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• Theory of lattice metamaterials under sinusoidal distributed static loads • Two basic modes of static damping of distributed pressure waves are identified • Dependence of effective shear modulus on a spatial frequency of the load • Pathway toward intelligent mechanical systems able to distinguish load patterns We discuss response properties of lattice metamaterials to sinusoidal distributed static loads applied on a material edge. Analytical displacement solutions are obtained using a Fourier domain transfer matrix for both essential and natural boundary conditions, which are valid for a state of plane strain in orthorhombic lattices, as well as for planar metasurfaces. These solutions give sinusoidal displacement profiles in the material interior of the same wavenumber (spatial frequency) as the boundary load. Their amplitudes decay in the material interior in one of two possible ways, exponential or oscillatory exponential, depending on the lattice design and on the spatial frequency of the load. There is a tendency for the oscillatory exponential behavior to occur at lower wavenumbers representing smoother boundary loads. As explained on a specific example, comparing the metamaterial's response amplitudes with those of a homogenous material also allows studying an effective, wavenumber-dependent shear modulus of the lattice, which can take both positive and negative values. [ABSTRACT FROM AUTHOR]

A class of beam-like lattice structures, or metabeams under static, sinusoidally distributed transverse loads is discussed. Their neutral axis deflects either in-phase, out-of-phase or shows no deflection, depending on the beam design parameters, and also on the spatial frequency of the static load. These outcomes contrast the behavior of continuum beams, deflecting always in-phase with the load, and they are interpreted on the basis of a positive, negative and near-infinite effective Young's modulus of the structured beams in bending. They also represent a collective effect of the behavior of multiple elements in the lattice that cannot be realized from the performance of an isolated unit cell. A long-range periodic order and nonlocality of the lattice interaction is essential for this unusual behaviors, and those are particularly pronounced at higher wavenumbers, when the load wavelength becomes comparable with the range of direct interactions in the lattice. Theoretical discussion and predictions agree well with numerical experiments performed on the basis of commonly accepted models. Practical applications could be found in advanced reinforcing materials for building foundations, deformation mitigation for lightweight structures and bridges, and in smart mechanical systems able to differentiate external stimuli and to respond selectively. [ABSTRACT FROM AUTHOR]

This discussion starts with a mechanics version of Parseval's energy theorem applicable to any discrete lattice material with periodic internal structure: a microtruss, grid, frame, origami or tessellation. It provides a simple relationship between the strain energy volumetric/usual and spectral distributions in the reciprocal space. The spectral energy distribution leads directly to a spectral entropy of lattice deformation (Shannon's type), whose variance with a material coordinate represents the decrease of information about surface loads in the material interior. Spectral entropy is also a basic measure of complexity of mechanical responses of metamaterials to surface and body loads. Considering transformation of the energy volumetric and spectral distributions with a material coordinate pointed away from a surface load, several interesting anomalies are seen even for simple lattice materials, when compared to continuum materials. These anomalies include selective filtering of surface Raleigh waves (sinusoidal pressure patterns), Saint-Venant effect inversion illustrated by energy spectral distribution contours, occurrence of 'hiding pockets' of low deformation, and redirection of strain energy maximum away from axis of a concentrated surface load. The latter phenomenon can be significant for impact protection applications of mechanical metamaterials. [ABSTRACT FROM AUTHOR]

Highlights • Mechanics analogue of the Parseval's energy theorem is discussed, leading to a spectral density of the strain energy (in a reciprocal space). • Energy spectral density reflects the ways how an elastic medium translates static deformation patterns between two points in space. • Spectral entropy of static deformation is proposed, as a measure of information available in the material interior about surface loads or disorder introduced into elastic medium by deformation. • Both differential and discrete/numerical entropies of Shannon's type are discussed, and the differential entropy is derived analytically for isotropic solids under Gauss loads. • Approaches to numerical calculation of spectral entropy in computational solid mechanics are discussed. Abstract A broader range of analytical tools can enhance understanding of the unusual mechanical properties of metamaterials and other advanced material systems. Here, we discuss a mechanics analogue of the Parseval's energy theorem that leads to a density of the strain energy in the reciprocal space. It reflects the ways for an elastic medium to translate static deformation patterns between two points in space. A normalized spectral density also provides an information entropy of deformation at those points. Both differential and discrete (numerical) entropies of the Shannon's type are discussed. Spectral entropy is a basic measure of information available in the material interior about surface loads, or a measure of disorder introduced into elastic medium by the deformation. An exact analytical entropy function is derived for an isotropic plane solid under Gauss-distributed and point loads. Approaches to numerical calculation of spectral entropy in computational solid mechanics are also discussed. Energy spectral density and spectral entropy of an elastic continuum is shown to translate, logically, in agreement with the Saint-Venant's principle. However, it also becomes clear that microstructured media may demonstrate anomalous pathways of evolution of the strain energy spectrum, enabling interesting transformation mechanics studies of engineered material systems. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

