Composite Unit Cell Research Articles

Development of a geometric modeling strategy for the generation of representative unit cells in 2D braids

This article presents, tests and validates a method for generating representative unit cells of braided composites based on a geometrical approach. The method focuses on the geometry of the tows and uses surface minimization to obtain the minimal equivalent area of a central surface that is used for the generation of volumes and orthotropic mechanical properties of the tows. The homogenization of the yarns is solved using analytical equations and the homogenization of the cell is solved using a representative volume element technique. The robustness of the method is evaluated using a benchmark comparison with experimental and numerical results to validate the generated ge.ometry. The method is also tested and shown to be robust in modeling the geometry for several values of geometrical parameters of the tows without user intervention, including for configurations yielding a high cover factor.

Realization of unidirectional zero reflection based on a loss–gain balanced metamaterial

In this work, we designed and fabricated an acoustic metamaterial with unidirectional zero reflection. The metamaterial was developed based on the concept of a parity-time symmetric material using one-dimensional (1D) orifice-type unit cells as a loss material and cylindrical closed-end tubes as a gain material. Twenty such composite unit cells were connected in series to construct a one-dimensional loss–gain balanced metamaterial. The characteristics of reflection and transmission were studied at frequencies between 1100 and 1800 Hz, ensuring that the metamaterial met the conditions of a homogeneous medium. From the experiments, it was found that the designed loss–gain balanced metamaterial had nearly complete unidirectional zero reflection (r≲1.6%) at f=1202 Hz; in addition, it was shown to exhibit bidirectional zero transmission (t≃0) at f=1501 Hz.

Interfacial strength and its regulation in the carbon monofiber/epoxy binder system

The strength of polymer composite materials (CMs) is largely determined by the strength of interfacial interactions at a fiber/matrix interface. In this work the strength in a unit cell of CM carbon monofiber/cured epoxy matrix is investigated. The relevance of the work is due to direct measurements of strength at the monofiber/matrix interface, excluding defects of micro-droplet and technological errors associated with impregnation in a traditional assessment of polymer composite materials strength. Changes of surface morphology and energy characteristics of fibers in plasma chemical treatment process is shown. The study of fiber surface energy and formation of carbon monofiber/epoxy matrix interface of carbon fiber reinforced composite unit cell was carried out on the specially developed original device Drop-Sting test. Micro pull-out test was used to investigate the shear mechanical properties of interface and to determine the strength of carbon fiber reinforced composite unit cells before and after treatment in oxygen discharge plasma. It is shown that the increase in the strength of the monofiber/matrix interfacial interface after the treatment of carbon fiber in plasma occurs due to the increase in the surface energy and wettability of monofibers.

Analytical simulation of the effects of local mechanisms and microstructure on the creep response of unidirectional ceramic matrix composites

A micromechanics-based method has been developed to analyze the creep response of uncoated ceramic matrix minicomposites. Although the global stress level at which the creep response is analyzed is lower than the composite proportional limit, local stresses are assumed to be high enough that localized damage is present in the composite in the form of matrix microcracks. To model the composite creep response including the effects of matrix cracking, a fiber shear lag-based methodology is employed. In this approach, stresses are assumed to vary in the fiber as a function of time and distance from the crack plane. The varying stresses are then used to compute the overall creep strain for the composite. Various assumptions regarding the level of matrix microcracking in the composite, and the level of creep in the fiber and matrix in various portions of the composite unit cell, are also examined. The creep response of the fiber is modeled using a linear Burgers model. The model is applied to a SiCf/SiC unidirectional minicomposite system. The computed creep results are compared to experimentally obtained values. The effects of the local fiber volume fraction on the overall creep response of the composite are also studied. This work will allow increased understanding of the key material damage mechanisms and load sharing that take place during creep conditions and can be expanded to provide improved analysis methods for full macrocomposites.

