We present general, computable, improvable, and rigorous bounds for the total energy of a finite heterogeneous volume element or a periodically distributed unit cell of an elastic composite of any known distribution of inhomogeneities of any geometry and elasticity, undergoing a harmonic motion at a fixed frequency or supporting a single-frequency Bloch-form elastic wave of a given wave-vector. These bounds are rigorously valid for \emph{any consistent boundary conditions} that produce in the finite sample or in the unit cell, either a common average strain or a common average momentum. No other restrictions are imposed. We do not assume statistical homogeneity or isotropy. Our approach is based on the Hashin-Shtrikman (1962) bounds in elastostatics, which have been shown to provide strict bounds for the overall elastic moduli commonly defined (or actually measured) using uniform boundary tractions and/or linear boundary displacements; i.e., boundary data corresponding to the overall uniform stress and/or uniform strain conditions. Here we present strict bounds for the dynamic frequency-dependent constitutive parameters of the composite and give explicit expressions for a direct calculation of these bounds.
In this study, we show that any system consisting of magnetic dipoles forming ordered or disordered configurations can be simplified to a form mathematically equivalent to a system consisting of two magnetic dipoles. It is shown that the energy of all kinds of magnetic dipole systems can be written as $E=\fracβ{α^3}$, where $α$ is the nearest distance between the dipoles and $β$ is a certain constant depending on the magnetic moments of dipoles and configuration. Using this fact we model any nano-magnetic composite material by a simple two-magnetic dipole system. Then we experimentaly and theo…
We present a comparative study of the energetic, structural and elastic properties of carbon and composite single-wall nanotubes, including BN, BC3 and BC2N nanotubes, using a non-orthogonal tight-binding formalism. Our calculations predict that carbon nanotubes have a higher Young modulus than any of the studied composite nanotubes, and of the same order as that found for defect-free graphene sheets. We obtain good agreement with the available experimental results.
In this review, we present our recent computational work on carbon-based nanostructured composites. These materials consist of carbon crystallites embedded in an amorphous carbon matrix and are modeled here through classical and semi-empirical quantum-mechanical simulations. We investigate the energetics, mechano-elastic, and optoelectronic properties of these materials. Once the stability of the composites is discussed, we move on to the calculation of their elastic moduli and constants, their anisotropy and elastic recovery. At a next step, we focus on diamond composites, which were found to…
In the present work a detailed thermodynamic consideration for the magnetic free energy of the composite material consisting of the ferromagnetic powder particles embedded into a polymer matrix is given. We estimate their magnetostatic interaction energy and its dependence on the microscopic distribution of the magnetization and the magnetic field in the composite material. We also define the hydrostatic component of the mechanical force developed and the volume change effect caused by the magnetostatic interactions in such composites.
The main aim of the present work is to estimate the effective elastic stiffnesses of a two-phase diamond/$β$-SiC composite thin film that is fabricated by chemical vapor deposition. The parameters of linear elasticity are determined by numerical homogenization. The database is sparse since for the 3D volume of interest only two micrographs displaying the phase distributions in perpendicular planes are available; micrographs each of a cross-section and the surface of the thin film. A representative volume element (RVE) is reconstructed by an optimization software and by means of identified mate…
It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the elastic and electro-conductive properties of a strongly inhomogeneous two-phase composite material, the steep rise of effective parameters occurs at different concentrations. To achieve the logical concordance between the cross-property relations, a modification of the effective medium theory of the elastic properties is introduced. It is shown that the qualit…
Many composite materials, both natural and fabricated, process a Voronoi like architecture or microstructure. Furthermore, the stochasticity and connectivity of Voronoi tessellation endow the composite materials constructed by this kind of structures a wide range of desired properties including high and tuneable stiffness, high strength and good manufacturability. Thus, Voronoi-based fibre network structures are regarded as promising designs of composite reinforcements, as well as powerful tools in composite mechanics simulations. In this paper, the elastic properties of composites reinforced …
