Heterogeneous Solids Research Articles

Linking Scalar Elastodynamics and Non-Hermitian Quantum Mechanics

Recent years have seen a fascinating pollination of ideas from quantum theories to elastodynamics---a theory that phenomenologically describes the time-dependent macroscopic response of materials. Here, we open route to transfer additional tools from non-Hermitian quantum mechanics. We begin by identifying the differences and similarities between the one-dimensional elastodynamics equation and the time-independent Schrodinger equation, and finding the condition under which the two are equivalent. Subsequently, we demonstrate the application of the non-Hermitian perturbation theory to determine the response of elastic systems; calculation of leaky modes and energy decay rate in heterogenous solids with open boundaries using a quantum mechanics approach; and construction of degeneracies in the spectrum of these assemblies. The latter result is of technological importance, as it introduces an approach to harness extraordinary wave phenomena associated with non-Hermitian degeneracies for practical devices, by designing them in simple elastic systems. As an example of such application, we demonstrate how an assembly of elastic slabs that is designed with two degenerate shear states according to our scheme, can be used for mass sensing with enhanced sensitivity by exploiting the unique topology near the exceptional point of degeneracy.

Structure of shock waves in particulate composites

The shock compression response of particulate heterogeneous solids was investigated using normal plate impact experiments and numerical simulations. A model composite system of silica glass spheres embedded in a matrix of thermoplastic polymer, polymethyl methacrylate, was developed to mimic the impedance mismatch of structural and energetic heterogeneous materials. Shock wave profiles were measured at multiple points on the rear surface of the composite specimens to characterize shock dispersion and spatial heterogeneity in material response due to the random distribution of particles. Composites with single mode as well as bimodal bead diameter distributions were subjected to plate impact loading at ∼1000 m/s resulting in an average shock stress of ∼4 GPa. Shock rise times were measured for composites of 30% and 40% glass by volume, with spherical particles of diameters in the range of 100–1000 μm. In the case of single mode composites, the shock wave rise times were observed to scale linearly with particle diameter divided by the bulk shock wave speed. The addition of a second bead size to a base size in a 30% glass by volume composite mix resulted in significant increases in shock rise time. Numerical simulations were used to develop insights into scattering and the development of shock structure in particulate composites. Shock disruption mechanisms due to particles and matrix/interface damage effects are discussed.

Elastostatic field distributions in polycrystals and cracked media

ABSTRACTThis work addresses the problem of the reconstruction of the local fields distribution occurring in heterogeneous linear elastic solids. The constitutive heterogeneities are crystals and cracks. Through comparisons with FFT computations, it is shown that self-consistent estimates together with an assumption of normal distribution at the phase scale provide an accurate description of the elastostatic field histograms in polycrystals without cracks. In the case of inter and transgranular cracks, full-field FFT simulations indicate that the field histograms present van Hove singularities. Their natures are determined analytically in the low-density regime, in the case of an homogeneous medium containing cracks.

On the use of manometry method for measurement of gas adsorption equilibria and characterization of clay texture with Derivative Isotherm Summation

Gas adsorption is widely used for characterization of clays. Apart from “classical” experiment of nitrogen or other gases adsorption/desorption at cryogenic temperatures, allowing the determination of the specific surface area, partial mesopore and micropore volume and size distributions, gas adsorption can also be used for the characterization of clay surface texture (energetic heterogeneity) related to layered structure of clays. Derivative Isotherm Summation applied to high-resolution gas adsorption isotherms was shown to be a powerful tool to access energetic characteristics and ratio between basal and lateral faces of clay particles. To date, the method is not commonly employed for characterization of clays and other heterogeneous solids, probably due to specificity of high-resolution isotherms acquisition technique described in the original literature: quasi-equilibrium volumetry with gas injection by microleak. We illustrated in the present work a possibility to use widely available static manometric commercial gas adsorption analysers for this purpose.

Band alignment and charge transfer in CsPbBr3-CdSe nanoplatelet hybrids coupled by molecular linkers.

Formation of a p-n junction-like with a large built-in field is demonstrated at the nanoscale, using two types of semiconducting nanoparticles, CsPbBr3 nanocrystals and CdSe nanoplatelets, capped with molecular linkers. By exploiting chemical recognition of the capping molecules, the two types of nanoparticles are brought into mutual contact, thus initiating spontaneous charge transfer and the formation of a strong junction field. Depending on the choice of capping molecules, the magnitude of the latter field is shown to vary in a broad range, corresponding to an interface potential step as large as ∼1 eV. The band diagram of the system as well as the emergence of photoinduced charge transfer processes across the interface is studied here by means of optical and photoelectron based spectroscopies. Our results propose an interesting template for generating and harnessing internal built-in fields in heterogeneous nanocrystal solids.