An extended full field self-consistent cluster analysis framework for woven composite

In this work, the self-consistent clustering analysis (SCA) framework is extended to include homogenization and full field analysis of 3D anisotropic woven composite Representative Unit Cell (RUC). The developed extended framework has two new features, namely, (i), to reconstruct the local field variables, a strain refinement stage is presented by solving full field Lippmann–Schwinger equations within 3D anisotropic woven composite RUC following the online predictive stage in SCA, and (ii), discrete Green’s operator based on finite difference is adopted to improve the accuracy of refined point-wise physical field variables. To demonstrate the accuracy and efficiency of the proposed method, benchmark problems are analyzed, and results are compared to directly numerical simulation (DNS). For the reproducibility of presented results, the developed code can be freely downloaded from https://github.com/Tong-RuiLiu/Extended-SCA-and-FFT-based-strain-refinement-method-.

Three-scale bridging for woven composites using homogenization techniques

Woven composites have a multiscale character, whose structural response is affected by mechanisms on different lower scales. The predicted macroscopic response of a carbon fiber reinforced woven composite is achieved by model order reduction and homogenization techniques, taking into account the structures and mechanisms on both mesoscopic and microscopic scales. Reduced order models based on piecewise uniform fields and mean field homogenization are integrated for the micro-meso-macro upscaling to finally determine the effective macroscopic response of a woven unit cell. A spatial decomposition for the woven composite unit cell on the mesoscale is implemented, achieving the model order reduction by taking into account the local microstructure of the yarns as well as inelastic fields emerging under selected deformation conditions. Following, different numerical tests are performed on the woven unit cell, containing complex and inelastic loading histories. Macroscopic homogenized predictions following the reduced order models and full-field direct numerical simulations are compared. Very high accuracies are achieved by the employed reduced order models, allowing for great computational savings.

Dual band-notched antenna design using composite right/left handed metamaterial

A small metamaterial notch-antenna with band reject at 3.5 and 4.4 GHz is proposed by introducing reactance to balanced composite left-right unit cell, thus making it non-resonant at the desired frequency without any change in overall size. Simulations were carried on HFSS and antenna with notch band implemented on RT\\Duroid substrate. The type I and type II CRLH metamaterial notch-antenna illustrate that the antenna notches at 3.5 and 4.4 GHz, with VSWR > 2. Such filters suitable for UWB application where there is interference.

Mechanical behaviors of the carbon fiber reinforced X-core sandwich structure under the dynamic compression

A split Hopkinson pressure bar technique was applied to investigate the dynamic response of carbon fiber composite sandwich structures with the X-cores. The compressive mechanical behaviors of the composite X-core unit cells and its foam reinforced unit cells at the strain rates ranging from 3•10−4 s−1 to 600 s−1 were obtained. During the dynamic tests, the dynamic stress equilibrium state in the unit cells was achieved by adopting the pulse sharpers and discussed comprehensively. The measured structural strength increased by 81.9 % on average at the high strain rates than that under the quasi-static compression. Under the dynamic compression, the failure modes captured by a high-speed camera were found similar with that of the quasi-static tests. Finite element analysis was utilized to study the variation history of stress and strain rate fields of the core. Because of the material failure strain enhancement effect, the experimental and simulated compressive strength of the composite unit cells both increased significantly at the high strain rates. At the same high-speed compressive strain rate, the dynamic reinforcement effect of the composite sandwich unit cell was smaller than that of the parent material.

Meso-scale progressive damage simulation of textile composites using mesh superposition

The paper demonstrates that the mesh superposition (MSP) based finite element (FE) models of a textile composite unit cell can be used for adequate prediction of damage- and matrix plasticity-induced nonlinearity of the composite stress-strain response under tensile and shear loading. An elasto-plastic thermodynamically consistent damage model is implemented for matrix damage simulations. The intra-yarn damage initiation and propagation are simulated using Puck’s damage criterion and a continuous damage mechanics model. The numerical simulations are validated by a comparison with experimental results for tension and shear loading of a plain weave glass/epoxy laminate.