We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing a statistically homogeneous set of multimodal spherical inclusions modeling the morphology of heterogeneous solid propellants (HSP). Estimates of effective elastic moduli are performed using the multiparticle effective field method (MEFM) directly taking into account the interaction of different inclusions. Because of this, the effective elastic moduli of the HSP evaluated by the MEFM are sensitive to both the relative size of the inclusions (i.e., their multimodal nature) and the RDFs estimated …
A systematic method for optimal design of layered periodic composites for mitigation of impact-induced shock waves is presented. Frequency spectrum of a pulse with a sharp rise-time is analyzed and the frequency range that carries most of the pulse energy is identified. A genetic algorithm is used to maximize the stop bands of a layered periodic composite over the target frequency range. Due to reflection of the pulse over the stop bands, the maximum stress and the energy of transmitted pulse become minimal. To verify the theoretical calculation a sample is fabricated and Hopkinson bar experim…
We review the theoretical bounds on the effective properties of linear elastic inhomogeneous solids (including composite materials) in the presence of constituents having non-positive-definite elastic moduli (so-called negative-stiffness phases). We show that for statically stable bodies the classical displacement-based variational principles for Dirichlet and Neumann boundary problems hold but that the dual variational principle for traction boundary problems does not apply. We illustrate our findings by the example of a coated spherical inclusion whose stability conditions are obtained from …
This work presents a comprehensive investigation of the elastic and fracture behavior of ply-to-ply angle interlock three-dimensional woven composites. The research investigated novel splitting and wedge-driven out-of-plane fracture tests to shed light on the tensile fracture behavior in the thickness direction and to provide estimates of the out-of-plane tensile strength and fracture energy. In addition, size effect tests on geometrically-scaled Single Edge Notch Tension (SENT) specimens were performed to fully characterize the intra-laminar fracture energy of the material and to study the sc…
We study the elastic response of composites of rods embedded in elastic media. We calculate the micro-mechanical response functions, and bulk elastic constants as functions of rod density. We find two fixed points for Poisson's ratio with respect to the addition of rods in 3D composites: there is an unstable fixed point for Poisson's ratio=1/2 (an incompressible system) and a stable fixed point for Poisson's ratio=1/4 (a compressible system). We also derive an approximate expression for the elastic constants for arbitrary rod density that yields exact results for both low and high density. The…
In this article we discuss the modelling of elastic and electromagnetic wave propagation through one- and two-dimensional structured piezoelectric solids. Dispersion and the effect of piezoelectricity on the group velocity and positions of stop bands are studied in detail. We will also analyze the reflection and transmission associated with the problem of scattering of an elastic wave by a heterogeneous piezoelectric stack. Special attention is given to the occurrence of transmission resonances in finite stacks and their dependence on a piezoelectric effect. A 2D doubly-periodic piezoelectric …
Investigation of inhomogeneities has wide applications in different areas of mechanics including the study of composite materials. Here, we analytically study an arbitrarily-shaped isotropic inhomogeneity embedded in a finite-sized heterogeneous medium. By modal decomposition of the influence of the inhomogeneity on the deformation of the composite, a relation is presented that determines the variation of effective elastic stiffness caused by the presence of the inhomogeneity. This relation indicates that the effective elastic stiffness of a composite is always a concave function of the proper…
We study the interfacial structure, stability, and elastic properties of composite carbon films containing nanotubes. Our Monte Carlo simulations show that Van der Waals forces play a vital role in shaping up the interfacial geometry, producing a curved graphitic wall surrounding the tubes. The most stable structures are predicted to have intermediate densities, high anisotropies, and increased elastic moduli compared to pure amorphous carbon films.