Negative extensibility metamaterials are able to contract against the line of increasing external tension. A bistable unit cell exhibits several nonlinear mechanical behaviors including the negative extensibility response. Here, an exact form of the total mechanical potential is used based on engineering strain measure. The mechanical response is a function of the system parameters that specify unit cell dimensions and member stiffnesses. A phase diagram is calculated, which maps the response to regions in the diagram using the system parameters as the coordinate axes. Boundary lines pinpoint the onset of a particular mechanical response. Contour lines allow various material properties to be fine-tuned. Analogous to thermodynamic phase diagrams, there exist singular “triple points” which simultaneously satisfy conditions for three response types. The discussion ends with a brief statement about how thermodynamic phase diagrams differ from the phase diagram in this paper. [ABSTRACT FROM AUTHOR]

When a usual material is loaded statically at surfaces, fine fluctuations of surface strain diminish fast in the material volume with the distance to the surface, a phenomenon widely known as the Saint-Venant edge effect. In this paper, highly nonlocal discrete lattices are explored to demonstrate structural metamaterials featuring reversal of the Saint-Venant edge effect. In these materials, certain coarse patterns of surface strain may decay faster than the finer ones. This phenomenon is shown to arise from anomalous behavior of the Fourier modes of static deformation in the material, and creates opportunities for blockage, qualitative modification and in-situ recognition of surface load patterns. Potential applications and useful practical techniques of spectral analysis of deformation, density of states and phase diagram mapping are outlined. [ABSTRACT FROM AUTHOR]

We report on excellent hydrogen sensing properties of a Pt/TiO 2 system based on mesoporous titania grown by plasma electrolytic oxidation of a Ti metal substrate. The Pt phase is deposited onto the titania surface as an electrically continuous Pt nanomesh layer with an e-beam process. Resistive sensor response between the Pt and Ti terminals of the resultant structure is studied at room temperature for different partial pressures of H 2 gas (0.003–3 Torr) and different source voltages (0.5–2.0 V). A maximum resistance effect, reaching four orders of the magnitude for 3 Torr H 2 in 160 Torr O 2 is obtained at the bias voltage 1.4 V, and a strong effect is detected for only 0.003 Torr, or 20 ppm H 2 concentration. For voltages in the range 1.0–1.4 V, electrical conductance of the sample is about a linear function of the H 2 partial pressure in the gas phase. Influence of the background atmosphere (O 2 , N 2 and vacuum) and the effect of bias reversal were investigated also, leading to a conclusion that the sensing mechanism can be related to ionic transport in the TiO 2 layer. [ABSTRACT FROM AUTHOR]

This work provides a discussion of bistability conditions, switching autowave properties and emergence of dissipative structures in semiconducting fibers with anomalous positive dependence of electrical resistivity on temperature of sigmoid type, (1 + e −T )−1. An open system thermodynamics approach is utilized for the analysis of this dissipative solid-state system. The approach aims to represent the structure of the solution space of its governing equation in the form of physical phase diagrams, known as non-equilibrium phase diagrams, and two specific binary diagrams have been obtained here. One of the diagrams, where the electrical power density and ambient temperature represent external parameters, shows a wide region with dissipative structures as non-uniform steady-state temperature profiles on the fiber. The possibility of efficient external control over the dissipative structure geometry is also demonstrated. [ABSTRACT FROM PUBLISHER]