Strength enhancement and modulus modulation in auxetic meta-biomaterials produced by selective laser melting

Meta-biomaterials are applied to orthopedic implants to avoid stress shielding effects; however, there is no reason for the yield strength to be comparable to that of human bone. In this study, a composite unit cell was designed by combining the positive Poisson's ratio (PPR) and negative Poisson's ratio (NPR) unit cells, inspired by the second-phase strengthening theory. The purpose was to increase the strength while maintaining the elastic modulus. All structures were successfully fabricated from Ti-6Al-4V via selective laser melting. The relative density is between 0.08 and 0.24, which falls within the optimal range for bone growth. Mechanical tests indicated that the center of the inclined rod fractured in a stepwise fracture mode, which was consistent with the predictions of the Johnson–Cook model. The elastic modulus ranged from 0.652 ± 0.016 to 5.172 ± 0.021 GPa, and the yield strength varied from 10.62 ± 0.112 to 87.158 ± 2.215 MPa. An improved Gibson–Ashby law was proposed to facilitate the design of gradient structures. When the re-entrant angle was 40°, a hybrid body-centered cubic NPR structure was formed, resulting in a significant improvement in the mechanical properties. Importantly, the yield strength of the proposed composite structures increased by 43.23%, and the compression strength increased by 44.70% under the same elastic modulus. The strengthening mechanism has been proven to apply to other bending-dominated structures. Overall, this imparts unprecedented mechanical performance to auxetic meta-biomaterials and provides insights into improving the reported porous structures. Statement of significanceAuxetic meta-biomaterials exhibit auxetic properties that can improve the contact between the bone-implant interface and reduce the risk of aseptic failure. To avoid the stress shielding effect, the elastic modulus has traditionally been decreased by increasing the porosity. However, the strength is simultaneously reduced. Therefore, a composite unit cell was proposed to increase strength rather than modulus by combining the positive and negative Poisson's ratio unit cells, inspired by the second-phase strengthening theory. We observed a 43.23% increase in the yield strength of the composite structure without increasing the elastic modulus. This strengthening mechanism has been proven to apply to other bending-dominated structures. Our approach provides insights into improving other bending-dominated structures and broadening their applications for bone implantation.

A simple green synthesis of pure and sterling silver nanoparticles via pulsed laser ablation in deionized water: characterization and comparison

Pure silver (Ag) and its alloy nanoparticles (NPs) with intense and tunable SPR bands in the visible region are widely exploited for biosensors, information storage, and solar energy systems. Pure Ag and Sterling silver (Ag92.5Cu7.5) NPs were synthesized by the laser ablation method in deionized water using a pulsed Nd:YAG laser. The prepared NPs were characterized and compared for their structural, morphological, and optical properties. The x-ray diffraction (XRD) and selected area electron diffraction (SAED) results revealed that the NPs have polycrystalline nature with five lattice directions. The diffraction peak positions for Ag92.5Cu7.5 NPs exhibited an average redshift of 0.1 ̊ compared to pure Ag NPs due to the presence of copper atoms in the composite crystal unit cell structure. The formation of spherical NPs with an average size of 9.1 nm and 8.4 nm for Ag and Ag92.5Cu7.5 NPs was confirmed using transmission electron microscopy (TEM) and high-resolution TEM (HRTEM). It was found that the concentration of synthesized Ag92.5Cu7.5 alloy NPs was considerably higher than that of pure Ag NPs. Going from pure to alloy silver NPs, the wavelength of surface plasmonic resonance (SPR) peak shifted from 400 nm to 395 nm. The UV–vis absorption spectra at different aging times revealed that pure Ag colloidal solution is relatively stable. Both colloidal solutions exhibited a similar pattern of photoluminescence (PL) emission spectra with peaks in the blue region.

Modeling of Internal Geometric Variability and Statistical Property Prediction of Braided Composites.

Due to the advantages of high specific strength, specific stiffness, and excellent fatigue resistance, carbon fiber reinforced braided composites have been widely applied in engineering. Since the molding process of braided composites is complex and immature, substantial variability of the internal geometry exists in composites, in which the yarn path with uncertainty is a main factor, so it is necessary to establish an uncertainty model to study the influence of randomness of the yarn path on mechanical properties, which is significantly related to the fatigue resistance properties of composite. An uncertain mesoscopic model with uniform distribution of yarn paths is proposed. Assuming the yarn path is spatially varying in interval range, the variability of yarn path is represented geometrically in the unit cell of composite. The three-dimensional coordinates of the yarn trajectory are calculated, the meso-uncertainty models of 2-D and 2.5-D braided composites are established. The equivalent elastic parameters and the thermal expansion coefficients are obtained by applying homogenization method and temperature field boundary conditions to the mesoscopic model. The effect of yarn path uncertainty on the statistical characteristics of elastic and thermal parameters of braided composites was studied by using Monte-Carlo simulation. A simulation method for modeling yarn path uncertainty of braided composites is provided in this paper for predicting the statistical characteristics of the equivalent elastic and thermal parameters.

