Elastic Composite Materials Research Articles

Effective field hypothesis in Hashin–Shtrikman bounds estimations for effective moduli of composites with noncanonical shape of inclusions

One consider linear elastic composite materials (CMs), which consist of a homogeneous matrix containing a statistically homogeneous random set of identical aligned inhomogeneous inclusions of non-canonical (i.e. nonellipsoidal) shape. Estimates of the Hashin-Shtrikman type are developed by extremizing of the classical variational functional involving a general integral equation (GIE) connecting the strain fields in the point being considered with the strain fields in the surrounding points. An improvement of the approach proposed is based on the use of a piece wise constant approximation of the trial effective field rather than the trial polarisation tensor that, in its turn, allows one to take into account any inhomogeneity of the strain distributions inside the inclusions. Due to a sensitivity of the proposed approach to the inhomogeneity of these strain distributions, a final Hashin-Shtrikman bounds representation demonstrates more significant dependence on the shape of noncanonical inclusions than the corresponding classical bounds (that is shown by the concrete numerical examples).

A simple procedure to evaluate Cauchy stress tensor at the macro level based on computational micromechanics under general finite strain states

This paper presents a new methodology to evaluate the Cauchy stress tensor at the macro level in computational micromechanics models. The use of control nodes to specify boundary conditions of a Representative Volume Element (RVE) allows deriving equations for the Cauchy stress components, with the consequence that numerical integration in the RVE is not performed. The proposed method allows use of computational micromechanics in commercial Finite Element software for a RVE subjected to general infinitesimal or finite strains. Because this methodology is obtained from the equivalence of power in the microscopic and macroscopic scales (Hill–Mandel principle) in a quasi-static problem, it is capable of dealing with micro-constituents under several constitutive laws. Numerical examples presented include simulations of elastic, hyper-elastic, and elasto-plastic fiber composite materials and a honeycomb microstructure. The present methodology can be used in multi-scale models to analyze non-linear structures made of heterogeneous materials.

Composite model of the dependence of mechanical properties of anodic aluminum oxide on porosity

Results of the application of a theory concerning elasticity of composite materials to calculate the elastic modulus of anodic aluminum oxide (AAO) are presented. The basis of the proposed AAO elasticity model is the assumption that the space of the anodic aluminum oxide may be represented as a composite material in the form of a matrix—bulk amorphous oxide filling the space between the pores reinforced by a hollow fiber with zero wall thickness. The maximum error of this simplification in the range of the actually used porosity values is 5% for the Young’s modulus and 0.7% for the shear modulus. The results are in proper agreement with the experimental data of other authors. Proper agreement of the results holds out a hope that this approach may be applied when the AAO pores are filled with some material (adsorbent, liquid, etc.), as is possible, for example, in cases of AAO application as a material for cantilever sensors.

Прочность и устойчивость морской эвакуационной системы из композитного эластичного материала

Прочность и устойчивость морской эвакуационной системы из композитного эластичного материала

Forces and torques on rigid inclusions in an elastic environment: Resulting matrix-mediated interactions, displacements, and rotations.

Embedding rigid inclusions into elastic matrix materials is a procedure of high practical relevance, for instance, for the fabrication of elastic composite materials. We theoretically analyze the following situation. Rigid spherical inclusions are enclosed by a homogeneous elastic medium under stick boundary conditions. Forces and torques are directly imposed from outside onto the inclusions or are externally induced between them. The inclusions respond to these forces and torques by translations and rotations against the surrounding elastic matrix. This leads to elastic matrix deformations, and in turn results in mutual long-ranged matrix-mediated interactions between the inclusions. Adapting a well-known approach from low-Reynolds-number hydrodynamics, we explicitly calculate the displacements and rotations of the inclusions from the externally imposed or induced forces and torques. Analytical expressions are presented as a function of the inclusion configuration in terms of displaceability and rotateability matrices. The role of the elastic environment is implicitly included in these relations. That is, the resulting expressions allow a calculation of the induced displacements and rotations directly from the inclusion configuration, without having to explicitly determine the deformations of the elastic environment. In contrast to the hydrodynamic case, compressibility of the surrounding medium is readily taken into account. We present the complete derivation based on the underlying equations of linear elasticity theory. In the future, the method will, for example, be helpful to characterize the behavior of externally tunable elastic composite materials, to accelerate numerical approaches, as well as to improve the quantitative interpretation of microrheological results.