Slicing heterogeneous solid using octree-based subdivision and trivariate T-splines for additive manufacturing

PurposeMajority of the existing direct slicing methods have generated precise slicing contours from different surface representations, they do not carry any interior information. Whereas, heterogeneous solids are highly preferable for designing and manufacturing sophisticated models. To directly slice heterogeneous solids for additive manufacturing (AM), this study aims to present an algorithm using octree-based subdivision and trivariate T-splines.Design/methodology/approachThis paper presents a direct slicing algorithm for heterogeneous solids using T-splines, which can be applied to AM based on the fused deposition modeling (FDM) technology. First, trivariate T-splines are constructed using a harmonic field with the gradient direction aligning with the slicing direction. An octree-based subdivision algorithm is then used to directly generate the sliced layers with heterogeneous materials. For FDM-based AM applications, the heterogeneous materials of each sliced layer are discretized into a finite number of partitions. Finally, boundary contours of each separated partition are extracted and paired according to the rules of CuraEngine to generate the scan path for FDM machines equipped with multi-nozzles.FindingsThe experimental results demonstrate that the proposed algorithm is effective and reliable, especially for solid objects with multiple materials, which could maintain the model integrity throughout the process from the original representation to the final product in AM.Originality/valueDirectly slicing heterogeneous solid using trivariate T-splines will be a powerful supplement to current technologies in AM.

Compatible-strain mixed finite element methods for 3D compressible and incompressible nonlinear elasticity

A new family of mixed finite element methods — compatible-strain mixed finite element methods (CSFEMs) — are introduced for three-dimensional compressible and incompressible nonlinear elasticity. A Hu–Washizu-type functional is extremized in order to obtain a mixed formulation for nonlinear elasticity. The independent fields of the mixed formulations are the displacement, the displacement gradient, and the first Piola–Kirchhoff stress. A pressure-like field is also introduced in the case of incompressible elasticity. We define the displacement in H1, the displacement gradient in H(curl), the stress in H(div), and a pressure-like field in L2. In this setting, for improving the stability of the proposed finite element methods without compromising their consistency, we consider some stabilizing terms in the Hu–Washizu-type functional that vanish at its critical points. Using a conforming interpolation, the solution and the test spaces are approximated with some piecewise polynomial subspaces of them. In three dimensions, this requires using the Nédélec edge elements for the displacement gradient and the Nédélec face elements for the stress. This approach results in mixed finite element methods that satisfy the Hadamard jump condition and the continuity of traction on all the internal faces of the mesh. This, in particular, makes CSFEMs quite efficient for modeling heterogeneous solids. We assess the performance of CSFEMs by solving several numerical examples, and demonstrate their good performance for bending problems, for bodies with complex geometries, and in the near-incompressible and the incompressible regimes. Using CSFEMs, one can capture very large strains and accurately approximate stresses and the pressure field. Moreover, in our numerical examples, we do not observe any numerical artifacts such as checkerboarding of pressure, hourglass instability, or locking.

Generalized Theory of Thermal Conductivity for Different Media: Solids to Nanofluids

The advent of nanotechnology in the twenty first century opened a new branch of nanoscience known as nanofluids finding wide range of industrial applications especially in heat transfer. Though the theory of thermal conductivity of solids is well established, there is no such conclusive model to explain the thermal conductivity of nanofluids. In the present work we propose a generalized theory for thermal conductivity applicable to materials ranging from heterogeneous solids, porous materials, nanofluids, and ferrofluids. The model could explain the effective thermal conductivity of not only the combination of solids but also solid-fluid mixtures. The proposed theory could successfully link the existing models for porous solid materials and nanofluid as its special cases. The proposed model is verified against the experimental data by simulating the theoretical equations.