Phononic crystal based sensor to detect acoustic variations in methyl & ethyl nonafluorobutyl ether

Phononic crystals and metamaterials have been widely studied for wave manipulation applications. In this study, we propose a conceptual framework for a new type of acoustic bio-chemical sensor that works based on the principle of phononic crystals and metamaterials to detect the temperature and pressure changes in active solvents like Methyl Nonafluorobutyl Ether (MNE) and Ethyl Nonafluorobutyl Ether (ENE). First, a wide low-frequency bandgap is obtained from the proposed composite unit cell structure with trampoline effect. Then a defect is introduced to adjust the localize cavity modes inside the reported bandgap. Later, the cavity is filled with MNE and ENE solvents that eventually resulted into fluid-solid coupling physics. The numerical wave dispersion curves and transmission profiles show presence of Fano-like interference/resonance effect evident from the observation of asymmetrical transmission profile. Such robust asymmetrical transmission peak is generated due to coupling of incident waves with scattered wave field emitted from the MNE and ENE solvents upon excitation. The variation in acoustic properties of MNE and ENE caused by temperature and pressure fields on newly born Fano-like asymmetrical transmission profile is studied. The proposed acoustic bio-chemical sensor governed by Fano-interference effect efficiently capture the variation in acoustic properties of MNE and ENE solvents at relatively low-frequency regime that makes this approach favorable for sensing applications. Such smart acoustic bio-chemical sensors can have useful applications in pharmaceutical production, petrochemicals and capturing ingredients of cosmetic and beauty products.

Influence of crack location and crack number on the responses of 3D representative unit cell of unidirectional composites under tension in the fiber direction

In this paper, numerical study on crack location and crack number on the responses of representative unit cell of unidirectional composites under tension is conducted by extended finite element method (XFEM). The composites studied here are single-crack composites, two-crack composites, and three-crack composites. Each of the composites is under tension in the fiber (x) direction. From the simulation results, the averaged strength decreases as the embedded crack number increases when composites are under tension. One interesting finding is that a crack could be a dominant crack but becomes inactive when other different cracks are in presence under the same loads. The responses of representative unit cell of composites depend upon crack location and the applied loading direction. The results from these simulations can also explain why there is discrepancy of strength prediction from the composites manufactured under the same conditions. The simulation method presented here in this paper can be used to model degree of defects (by modelling the number of cracks) and stochastic characteristics of ultimate strength (by modelling distribution of crack strength).

A novel method for investigating the isotropy of response for randomly generated unit cells of particulate composites

This work investigates the isotropy of mechanical response of randomly generated unit cells of particulate composites. We propose a novel algorithm for assessing the isotropic behavior of such microstructures by applying different loading in random planes in space. The Random Plane Evaluation of Isotropy (RPEI) is based on calculating the averaged stress and strain under periodic boundary conditions and finding the maximum angle difference between the principal directions of them as a measure for deviation from coaxiality/isotropy. We show that an average of such data at a statistical level can be used for assessing closeness to isotropy. To put the RPEI in use, we have also proposed a new method for generating unit cells containing a random distribution of ellipsoidal particles. Then the isotropy of mechanical behavior for various unit cells enclosing random suspensions of spheres and ellipsoids was investigated. Our results show that (i) Merely random distribution of particles does not guarantee the isotropy of the response (ii) Checking the isotropy in limited directions can be misleading and data at a statistical level is needed (iii) RPEI proves a reliable tool for checking the isotropy of response of unit cells of heterogeneous materials for a variety of behaviors.