Flexible, elastic, and superhydrophobic silica-polymer composite aerogels by high internal phase emulsion process

Flexible, elastic, low density, superhydrophobic, and low thermal conductive silica-polymer composite aerogel materials were prepared by a high internal phase emulsion (HIPE) process followed with sol-gel process. Flexible silica aerogels were grown in the scaffold of macro-porous flexible polymer monolith to overcome the brittle nature of silica aerogels. Initially, porous polymer monolith was prepared by HIPE and was used as a scaffold for preparation of flexible silica aerogels by sol-gel process followed by supercritical drying. Polymer monolith was soaked in a pre-hydrolyzed methyltrimethoxysilane (MTMS) based silica sol and gelation was achieved by two step sol-gel process. Composite monolith possess extreme properties such as high flexibility, elasticity, superhydrophobicity (165°), low density (0.045 g/cm3) and thermal conductivity (0.040 W/m·K). This novel way of preparation allows us to overcome the fragile nature of MTMS based flexible silica aerogels while maintaining textural, physical, and functional properties. Hence such materials are highly useful for corrosion resistant thermal insulation in various fields.

Topology optimization of anisotropic broadband double-negative elastic metamaterials

As the counterpart of electromagnetic and acoustic metamaterials, elastic metamaterials are artificial periodic elastic composite materials offering the possibility to manipulate elastic wave propagation in the subwavelength scale through different mechanisms. For the promising superlensing in the medical ultrasonic detection, double-negative metamaterials possessing the negative effective mass density and elastic modulus simultaneously can be utilized as the ideal superlens for breaking the diffraction limit. In this paper, we present a topology optimization scheme to design the two-dimensional (2D) single-phase anisotropic elastic metamaterials with broadband double-negative effective material properties and demonstrate the superlensing effect at the deep-subwavelength scale. We also discuss the impact of several design parameters adopted in the objective function and constraints on the optimized results. Unlike all previously reported mechanisms, the present optimized structures exhibit the novel quadrupolar or multipolar resonances for the negative effective mass density and negative effective elastic modulus. In addition, negative refraction of the transverse waves in a single-phase material is observed. Most optimized structures in this paper can serve as the anisotropic zero-index metamaterials for the longitudinal or transverse waves at a certain frequency. The cloaking effect is demonstrated for both the longitudinal and transverse waves. Moreover, with the particular constraints in the optimization procedure, a super-anisotropic metamaterial exhibiting the double-negative and hyperbolic dispersions in two principal directions within two different frequency ranges is obtained. The developed optimization scheme provides a robust computational tool for negative-index engineering of elastic metamaterials and may guide the design and optimization of other types of metamaterials, including the electromagnetic and acoustic metamaterials. The unusual properties of our optimized structures can inspire new ideas and novel applications including the low-frequency vibration attenuation, flat lens and ultrasonography for elastic waves.

Material, structure, chosen mechanical and comfort properties of kinesiology tape

The main objective of this paper is to determine material composition, structure, and chosen mechanical and thermo-physiological comfort properties of selected kinesiology tape. The results of experiments show that kinesiology tape is a non-linear elastic and porous composite material. Warp yarns are core-spun elastic yarns, while weft yarns are 100% cotton yarns. Fabric has a plain weave and its back side is equipped with an adhesive. Tensile strength of kinesiology tape ranges from 80 to 180 N depending on the tape width. In a relaxed state, porosity together with air permeability and other heat and mass transfer characteristics are mainly affected by the compact layer of adhesive on the surface of woven fabric. During tensioning, pores are expanding and therefore transfer of air and water vapor is significantly increased and at the same time heat transfer is reduced which can positively affect wearer comfort.