Abstract: We demonstrate a concept of molecular hydrogen sensor operable continuously in oxygen-rich atmosphere, using a Pd/n-SiC heterojunction structure with nanometer thickness metallization. The sensing mechanism is based on the excitation of hot electrons in the Pd nanofilm traveling ballistically over the Schottky barrier and toward the semiconductor layer to constitute a detectable electric current. If molecular oxygen is also present in the host ambient, the hydrogen sensitivity of the device increases by an order of the magnitude and the generated current acquires a stationary character. Magnitude of the stationary current is linearly proportional to the mixture pressure and to the rate of hydrogen-to-water oxidation process occurring on the Pd nanofilm surface. Hydrogen sensors of the present type can have very fast response and recovery times of only several seconds. [Copyright &y& Elsevier]

Coupled multiscale approaches for the analysis and simulation of complex multiphysics phenomena in solids have been of great interest during the past decade. These include concurrent MD/FEM models, atomistic-to-continua homogenization techniques and deterministic multiple time scale approaches. In this article we discuss a generic approach to concurrently couple the Monte-Carlo master equation of microscopic kinetic processes, not accessible by the direct particle dynamics, with the continuum mechanics formulation. This approach can be adequate for the modeling and validation of advanced contemporary materials with dynamic internal structure, as well as evolutionary and degradation processes in materials. The approach is illustrated in the application to the models of interstitial and vacancy diffusion in fuel cell catalysts and binary material systems. [ABSTRACT FROM AUTHOR]

Abstract: We report on the luminescence of Eu3+-doped yttrium oxide phosphors brought in contact with oxyhydrogen gas mixtures at temperatures much below the gas-phase ignition point. Chemical energy released in the catalytic hydrogen oxidation is passed directly to the electron subsystem of the powder and subsequently converted into the visible luminescence radiation at 2×10−6 quantum yield per H2O molecule produced. Luminescence kinetics at various conditions are investigated to reveal the constituent stages of the catalytic energy conversion process. This observation could have far-reaching consequences including possibilities for the development of original chemiluminescent light sources, and novel electrochemical energy converters. [Copyright &y& Elsevier]

Abstract: In this paper, a quasi-static formulation of the method of multi-scale boundary conditions (MSBCs) is derived and applied to atomistic simulations of carbon nano-structures, namely single graphene sheets and multi-layered graphite. This domain reduction method allows for the simulation of deformable boundaries in periodic atomic lattice structures, reduces the effective size of the computational domain, and consequently decreases the cost of computations. The size of the reduced domain is determined by the value of the domain reduction parameter. This parameter is related to the distance between the boundary of the reduced domain, where MSBCs are applied, and the boundary of the full domain, where the standard displacement boundary conditions are prescribed. Two types of multi-scale boundary conditions are derived: one for simulating in-layer multi-scale boundaries in a single graphene sheet and the other for simulating inter-layer multi-scale boundaries in multi-layered graphite. The method is tested on benchmark nano-indentation problems and the results are consistent with the full domain solutions. [Copyright &y& Elsevier]

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

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

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

We present a method for deriving molecular dynamics boundary conditions for use in multiple scale simulations that can be applied at a planar boundary for any solid that has a periodically repeating crystal lattice. The method is based on a linearization in the vicinity of the boundary, and utilizes a Fourier and Laplace transforms in space and time to eliminate the degrees of freedom associated with atoms outside the boundary. This method is straightforward to implement numerically, and thus can be automated for a general crystal lattice. We show that this method reproduces the known kernel for a 1D linear chain, and apply the approach to obtain the damping kernel matrices for two real crystal lattices: the graphene and diamond structures of carbon. [Copyright &y& Elsevier]