Nanostructured and architectured copper niobium composite wires are excellent candidates for the generation of intense pulsed magnetic fields (>90T) as they combine both high strength and high electrical conductivity. Multi-scaled Cu-Nb wires are fabricated by accumulative drawing and bundling (a severe plastic deformation technique), leading to a multiscale, architectured, and nanostructured microstructure exhibiting a strong fiber crystallographic texture and elongated grain shapes along the wire axis. This paper presents a comprehensive study of the effective elastic behavior of this compos…
. A kind of "Elastic Composite, Reinforced Lightweight Concrete (ECRLC)" with the mentioned specifics is a type of "Resilient Composite Systems (RCS)" in which, contrary to the basic geometrical assumption of flexure theory in Solid Mechanics, "the strain changes in the beam height during bending" is typically "Non-linear". . Through employing this integrated structure, with significant high strain capability and modulus of resilience in bending, we could constructively achieve high bearing capacities in beams with secure fracture pattern, in less weight. . Due to the system particulars and it…
In many applications, viscoelastic properties of reinforced composites need to be determined prior to their real service life. Such properties can be assured by destructive and non-destructive tests. In this paper, a novel non-destructive test (NDT) method based on flexural free vibration is introduced to investigate the viscoelastic properties of fiber-reinforced composites. Three different types of industrial fibers (carbon, glass, and hemp) and an unsaturated polyester resin were selected to produce bar-shaped composites via pultrusion technique. These composite bars were used in a simple N…
Analytical method for the second-order homogenization of two-phase composites within Mindlin-Toupin strain gradient elasticity theory is proposed. Direct approach and self-consistent approximation are used to reduce the homogenization problem to the problem of determination of averaged Cauchy stresses, double stresses and static moments of Cauchy stresses inside the inclusions under prescribed quadratic boundary conditions. The ellipsoidal shape of inclusions and orthotropic properties of phases are assumed. Extended equivalent inclusion method with linear eigenstrain is proposed to derive the…
We report detailed theoretical investigations of the micro-mechanics and bulk elastic properties of composites consisting of randomly distributed stiff fibers embedded in an elastic matrix in two and three dimensions. Recent experiments published in Physical Review Letters [102, 188303 (2009)] have suggested that the inclusion of stiff microtubules in a softer, nearly incompressible biopolymer matrix can lead to emergent compressibility. This can be understood in terms of the enhancement of the compressibility of the composite relative to its shear compliance as a result of the addition of sti…
Theoretical calculations of the elastic response of carbon composites and amorphous carbon are reported. The studied composites consist of crystalline nanoinclusions, either spherical diamonds or carbon nanotubes, embedded in amorphous carbon matrices. The elastic constants of the composites were calculated and found to systematically increase as the density increases. The elastic recovery under hydrostatic pressure for all structures was also investigated and was found to be significantly high for both nanocomposite and amorphous carbon, but decreases as the material becomes more dilute.
Finite element analysis has been used successfully to estimate the effective properties of many types of composites. The prediction of effective elastic moduli of polymer-bonded explosives provides a new challenge. These particulate composites contain extremely high volume fractions of explosive particles ($>$ 0.90). At room temperature and higher, the Young's modulus of the particles can be 20,000 times that of the binder. Under these conditions, rigorous bounds and analytical approximations for effective elastic properties predict values that are orders of magnitude different from the experi…
A method for the homogenization of 3-D periodic elastic composites is presented. It allows for the evaluation of the averaged overall frequency dependent dynamic material constitutive tensors relating the averaged dynamic field variable tensors of velocity, strain, stress, and linear momentum. The formulation is based on micromechanical modeling of a representative unit cell of a composite proposed by Nemat-Nasser & Hori (1993), Nemat-Nasser et. al. (1982) and Mura (1987) and is the 3-D generalization of the 1-D elastodynamic homogenization scheme presented by Nemat-Nasser & Srivastava (2011).…
The prediction of the effective elastic properties of polymer bonded explosives using direct numerical simulations is computationally expensive because of the high volume fraction of particles in these particulate composites ($\sim$0.90) and the strong modulus contrast between the particles and the binder ($\sim$20,000). The generalized method of cells (GMC) is an alternative to direct numerical simulations for the determination of effective elastic properties of composites. GMC has been shown to be more computationally efficient than finite element analysis based approaches for a range of com…