Statistical average of residual stresses in elastically homogeneous medium with random field of noncanonical inclusions

We consider a linearly elastic composite material (CM), which consists of a homogeneous matrix containing a statistically homogeneous random set of noncanonical (i.e. nonellipsoidal) inclusions. The elastic properties of the matrix and the inclusions are the same, but the stress-free strains are different. One proposes a new exact representation for the first statistical moments of stresses in the phases expressed trough the averaged boundary integrals over the inclusion boundaries. These integrals presenting the perturbations introduced by a single inclusion inside the infinite matrix are evaluated by a meshfree method based on fundamental solutions basis functions for a transmission problem in linear elasticity. Increasing of volume fraction of inclusions can lead to change of a sign of local residual stresses estimated by either the new approach or the classical one. The main properties of the method are analyzed and illustrated with several numerical simulations in 2D infinite domains containing statistically homogeneous random field of inclusions.

Force-induced elastic matrix-mediated interactions in the presence of a rigid wall.

We consider a soft elastic matrix that contains particulate inclusions and is bounded by a rigid wall, e.g., the substrate. Such a situation arises in elastic composite materials. They may serve as soft actuators when 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. First, 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. Then, we list the general expressions to describe the situation for point-like particles in the presence of no-slip and free-slip surface conditions. To compare the effect of the different surface conditions to each other and to the bulk behavior, we address the example situation of pairwise interactions between two embedded particles. The axis through both particle centers is either aligned parallel or perpendicular to the surface. Our results suggest that walls with free-slip surface conditions are preferred when they serve as substrates for soft actuators made from elastic composite materials. As we further demonstrate, the presence of a rigid wall can qualitatively change the interactions between the inclusions. In effect, it can switch attractive interactions into repulsive ones (and vice versa). It should be straightforward to observe the effects in future experiments and to combine our results, e.g., with the modeling of biological cells and tissue on rigid surfaces.

Modelling of the elastoplastic dynamics of longitudinally reinforced wall beams based on a time-explicit central difference method

Abstract A numerical analytical method for modelling the elastoplastic deformation of longitudinally reinforced wall beams with isotropically strengthened composite component materials, which enables a solution of the corresponding elastoplastic problem to be obtained at discrete instants of time using an explicit scheme, is developed by a time step method involving central finite differences. In the case of linear elastic composite component materials in the reinforced beams, the proposed model reduces to Bolotin's well-known structural model of the mechanics of composites. An initial-boundary-value problem of the dynamic deformation of longitudinally reinforced flexible wall beams is formulated in the von Karman approximation with consideration of their weakened resistance to transverse shearing. Equations and relations corresponding to two versions of Timoshenko's theory are obtained from a few positions. An explicit “cross” scheme for numerical integration of the initial-boundary-value problem posed, which is consistent with the step-by-step scheme used to model the elastoplastic deformation of a composite beam material, is constructed. Calculations of the dynamic and quasistatic bending behaviour of reinforced wall beams during the linear elastic and elastoplastic deformation of the composite component materials are performed. It is found that the classical theory is totally unacceptable for performing such calculations (except for beams of very small relative height) and that the first version of Timoshenko's theory gives adequate results only in the case of linear elastic composite component materials. Use of the second version of Timoshenko's theory is recommended as more accurate for calculations of the elastoplastic deformation of reinforced wall beams.

