications. Densification of these pristine films provides an important way to manipulate the mechanical, electronic, and optical properties. To elucidate the underlying microstructural level restructuring, which is ultimately responsible for the change in properties, we perform large scale vector-based mesoscopic distinct element method simulations in conjunction with electron microscopy and spectroscopic ellipsometry characterization of pristine and densified films by drop-cast volatile liquid processing. Matching the microscopy observations, pristine CNT films with finite thickness are modeled as self-assembled CNT networks comprising entangled dendritic bundles with branches extending down to individual CNTs. Simulations of the film under uniaxial compression uncover an ultra-soft densification regime extending to a ~75% strain, which is likely accessible with the surface tensional forces arising from liquid surface tension during the evaporation. When removing the loads, the pre-compressed samples evolve into homogeneously densified films with thickness values depending on both the pre-compression level and the sample microstructure. The significant reduction in thickness, confirmed by our spectroscopic ellipsometry, is attributed to the underlying structural changes occurring at the 100 nm scale, including the zipping of the thinnest dendritic branches., Comment: 12 figures

Collapse modes in compressed simple cubic (SC) and body-centered cubic (BCC) periodic arrangements of elastic frictionless beads were studied numerically using the discrete element method. Under pure hydrostatic compression, the SC arrangement tends to transform into a defective hexagonal close-packed or amorphous structure. The BCC assembly exhibits several modes of collapse, one of which, identified as cI16 structure, is consistent with the behavior of BCC metals Li and Na under high pressure. The presence of a deviatoric stress leads to the transformation of the BCC structure into face-centered cubic (FCC) one via the Bain path. The observed effects provide important insights on the origins of mechanical behavior of atomic systems, while the elastic spheres model used in our work can become a useful paradigm, expanding the capabilities of a hard sphere model widely used in many branches of science.

In this paper we report a new promising idea on the design and manufacturing of ply composite structures, tailored to exhibit maximum stiffness under given weight constraints and loading conditions. It is based on the idea behind an artistic technique known as "string art" - the representation of an image with a single thread, tensioned between pins on the flat frame. A discrete optimization algorithm has been employed recently to formalize the process of finding a configuration of thread windings that fuses into a given greyscale image. We demonstrate how this algorithm can be employed to approximate the two-dimensional distribution of isotropic material, computed by a conventional topology optimization algorithm. An optimal composite design is thus found as a result of the following two-stage process. At the first stage, topology optimization procedure produces regular grid of greyscale values of stiffness. At the second stage, this distribution is approximated with a polyline, representing the stiff reinforcement fiber in a soft matrix, according to ``string art'' optimization algorithm. The efficiency of the proposed approach is illustrated with few simple numerical examples. Our development opens a wide avenue for the industrial design of the new generation of fibrous composite structures.

In this work we present a computational study of the small strain mechanics of freestanding ultrathin CNT films under in-plane loading. The numerical modeling of the mechanics of representatively large specimens with realistic micro- and nanostructure is presented. Our simulations utilize the scalable implementation of the mesoscopic distinct element method of the waLBerla multi-physics framework. Within our modeling approach, CNTs are represented as chains of interacting rigid segments. Neighboring segments in the chain are connected with elastic bonds, resolving tension, bending, shear and torsional deformations. These bonds represent a covalent bonding within CNT surface and utilize Enhanced Vector Model (EVM) formalism. Segments of the neighboring CNTs interact with realistic coarse-grained anisotropic vdW potential, enabling relative slip of CNTs in contact. The advanced simulation technique allowed us to gain useful insights on the behavior of CNT materials. In particular, it was established that the energy dissipation during CNT sliding leads to extended load transfer that conditions material-like mechanical response of the weakly bonded assemblies of CNTs.