Non-local dispersion and ultrasonic tunneling in concentrationally graded solids

The non-local dispersion of longitudinal ultrasonic waves is shown to appear in the heterogeneous solids due to continuous spatial distributions of their density and/or elasticity (gradient solids). This dispersion gives rise to the diversity of ultrasonic transmittance spectra, including the broadband total reflectance plateau, total transmission and tunneling spectral ranges. The ultrasonic wave fields in gradient solids, formed by interference of forward and backward travelling waves as well as by evanescent and antievanescent modes are examined in the framework of exactly solvable models of media with continuously distributed density and elasticity. Examples of transmittance spectra for both metal and semiconductor gradient structures are presented, and the generality of concept of artificial non-local dispersion for gradient composite materials is considered. It should also be noted that the wave equation for acoustic waves in gradient media with a constant elasticity modulus and a certain predetermined density distribution reduces to an equation describing the electromagnetic wave propagation in transparent dielectric media. This formal similarity shows that the concept of nonlocal dispersion is common for both optical and acoustic phenomena, which opens the way to the direct use of physical concepts and exact mathematical solutions, developed for gradient optics, to solve the corresponding acoustic problems.

Early prediction of the relapse of bleeding from acute gastroduodenal ulceration in patients with chronic pancreatitis

This chapter introduces the multipole expansion approach to the micromechanics of heterogeneous solids. A brief introduction reviews the current state-of-the-art in the research area. The ordered in ascending complexity set of geometry models of heterogeneous solids is considered, and their application to the study of local fields and macroscopic properties is discussed. The typical bulk and interface field models in conductivity and elasticity are formulated. The motivation in favor of the chosen approach is provided, and the general scheme of the multipole expansion method is outlined. The rational way of introducing the macroscopic field parameters is justified. The basic theory of the induced dipole moments is provided. The Maxwell and Rayleigh homogenization schemes for both the conductivity and elasticity are formulated in terms of the dipole moments and property contribution tensors.

Characterization of hierarchical zeolites: Combining adsorption/intrusion, electron microscopy, diffraction and spectroscopic techniques

Abstract Conventional and hierarchical faujasite zeolites, which are relevant to xylene separation by adsorption processes, are characterized using a broad set of complementary experimental techniques. In addition to a conventional faujasite zeolite, hierarchical faujasite zeolites consisting either of nanoparticle aggregates or of a layer-like zeolite are considered. For all samples, both the sodium and barium forms of these X zeolites are investigated. With the goal to predict and rationalize the efficiency of these materials for a given application, the fine characterization reported here aims at identifying key parameters such as their multiscale pore size distribution, pore connectivity/morphology, and external surface physical chemistry. X-ray diffraction is first used to probe the different crystalline phases and domain sizes coexisting in each sample. Electron microscopy at different scales (scanning and transmission microscopies) is also used to determine the morphology of the different porosity domains as well as to investigate the core-shell structure of the samples. N2 adsorption and mercury intrusion are then combined to provide a consolidated multiscale pore size distribution of each sample. Furthermore, adsorption scanning curves are determined to analyze the topology/connectivity of the porosity domains. Finally, infrared spectroscopy and nuclear magnetic resonance are used to assess the chemistry of the samples with special focus on their external surface. The combination of these different techniques is found to provide a rich and detailed picture of these heterogeneous and multiscale solids that goes beyond standard routine characterization.

TECTONIC DEFORMATION INFLUENCE ON FILTRATION-CAPACITIVE PROPERTIES OF DEEP-LYING ROCKS

The paper is dealing with the study of deformation and strength properties of various rocks, as well as collector properties of oil and gas reservoirs under various stress conditions, that are typical for large depths. Some features of fractures formation and development in heterogeneous solids under extension and compression are identified. The characteristic features of the mechanism of irreversible deformation of rocks under uneven volume-strained state are considered. It has been defined that under conditions typical for depths of 8–10 km, irreversible deformation occurs with decompression of their structure, increasing the coefficients of porosity and permeability. Different dependences of volume growth and coefficient of permeability on the all-round compression under uneven triaxial stress, based on data of sandstone and marble, are shown. Typical diagrams of rocks deformations under uneven allround compression also are shown.

A new three-dimensional finite-volume model for evaluation of thermal conductivity of periodic multiphase composites

This paper proposes a three-dimensional micromechanical model for evaluation of effective thermal conductivity of multiphase composite materials with periodic microstructure. The model consists in an extension of the parametric finite-volume theory which has demonstrated to be a promising tool for the analysis and homogenization of multiphase heterogeneous solids. The applicability and performance of the proposed formulation are examined through the solutions of different numerical examples of two- and three-phase composites. Such examples consist of composites reinforced with unidirectional solid and hollow long fibers and aligned short fibers. In order to verify the effectiveness of the model, its predictions are compared with analytical and finite-element results, as well as experimental data. The results indicate that the proposed model is efficient and accurate in predicting the effective thermal conductivity of periodic composites and can be seen as a competitive alternative to other existing procedures based on traditional numerical tools like the finite element method.