Inner resonance in fiber-matrix composites with homogeneous fibers

The microstructure of elastic composite materials can be adjusted in order to provide inner resonance, leading to negative dynamic density. In a first step, the results on the process using asymptotic expansion that provides the structure of the effective behaviour and the scaling of physical parameters leading to inner resonance are recalled. The process allows to describe the dynamic localization problem that must be considered in order to provide the effective behaviour. The localization problem is solved for elastic composites containing cylindrical fibers with circular cross-section. It involves the recovering of eigenfrequencies of a cylindrical domain through Bessel functions. While there are several sets of eigenfrequencies, it will be shown that only one set of eigenfrequencies contributes to the dynamic density. The eigenfrequencies and the participation factors for each resonance are provided, leading to a full description of the dynamic density.

Forces on Rigid Inclusions in Elastic Media and Resulting Matrix-Mediated Interactions.

To describe many-particle systems suspended in incompressible low-Reynolds-number fluids, effective hydrodynamic interactions can be introduced. Here, we consider particles embedded in elastic media. The effective elastic interactions between spherical particles are calculated analytically, inspired by the approach in the fluid case. Our experiments on interacting magnetic particles confirm the theory. In view of the huge success of the method in hydrodynamics, we similarly expect many future applications in the elastic case, e.g., for elastic composite materials.

Tetherless mobile micrograsping using a magnetic elastic composite material

In this letter, we propose and characterize a new type of tetherless mobile microgripper for micrograsping that is made of a magnetic elastic composite material. Its magnetically-programmable material and structures make it the first three-dimensional (3D) mobile microgripper that is directly actuated and controlled by magnetic forces and torques. With a symmetric four-limb structure, the microgripper is 3.5 mm long from tip to tip when it is open and 30 μm thick. It forms an approximate 700 μm cube when it is closed. The orientation and 3D shape of the microgripper are determined by the direction and strength of the applied magnetic field, respectively. As a mobile device, the microgripper can be moved through aqueous environments for precise grasping and transportation of micro-objects, pulled by magnetic gradients directly or rolled in rotating magnetic fields. The deformation of the microgripper under magnetic actuation is characterized by modeling and confirmed experimentally. Being directly controlled by magnetic forces and torques, the microgripper is easier and more intuitive to control than other magnetic microgrippers that require other inputs such as thermal and chemical responses. In addition, the microgripper is capable of performing fast repeatable grasping motions, requiring no more than 25 ms to change from fully open to fully closed in water at room temperature. As a result of its large-amplitude 3D deformation, the microgripper can accommodate cargoes with a wide range of geometries and dimensions. A pick-and-place experiment demonstrates the efficacy of the microgripper and its potentials in biomedical, microfluidic, and microrobotic applications.

Mathematical models for nonlocal elastic composite materials

Abstract In this paper we derive and solve nonlocal elasticity a model describing the elastic behavior of composite materials, involving the fractional Laplacian operator. In dimension one we consider in (($\mathcal{D}$)) the case of a nonlocal elastic rod restrained at the ends, and we completely solve the problem showing the existence of a unique weak solution and providing natural sufficient conditions under which this solution is actually a classical solution of the problem. For the model (($\mathcal{D}$)) we also perform numerical simulations and a parametric analysis, in order to highlight the response of the rod, in terms of displacements and strains, according to different values of the mechanical characteristics of the material. The main novelty of this approach is the extension of the central difference method by the numerical estimate of the fractional Laplacian operator through a finite-difference quadrature technique. For higher dimensions N ≥ 2 {N\geq 2} we study more general problems for which the existence of weak solutions is proved via variational methods. The obtained results provide an original contribute in the knowledge of composite materials with properties of nonlocal elasticity.