A new mesoscale mechanical model, describing elastic interactions in carbon nanotubes (CNT) and other nanofilaments, is proposed. Functional form of the developed model is based on enhanced vector model (EVM) that describes basic types of bond deformations: tension, torsion, bending and shear. Calibration of bond stiffnesses is performed by adjusting EVM parameters to reproduce both CNT's deformation energies and shape observed in a full-atomistic simulation. The parameters obtained are compared with the ones obtained from Euler-Bernoulli beam theory considerations. It is found that after certain critical length of a tested CNT specimen its stiffness parameters become length-independent and can be used in mesoscale simulations of CNTs of arbitrary length.

A universal framework for modeling composites and fabrics of micro- and nanofibers, such as carbon nanotubes, carbon fibers and amyloid fibrils, is presented. Within this framework, fibers are represented with chains of rigid bodies, linked with elastic bonds. Elasticity of the bonds utilizes recently developed enhanced vector model formalism. The type of interactions between fibers is determined by their nature and physical length scale of the simulation. The dynamics of fibers is computed using the modification of rigid particle dynamics module of the waLBerla multiphysics framework. Our modeling system demonstrates exceptionally high parallel performance combined with the physical accuracy of the modeling. The efficiency of our approach is demonstrated with illustrative mechanical test on a hypothetical carbon nanotube textile.

In this paper we investigate numerically an instance of the problem of G-closure for two-dimensional periodic metamaterials. Specifically, we consider composites with isotropic homogenized elasticity tensor, obtained as a mixture of two isotropic materials, focusing on the case of a single material with voids. This problem is important, in particular, in the context of designing small-scale structures for metamaterials in the context of additive fabrication, as this type of metamaterials makes it possible to obtain a range of material properties using a single base material. We demonstrate that two closely related simple parametric families based on the structure proposed by O. Sigmund attain good coverage of the space of isotropic properties satisfying Hashin-Shtrikman bounds. In particular, for positive Poisson ratio, we demonstrate that Hashin-Shtrikman bound can be approximated arbitrarily well, within limits imposed by numerical approximation: a strong evidence that these bounds are achievable in this case. For negative Poisson ratios, we numerically obtain a bound which we hypothesize to be close to optimal, at least for metamaterials with rotational symmetries of a regular triangle tiling.

The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a topological derivative. The numerical solution of the elasticity boundary value problem at every iteration is performed with the boundary element formulation and the kernel-independent fast multipole method. Providing excellent single node performance, scalable parallelization and the best available asymptotic complexity, our method is among the fastest optimization tools available today. The performance of our approach is studied on few illustrative examples, including the optimization of engineered constructions for the minimum compliance and the optimization of the microstructure of a metamaterial for the desired macroscopic tensor of elasticity.

We apply the modern technique of approximation of multivariate functions - tensor train cross approximation - to the problem of the description of physical interactions between complex-shaped bodies in a context of computational nanomechanics. In this note we showcase one particular example - van der Waals interactions between two cylindrical bodies - relevant to modeling of carbon nanotube systems. The potential is viewed as a tensor (multidimensional table) which is represented in compact form with the help of tensor train decomposition. The described approach offers a universal solution for the description of van der Waals interactions between complex-shaped nanostructures and can be used within the framework of such systems of mesoscale modeling as recently emerged mesoscopic distinct element method (MDEM)., Comment: http://www.sciencedirect.com/science/article/pii/S0021999117303352

Wide variety of engineering design tasks can be formulated as constrained optimization problems where the shape and topology of the domain are optimized to reduce costs while satisfying certain constraints. Several mathematical approaches were developed to address the problem of finding optimal design of an engineered structure. Recent works have demonstrated the feasibility of boundary element method as a tool for topological-shape optimization. However, it was noted that the approach has certain drawbacks, and in particular high computational cost of the iterative optimization process. In this short note we suggest ways to address critical limitations of boundary element method as a tool for topological-shape optimization. We validate our approaches by supplementing the existing complex variables boundary element code for elastostatic problems with robust tools for fast topological-shape optimization. The efficiency of the approach is illustrated with a numerical example., Comment: Submitted as a technical brief to ASME Journal of Computing and Information Science in Engineering