We present a Bayesian methodology to infer the elastic modulus of the constituent polymer and the fiber orientation state in a short-fiber reinforced polymer composite (SFRP). The properties are inversely determined using only a few experimental tests. Developing composite manufacturing digital twins for SFRP composite processes, including injection molding and extrusion deposition additive manufacturing (EDAM) requires extensive experimental material characterization. In particular, characterizing the composite mechanical properties is time consuming and therefore, micromechanics models are u…
Dense ceramics are irreplaceable in applications requiring high mechanical stiffness, chemical and temperature resistance and low weight. To improve their toughness, ceramics can be reinforced with elongated inclusions. Recent manufacturing strategies have been developed to control the orientations of disc-like micro-particles in polymeric and ceramic matrices and to build periodic microstructures. Given the infinite number of possible microstructures available, modeling tools are required to select the potentially best design. Periodic microstructures can be involved in elastic wave scatterin…
Bounds are obtained on the volume fraction in a two-dimensional body containing two elastically isotropic materials with known bulk and shear moduli. These bounds use information about the average stress and strain fields, energy, determinant of the stress, and determinant of the displacement gradient, which can be determined from measurements of the traction and displacement at the boundary. The bounds are sharp if in each phase certain displacement field components are constant. The inequalities we obtain also directly give bounds on the possible (average stress, average strain) pairs in a t…
We derive exact expressions for effective elastodynamic properties of two-phase composites in the long-wavelength (quasistatic) regime via homogenized constitutive relations that are local in space. This is accomplished by extending the "strong-contrast" expansion formalism that was previously applied to the static problem. These strong-contrast expansions explicitly incorporate complete microstructural information of the composite via an infinite set of $n$-point correlation functions. Utilizing the rapid-convergence properties of these series expansions (even for extreme contrast ratios), we…
An anisotropic equation of state (EOS) is proposed for the accurate extrapolation of high-pressure shock Hugoniot (anisotropic and isotropic) states to other thermodynamic (anisotropic and isotropic) states for a shocked carbon-fibre epoxy composite (CFC) of any symmetry. The proposed EOS, using a generalised decomposition of a stress tensor [Int. J. Plasticity \textbf{24}, 140 (2008)], represents a mathematical and physical generalisation of the Mie-Grüneisen EOS for isotropic material and reduces to this equation in the limit of isotropy. Although a linear relation between the generalised an…
In this paper, we present a thorough stress analysis of the Cu-Zr metallic-glass composite with embedded B2 particles subject to a martensitic transformation. Within the framework of the Eshelby theory, we are able to explain, in a quantitative manner, (1) the formation of three types of shear bands with distinct morphologies as observed experimentally in the severely deformed Cu-Zr metallic-glass composite and (2) the work hardening ability of the Cu-Zr metallic-glass composite as related to the coupled effects of elastic back stress and elastic mismatch caused by the martensitic transformati…
Very recently, the construction of twist actuators from magnetorheological gels and elastomers has been suggested. These materials consist of magnetizable colloidal particles embedded in a soft elastic polymeric environment. The twist actuation is enabled by a net chirality of the internal particle arrangement. Upon magnetization by a homogeneous external magnetic field, the systems feature an overall torsional deformation around the magnetization direction. Starting from a discrete minimal mesoscopic model set-up we work towards a macroscopic characterization. The two scales are linked by ide…
Conducting polymers have wide technological applications in sensors, actuators, electric and optical devices, solar cells etc. To improve their operational performance, mechanical, thermal, electrical and optical properties, such polymers are doped with carbon allotrope nanofillers. Functionality of the novel nanocomposite polymers may be stipulated by size characteristics of nanoparticles and the polymer, different physical effects like charge transfer in such objects etc. We characterize and analyze structure, elastic, electric properties and of novel polymer nanocomposites, isotactic polypr…
A heterogeneous Cauchy elastic material may display micromechanical effects that can be modeled in a homogeneous equivalent material through the introduction of higher-order elastic continua. Asymptotic homogenization techniques provide an elegant and rigorous route to the evaluation of equivalent higher-order materials, but are often of difficult and awkward practical implementation. On the other hand, identification techniques, though relying on simplifying assumptions, are of straightforward use. A novel strategy for the identification of equivalent second-gradient Mindlin solids is propose…