Piezoelectric Bending Motion Sensor for Simultaneous Detection of Bending Curvature and Speed

Development of portable and flexible bending motion sensors has been recently flourished for a variety of devices involving integration with wearable electronics, human artificial skin, and biomimetic robots. Most studies on bending motion sensors exploit transduction mechanism including resistivity, capacitance changes and optical phenomena, which essentially require external power supplies for operation of sensor system. However, self-powered system might be significant for portable and environmentally compatible and persistent system for potential uses in robotics or portable mobile electronics. In this regard, adopting piezoelectric bending elements is desirable for active sensing system as well as the superiority for ultra-flexible properties for wearable manufacturing. Multi-functional capabilities of motion sensing will enable high accurate detection of any external stimuli of bending motions. Most researches on piezoelectric bending motion sensors, however, have demonstrated a sensing algorithm based on the change of piezoelectric potential as a function of solely bending curvature. In fact, the piezoelectric signals are comprehensive results affected by various factors such as bending curvature and speed. More precisely, the output signal values are differentiated as a function of bending curvature, otherwise also distinguished by different bending speed at the same time. In this point of view, the piezoelectric output signals at the same bending curvature conditions with different bending speed will apparently have different signal values. Therefore, the dependence on output signals in response of bending motion across the piezo elements should be separately investigated in order to enhance the accuracy of sensing. For analysis of bending curvature and speed for detection of bending motions across the piezo elements, a systematic algorithm tool is required to be organized. Herein, a piezoelectric bending motion sensor has been developed for simultaneous recognition of bending curvature and speed through systematic analysis based on experimentally ratiocinative algorithm tool. Logically, the strategy for detection bending motion is to separate the influence of the bending curvature and speed while figure out the relationship between dependent variables characterizing a given piezoelectric signals with the independent variables. The dependent variables to be measured are a height, an area, and a width of voltage signals, whereas the independent variables to be estimated are bending curvature and speed. On the basis of the hypothesis, an experimentally ratiocinative algorithm was established for simultaneous recognition of bending curvature and speed across the piezoelectric bending motion sensors. Through simple three steps: measurement of output signals; construction of an algorithm; estimation of independent variables, sensing of the bending curvature and speed is simultaneously available with high accuracy. In addition, elastic piezoelectric composite material; ZnO nanorods (NR) - polydimethylsiloxane (PDMS) sandwiched structure and the mechanically stable and robust electrodes; Ag nanowire (NW) -single-wall carbon nanotube (SWCNT) hybrids are both remarkable to apply in flexible bending motions in piezoelectric sensory system. The hydrothermally grown ZnO NRs with bi-axial configuration were facile for bending motion sensing. The bi-axially grown ZnO NRs form uniform monolayer by simple rubbing process because of strong Van der Waals forces. Moreover, adoption of elastic electrodes of Ag NW-SWCNT guarantees flexibility without any structural cracks with consistent maintenance of electrical conductivity. From the configuration of piezoelectric structures, highly flexible piezoelectric bending motion sensing was actualized for any external stimuli. This reciprocal piezoelectric bending motion sensor and algorithm system can be a practical sensing methodology toward realization of artificial and wearable motion sensors. Figure 1

Hydrodynamic description of elastic or viscoelastic composite materials: Relative strains as macroscopic variables.

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 present a hydrodynamic description of (visco)elastic composite materials. For this purpose, additional strain variables reflect the state of the inclusions and their immediate environment. These additional strain variables in general are not set by a coarse-grained macroscopic displacement field. Apart from that, during our derivation, we also include the macroscopic variables of relative translations and relative rotations that were previously introduced in different contexts. As a central point, our approach reveals and classifies the importance of a macroscopic variable termed relative strains. We analyze two simplified minimal example geometries as an illustration.

Modeling and design of lightweight, hyperdamping metamaterials for large, broadband vibroacoustic energy attenuation

The absorption and dissipation of spectrally broadband vibration and wave energy are long-standing pursuits for researchers and engineers. In vehicular applications, light-weighting demands have led to the common use of flexible structural components that exacerbate concerns of low frequency energy transmission and radiation while joints and geometrical features result in higher frequency vibrations that produce adverse noise fields for occupants. To address the needs for broadband vibroacoustic energy attenuation via a lightweight material solution, this research integrates concepts from recent studies on elastic and poroelastic composite materials and investigates a new idea to cultivate hyperdamping effects in an engineered metamaterial. A finite element (FE) model is developed to identify ways in which to effect hyperdamping properties by virtue of controlled instability mechanisms embedded within the metamaterial. Throughout the design space, the simulations predict numerous design parameter selections that generate hyperdamping properties for large, broadband energy trapping and dissipation. Experimental studies verify the trends of FE model predictions and exemplify the potentials for hyperdamping phenomena once leveraged in practice.