Isosteric Heat: Comparative Study between Clausius–Clapeyron, CSK and Adsorption Calorimetry Methods

This work presents the calorimetric study of five adsorbents with different chemical and textural characteristics: MOF-199, MCM-41, SBA-15, activated carbon prepared from corn cob (GACKP) and graphite. These solids were used to establish the differences between isosteric heats evaluated by three different methods: Clausius–Clapeyron (C-C), Chakraborty, Saha and Koyama (CSK) and Adsorption Calorimetry (A-Cal). The textural characterization results show solids that have values of specific surface area between 2271 m2·g−1 for the MOF-199 and 5.2 m2·g−1 for the graphite. According to the results obtained for the isosteric heats for each sample, the magnitude varies depending on the coverage of the adsorbate and the textural characteristics of each adsorbent. Solids with an organized structure have isosteric heat values that are coincident among the three methods. Meanwhile, heterogeneous solids such as activated carbon values evaluated by the CKS and C-C have a high dispersion method regarding the adsorption calorimetry method. The results obtained show that the adsorption calorimetry, being a direct experimental measurement method, presents less dispersed data. At low quantities, the isosteric heat of nitrogen adsorption decreased in the order MOF-199, GACKP, MCM-41, SBA-15 and Graphite. The order for the isosteric heats values was coherent with the surface characteristics of each of the solids, especially with the pore size distribution. Finally, throughout the coverage examined in this work, the isosteric heats for nitrogen adsorption determined by adsorption calorimetry (A-Cal) were larger than the evaluated by C-C and CSK indirect methods of vaporization. According to the results, it is shown that the adsorption calorimetry allows values of the isosteric heats of adsorption with an error of less than 2% to be established and also reveals the complex nature of the heterogeneity or homogeneity of the adsorbent.

A novel computational multiscale approach to model thermochemical coupled problems in heterogeneous solids: Application to the determination of the “state of cure” in filled elastomers

In this paper, we present a computational homogenization framework to model coupled transient heat conduction with heat generation and chemical kinetics in solids. The proposed method considers that both macro and microscales are under transient heat conduction, being the chemical kinetics (which gives rise to internal heat generation source in the heat conduction problem) defined either in some of the constituents of the microscale or even in the whole microscale. The numerical solution is based on a nested solution strategy, in which the finite element method is used for solving both the macro and the microscale problems, configuring a FE2 scheme. By solving the coupled problem of transient heat conduction with internal heat generation and chemical kinetics defined in a finite representative volume element, we extract the effective thermal properties and chemical kinetics contribution of the composite and employ them to solve the transient macroscale heat conduction problem (also with internal heat generation). This novel numerical framework is employed in the prediction of the State Of Cure (SOC) in filled elastomers. Numerical solutions of some in-plane heat conduction problems are presented in order to assess the proposed numerical strategy, showing that the multiscale model developed is capable of numerically determining transient non-homogeneous maps of the SOC at the microscale.

Explicit multistep time integration for discontinuous elastic stress wave propagation in heterogeneous solids

SummaryA multistep explicit time integration algorithm is presented for tracking the propagation of discontinuous stress waves in heterogeneous solids whose subdomain‐to‐subdomain critical time step ratios range from tens to thousands. The present multistep algorithm offers efficient and accurate computations for tracking discontinuous waves propagating through such heterogeneous solids. The present algorithm, first, employs the partitioned formulation for representing each subdomain, whose interface compatibility is enforced via the method of the localized Lagrange multipliers. Second, for each subdomain, the governing equations of motion are decomposed into the extensional and shear components so that tracking of waves of different propagation speeds is treated with different critical step sizes to significantly reduce the computational dispersion errors. Stability and accuracy analysis of the present multistep time integration is performed with one‐dimensional heterogeneous bar. Analyses of the present algorithm are also demonstrated as applied to the stress wave propagation in one‐dimensional heterogeneous bar and in heterogeneous plain strain problems.