In this paper we review the recent advances which have taken place in the understanding and applications of acoustic/elastic metamaterials. Metamaterials are artificially created composite materials which exhibit unusual properties which are not found in nature. We begin with presenting arguments from discrete systems which support the case for the existence of unusual material properties such as tensorial and/or negative density. The arguments are then extended to elastic continuums through coherent averaging principles. The resulting coupled and nonlocal homogenized relations, called the Wil…
We statistically reconstruct a three-dimensional model of a tungsten-silver composite from an experimental two-dimensional image. The effective Young's modulus ($E$) of the model is computed in the temperature range 25-1060^o C using a finite element method. The results are in good agreement with experimental data. As a test case, we have reconstructed the microstructure and computed the moduli of the overlapping sphere model. The reconstructed and overlapping sphere models are examples of bi-continuous (non-particulate) media. The computed moduli of the models are not generally in good agreem…
Interface cracking is one of the most prominent failure modes in fibre reinforced polymer (FRP) composites. Recent trends in high-tech applications of FRP composites exploit the limits of the load bearing capacity, generally encompassing the development of notable nonlinear effects from geometrical and material signatures. In this investigation, we present a comprehensive assessment of the new Linear Elastic Brittle Interface Model (LEBIM) in geometrically nonlinear applications undergoing mixed-mode fracture conditions. This interface model for triggering fracture events is formulated through…
In this study, viscoelastic properties of polymeric composites were investigated through a non-destructive test (NDT) method based on longitudinal free vibration. First, three different polyester composites reinforced separately with carbon, glass, and hemp fibers, as well as, one polyester composite sample reinforced with poplar wood powder were manufactured via pultrusion and hand lay-up methods, respectively. In the proposed resonant free vibration non-destructive method, each rod-shaped test specimen was hit by a hammer at one end of specimen and immediately the acoustic response of the sp…
Composites are ideally suited to achieve desirable multifunctional effective properties since the best properties of different materials can be judiciously combined with designed microstructures. Here we establish cross-property relations for two-phase composite media that link effective elastic and electromagnetic wave characteristics to one another, including the respective effective wave speeds and attenuation coefficients, which facilitate multifunctional material design. This is achieved by deriving accurate formulas for the effective electromagnetic and elastodynamic properties that depe…
The paper presents a comprehensive analysis of elastic properties of polystyrene-based nanocomposites filled with different types of inclusions: small spherical particles (SiO2 and Al2O3), alumosilicates (montmorillonite, halloysite natural tubules and Mica) and carbon nanofillers (carbon black and multi-walled carbon nanotubes). Composites were fabricated by melt technology. The analysis of composite melts showed that the introduction of Montmorillonite, Multi-walled carbon nanotubes, and Al2O3 particles provided an increase in melt viscosity by an average of 2 to 5 orders of magnitude over t…
One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)elastic substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we…
We consider an elastic composite material containing particulate inclusions in a soft elastic matrix that is bounded by a rigid wall, e.g., the substrate. If such a composite serves as a soft actuator, forces are imposed on or induced between the embedded particles. We investigate how the presence of the rigid wall affects the interactions between the inclusions in the elastic matrix. For no-slip boundary conditions, we transfer Blake's derivation of a corresponding Green's function from low-Reynolds-number hydrodynamics to the linearly elastic case. Results for no-slip and free-slip surface c…
The effect of the clusterization on the effective properties of a composite material reinforced by MXene or graphene platelets is studied using the finite element method with periodic representative volume element (RVE). A hybrid 2D/3D finite element mesh is used to reduce the computational complexity of the numerical model. Several realizations of an RVE were generated with increasing volume fractions of inclusions, resulting in progressive clusterization of the platelets. Numerically obtained effective properties of the composite are compared with analytical predictions by the Mori-Tanaka me…
We present a model to study Young's modulus and Poisson's ratio of the composite material of amorphous nanowires. It is an extension of the model derived by two of us [Da Fonseca and Galvao, Phys. Rev. Lett. 92, 175502 (2004)] to study the elastic properties of amorphous nanosprings. The model is based on twisting and tensioning a straight nanowire and we propose an experimental setup to obtain the elastic parameters of the nanowire. We used the Kirchhoff rod model to obtain the expressions for the elastic constants of the nanowire.