A micromechanics-based nonlocal constitutive equation incorporating three-point statistics for random linear elastic composite materials

A variational formulation employing the minimum potential and complementary energy principles is used to derive a micromechanics-based nonlocal constitutive equation for random linear elastic composite materials, relating ensemble averages of stress and strain in the most general situation when mean fields vary spatially. All information contained in the energy principles is retained; we employ stress polarization trial fields utilizing one-point statistics so that the resulting nonlocal constitutive equation incorporates up through three-point statistics. The variational structure is developed first for arbitrary heterogeneous linear elastic materials, then for randomly inhomogeneous materials, then for general n-phase composite materials, and finally for two-phase composite materials, in which case explicit variational upper and lower bounds on the nonlocal effective modulus tensor operator are derived. For statistically uniform infinite-body composites, these bounds are determined even more explicitly in Fourier transform space. We evaluate these in detail in an example case: longitudinal shear of an aligned fiber or void composite. We determine the full permissible ranges of the terms involving two- and three-point statistics in these bounds, and thereby exhibit explicit results that encompass arbitrary isotropic in-plane phase distributions; we also develop a nonlocal “Milton parameter”, the variation of whose eigenvalues throughout the interval [0, 1] describes the full permissible range of the three-point term. Example plots of the new bounds show them to provide substantial improvement over the (two-point) Hashin–Shtrikman bounds on the nonlocal operator tensor, for all permissible values of the two- and three-point parameters. We next discuss further applications of the general nonlocal operator bounds: to any three-dimensional scalar transport problem e.g. conductivity, for which explicit results are given encompassing the full permissible ranges of the two- and three-point statistics terms for arbitrary three-dimensional isotropic phase distributions; and to general three-dimensional composites, where explicit results require future research. Finally, we show how the work just summarized, treating elastostatics, can be generalized to elastodynamics, first in general, then explicitly for the longitudinal shear example.

Effective properties of thermoperistatic random structure composites: Some background principles

The basic feature of the peridynamic model considered here is a continuum description of a material’s behavior as the integrated nonlocal force interactions between infinitesimal particles. In contrast to classical local and nonlocal theories, the peridynamic equation of motion introduced by Silling (J Mech Phys Solids 2000; 48: 175–209) is free of any spatial derivatives of displacement. A theory of thermoelastic composite materials (CMs) with nonlocal thermoperistatic properties of multiphase constituents of arbitrary geometry is analyzed for statistically homogeneous CMs subjected to homogeneous loading. A generalization of the Hill’s equality to peristatic composites is proved. The classical representations of effective elastic moduli through the mechanical influence functions for elastic CMs are generalized to the case of peristatics, and the energetic definition of effective elastic moduli is proposed. The general results establishing the links between the effective properties (effective elastic moduli, effective thermal expansion) and the corresponding mechanical and transformation influence functions are obtained by the use of the decomposition of local fields into load and residual fields. Effective properties of thermoperistatic CM are expressed through the introduced local stress polarization tensor averaged over the extended inclusion phase. A detected similarity of results for both the peristatic and locally elastic composites is explained fundamentally, as the methods used for obtaining the results widely exploit the Hill’s condition and the self-adjointness of the stress operator. However, the representation of effective properties for composites with both the local thermoelastic and nonlocal thermoperistatic properties do not always coincide. Therefore, the representation of effective eigenfields through mechanical influence functions generalizing Levin’s representation does not in general hold for thermoperistatic CMs; this is demonstrated for a one-dimensional numerical example.