Phase field modeling of heterogeneous microcrystalline ceramics

Diffuse interface models and simulations capture deformation and failure of polycrystalline ceramics with multiple phases. Two heterogeneous ceramic solids are investigated. The first consists of a boron carbide matrix phase embedded with titanium diboride grains. Boron carbide may undergo cleavage fracture, twinning, and amorphization under sufficient mechanical loading. Titanium diboride demonstrates cleavage fracture and limited plastic slip. The second ceramic composite consists of diamond crystals with a smaller fraction of silicon carbide grains, where the latter may encapsulate the former in a micro- or nano-crystalline matrix and/or may be interspersed as larger micro-crystals among the diamond grains. Diamond may undergo cleavage fracture while the cubic phase of silicon carbide may fracture and twin. A general constitutive framework suitable for representing behaviors of all phases of each material system is reported. This phase field framework is implemented in three-dimensional (3D) finite element (FE) simulations of polycrystalline aggregates under compressive loading. Numerical results demonstrate effects of grain and phase morphology and activation or suppression of slip or twinning mechanisms on the overall strength and ductility of each material system. Efforts to inhibit localization and cleavage in boron carbide crystals, including addition of titanium diboride, promote increases in strength of the first composite, though residual stresses may be necessary to realize toughness improvements observed experimentally. In the second composite, layers of softer silicon carbide nanocrystals along grain boundaries (GBs) improve overall strength and ductility relative to addition of larger bulk silicon carbide grains.

A semi-analytical model for evaluation of effective thermal conductivity of composites with periodic microstructure

This paper presents a semi-analytical micromechanical model for evaluation of effective thermal conductivity of composite materials with periodic microstructure. The model is based on the equivalent inclusion thermal problem and utilizes Fourier series for representation of periodic functions involved in the material homogenization approach. Two main objectives can be highlighted in the work. The first of them is the derivation of the thermal micromechanical model, which consists in an extension of a formulation originally derived for homogenization of elastic heterogeneous solids. The second objective consists in a detailed investigation on the performance of the model, considering convergence of results and efficiency of strategies employed for the approximate solution of the thermal homogenization problem. Analyses on the complexity of transformation temperature gradient functions are also included in this investigation. The results obtained for two examples of periodic composites with different microstructural architectures are presented and discussed in detail.

On the full-waveform inversion of Lamé parameters in semi-infinite solids in plane strain

We are concerned with imaging the spatially varying Lamé parameters of semi-infinite, arbitrarily heterogeneous solids, when probed by elastic waves in the time domain. We use a full-waveform inversion approach to tackle the inverse medium problem, and seek the Lamé distributions that minimize the misfit between measured and computed responses, subject to the governing PDEs. As is commonly the case, the resulting inverted profiles of the second Lamé parameter (μ) are of better quality than those of the first (λ). To improve the resolution of both Lamé parameters, we discuss the use of three robustifying schemes, namely, source-frequency continuation, regularization factor continuation, and a search direction-biasing scheme. We demonstrate with numerical experiments the effect the schemes have on the inversion process and conclude with an application of the robustified full-waveform method to a challenging adaptation of the Marmousi2 model.

Spatially-resolved 1H NMR relaxation-exchange measurements in heterogeneous media.

In the last decades, the 1H NMR T2-T2 relaxation-exchange (REXSY) technique has become an essential tool for the molecular investigation of simple and complex fluids in heterogeneous porous solids and soft matter, where the mixing-time-evolution of cross-correlated T2-T2 peaks enables a quantitative study of diffusive exchange kinetics in multi-component systems. Here, we present a spatially-resolved implementation of the T2-T2 correlation technique, named z-T2-T2, based on one-dimensional spatial mapping along z using a rapid frequency-encode imaging scheme. Compared to other phase-encoding methods, the adopted MRI technique has two distinct advantages: (i) is has the same experimental duration of a standard (bulk) T2-T2 measurement, and (ii) it provides a high spatial resolution. The proposed z-T2-T2 method is first validated against bulk T2-T2 measurements on homogeneous phantom consisting of cyclohexane uniformly imbibed in finely-sized α-Al2O3 particles at a spatial resolution of 0.47 mm; thereafter, its performance is demonstrated, on a layered bed of multi-sized α-Al2O3 particles, for revealing spatially-dependent molecular exchange kinetics properties of intra- and inter-particle cyclohexane as a function of particle size. It is found that localised z-T2-T2 spectra provide well resolved cross peaks whilst such resolution is lost in standard bulk T2-T2 data. Future prospective applications of the method lie, in particular, in the local characterisation of mass transport phenomena in multi-component porous media, such as rock cores and heterogeneous catalysts.