The overall behavior of a 2D lattice of voids embedded in an anisotropic matrix is investigated in the limit of vanishing porosity f. An effective-medium model (of the Hashin-Shtrikman type) which accounts for elastic interactions between neighboring voids, is compared to Fast Fourier Transform numerical solutions and, in the limits of infinite anisotropy, to exact results. A cross-over between regular and singular dilute regimes is found, driven by a characteristic length which depends on f and on the anisotropy strength. The singular regime, where the leading dilute correction to the elastic…
Many biological materials consist of sparse networks of disordered fibres, embedded in a soft elastic matrix. The interplay between rigid and soft elements in such composite networks leads to mechanical properties that can go far beyond the sum of those of the constituents. Here we present lattice-based simulations to unravel the microscopic origins of this mechanical synergy. We show that the competition between fibre stretching and bending and elastic deformations of the matrix gives rise to distinct mechanical regimes, with phase transitions between them that are characterized by critical b…
An efficient approach to the evaluation of effective elastic properties of carbon-carbon plain weave textile composites using the Mori-Tanaka method is presented. The method proves its potential even if applied to real material systems with various types of imperfections including the non-uniform waviness of the fiber-tow paths, both along its longitudinal direction and through the laminate thickness. Influence of the remaining geometrical parameters is accounted for by optimal calibration of the shape of the equivalent ellipsoidal inclusion. An application of the method to a particular sample…
Architected materials that control elastic wave propagation are essential in vibration mitigation and sound attenuation. Phononic crystals and acoustic metamaterials use band gap engineering to forbid certain frequencies from propagating through a material. However, existing solutions are limited in the low frequency regimes and in their bandwidth of operation because they require impractical sizes and masses. Here, we present a class of materials (labeled elastic meta-structures) that supports the formation of wide and low frequency band gaps, while simultaneously reducing their global mass. …
We investigate the effective properties (conductivity, diffusivity and elastic moduli) of model random composite media derived from Gaussian random fields and overlapping hollow spheres. The morphologies generated in the models exhibit low percolation thresholds and give a realistic representation of the complex microstructure observed in many classes of composites. The statistical correlation functions of the models are derived and used to evaluate rigorous bounds on each property. Simulation of the effective conductivity is used to demonstrate the applicability of the bounds. The key morphol…
Metamaterials are artificially structured media that can focus (lensing) or reroute (cloaking) waves, and typically this is developed for electromagnetic waves at millimetric down to nanometric scales or for acoustics or thin elastic plates at centimeter scales. Extending the concepts of Kadic et al. 2013 we show that the underlying ideas are generic across wave systems and scales by generalizing these concepts to seismic waves at frequencies, and lengthscales of the order of hundreds of meters, relevant to civil engineering. By applying ideas from transformation optics we can manipulate and s…
The response of a neo-Hookean fiber composite undergoing finite out-of-plane shear deformation is examined. To this end an explicit close form solution for the out-of-plane shear response of a cylindrical composite element is introduced. We find that the overall response of the cylindrical composite element can be characterized by a fictitious homogeneous neo-Hookean material. Accordingly, this macroscopic response is identical to the response of a composite cylinder assemblage. The expression for the effective shear modulus of the composite cylinder assemblage is identical to the correspondin…
We report temperature-responsive soft composites of semiflexible biopolymer networks (fibrin) containing dispersed microgel colloidal particles of poly(N-isopropylacrylamide) (pNIPAM) that undergo a thermodynamically driven de-swelling transition above a Lower Critical Solution Temperature (LCST). Unlike standard polymer-particle composites, decreasing the inclusion volume of the particles (by increasing temperature)is concomitant with a striking increase of the overall elastic stiffness of the composite. We observe such a behavior over a wide composition space. The composite elastic shear mod…