• Analytical nodal displacement solutions are derived in 2D plate-like lattices • Periodic boundary conditions on side surfaces form the topological cylinder • Solutions are the superposition of Fourier mode dependent states of deformation • Analytical solutions are validated with finite element analysis software Abaqus™ Nodal displacements for two dimensional plate-like lattices under static loading are solved in exact analytical form, when periodic boundary conditions are applied to the top and bottom surfaces of the lattice forming a topological cylinder. Discrete Fourier transform converts the governing equation of static equilibrium into a set of one dimensional wavenumber dependent problems. Characteristic solutions are developed for each Fourier mode of deformation. Inverse discrete Fourier transform converts the wavenumber domain function back to the spatial domain by taking a linear combination of the one dimensional harmonic solutions. As an example, the point force is decomposed into a set of wavenumber dependent loading profiles. A linear combination of the displacement solutions for the individual harmonic loading profiles is sufficient to reproduce the overall displacement solution for the point load. This property holds for any type of the load. Nodal displacements, expressed with analytical dependence on the nodal indices n and m , match the results of commercial finite element analysis software. Overall, this paper demonstrates that the static response of discrete lattices is equivalently represented as a superposition of the wavenumber domain solutions, which is analogous to frequency domain analysis in acoustic metamaterials and phononics. [ABSTRACT FROM AUTHOR]

This paper discusses an x-braced metamaterial lattice with the unusual property of exhibiting bandgaps in their deformation decay spectrum, and, hence, the capacity for reprogramming deformation patterns. The design of polarizing non-local lattice arising from the scenario of repeated zero eigenvalues of a system transfer matrix is also introduced. We develop a single mode fundamental solution for lattices with multiple degrees of freedom per node in the form of static Raleigh waves. These waves can be blocked at the material boundary when the solution is constructed with the polarization vectors of the bandgap. This single mode solution is used as a basis to build analytical displacement solutions for any applied essential and natural boundary condition. Subsequently, we address the bandgap design, leading to a comprehensive approach for predicting deformation pattern behavior within the interior of an x-braced plane lattice. Overall, we show that the stiffness parameter and unit-cell aspect ratio of the x-braced lattice can be tuned to completely block or filter static boundary deformations, and to reverse the dependence of deformation or strain energy decay parameter on the Raleigh wavenumber, a behavior known as the reverse Saint Venant's edge effect (RSV). These findings could guide future research in engineering smart materials and structures with interesting functionalities, such as load pattern recognition, strain energy redistribution, and stress alleviation. [ABSTRACT FROM AUTHOR]

A negative extensibility material structure pulls back and contracts when the external tensile load reaches a certain critical level. In this paper, we reveal basic mathematical features of the nonlinear strain energy function responsible for this unusual mechanical property. A systematic discussion leads to a comprehensive phase diagram in terms of design parameters for a simple unit cell structure that provides a panoramic view of all possible nonlinear mechanical behaviors. A negative extensibility region clearly is identified in the diagram. The sought property is seen to be rare, occurring only for a very narrow range of the design parameters. Nonetheless, due to the simplicity of the studied structure we suggest that the negative extensibility should be a more common phenomenon than previously thought. It can appear in simple bistable cells made of only several linearly elastic links, although at some peculiar combinations of their properties. These bistable unit cells can be used to design periodic mechanical metamaterials whose examples are shown as well as innovative architectural metastructures. [ABSTRACT FROM AUTHOR]

We report on conversion of energy released due to chemical reactions into current for the decomposition of aqueous hydrogen peroxide solution on single phases Pt and TiO 2 , in addition to Pt and TiO 2 simultaneously. We observe that H 2 O 2 decomposition-induced current on TiO 2 drastically overshadows the current generated by H 2 O 2 decomposition on Pt. Photo-effects avoided, H 2 O 2 decomposition was found to yield a conversion efficiency of 10 −3 electrons generated per H 2 O 2 molecule. Further understanding of chemical reaction-induced current shows promise as a metric with which the surface reaction may be monitored and could be greatly extended into the field of analytical chemistry. [ABSTRACT FROM AUTHOR]

Negative thermal expansion is an interesting and appealing phenomenon for various scientific and engineering applications, while rarely occurring in natural materials. Here, using a universal antichiral metamaterial model with bimetal beams or strips, a generic theory has been developed to predict magnitude of the negative thermal expansion effect from model parameters. Thermal expansivity of the metamaterial is written as an explicit function of temperature and only three design parameters: relative node size, chirality angle, and a bimetal constant. Experimental measurements follow theoretical predictions well, where thermal expansivity in the range of negative 0.0006–0.0041 °C−1 has been seen. [ABSTRACT FROM AUTHOR]

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