Periodic and aperiodic 3-D composite metastructures with ultrawide bandgap for vibration and noise control

Periodic composite structures as acoustic metamaterials have caught enormous research interest for the inherent peculiar dynamics characteristics, effective medium properties, and fantastic mechanical features to control vibration and noises at deep subwavelength scales. A 3-D composite metastructure design endowed with ultrawide three-dimensional bandgap is highly desirable for low frequency broadband vibration and noise control. In that context, the present study proposes two types of 3-D composite mechanical metastructure unit cell designs that are capable enough to induce low frequency ultrawide bandgaps by principle of mode separation. A 3-D polymeric casing is designed and spherical/cylindrical steel masses are embedded to enhance the dynamical characteristics and mechanical properties of the resonant systems. By a numerical study on wave dispersion, the presence of ultrawide bandgap and governing physical mechanism resulting in such broadband bandgap are discussed. An asymptotic parametric study is performed to investigate the effect of metastructure geometric parameters on the reported bandgaps. We performed numerical and experimental frequency response study on the periodic and aperiodic arrangements of the composite metastructures to envisage wave attenuation inside the bandgaps. Both periodic and aperiodic arrays of metastructures yield vibration attenuation over ultrawide frequency range that is promising for low frequency broadband vibration and noise control applications. The proposed composite metastructure design morphology and manufacturing/fabrication processes are also explained for practical design and applications. The proposed mechanical metastructure designs, our modelling technique, research methodology, and the reported findings may contribute to the design and application of metadevices where low frequency broadband vibration and noise control are desirable.

Homogenization based kinematic limit analysis for finding the stability of an embankment over soft clay reinforced with granular columns

The present study examines the stability of an embankment of cohesive-frictional material placed over a purely cohesive stratum which is reinforced by means of uniformly spaced vertical granular cylindrical columns. By using the kinematic yield homogenization concept, the macroscopic yield strength envelope associated with the reinforced clay layer has been obtained numerically for different volumetric fractions of the granular column to the composite unit cell by using the semidefinite programming (SDP) technique. An upper bound approximation of the macroscopic yield criterion, using the least square method, is expressed as a summation of a number of convex ellipsoidal envelopes so that the solution for computing the stability factors for the embankment on granular column (in the presence of surcharge pressure) can be obtained later with the usage of the second order cone programming (SOCP) while performing the upper bound finite elements limit analysis. The methodology avoids the usage of any stress variable and the complete procedure has been clearly described and the associated code has been written in MATLAB. The study will be not only useful for designing embankments constructed over soft clay reinforced with granular columns but also for solving different geomechanics stability problems by using the homogenization based kinematic limit analysis approach.

3-D Semi-Analytical Homogenization Model for Soft Magnetic Composites

A 3-D semi-analytical homogenization model for soft magnetic composites (SMCs) is presented. The model is able to handle the nonlinear magnetic behavior of the ferromagnetic particles and estimate the eddy current (EC) losses. Comparisons to finite element (FE) results show a very good agreement for a unit cell of composite. The model can be used in a structural FE study of electromagnetic devices made of SMCs.

Quantum phase transitions in frustrated 1D Heisenberg spin systems

A class of frustrated one-dimensional periodic Heisenberg spin systems formed either by triangular unit cells with spin 1/2 or by composite unit cells formed by two different structural units, triangles and small linear segments formed by an odd number of spin-1/2 is investigated. Based on perturbative processing and numerical calculations of the density matrix renormalization group method, the gapless character of the exact energy spectrum of excitation for these systems was found. Their instability with respect to regular (Peierls) oscillations of interactions between structural units is demonstrated. The corresponding critical exponents for the energies of the ground state are estimated numerically. For some frustrated systems, a quantum phase transition associated with the spin symmetry of the ground state, caused by frustration, has been discovered.

Fiber identification of braided composites using micro-computed tomography

Braided composites contain interwoven fibers that are embedded in a matrix material. Advanced measurement methods are required to accurately measure and characterize braided composites due to their interwoven composition. Micro-computed tomography (μCT) is an X-ray based measurement method that allows for the internal structure of objects to be examined. High-resolution μCT of braided composites allows for their internal geometry to be accurately measured. Braid samples were measured with a voxel size of 1.0 μm3, which resulted in a field of view of 4.904 x 4.904 x 3.064 mm3. With this field of view, individual fibers within the braid yarns could be identified and measured. The scientific visualization software package Avizo and the XFiber extension was used to identify and measure braid yarn fibers from the collected μCT measurements. Fiber properties such as orientation angles (φ and θ), curved fiber length, tortuosity, and fiber diameter were obtained. Additionally, finite element mesh geometries of the braid yarns within a braided structure were created. The presented methodology provides a roadmap for the accurate modeling of braided composite unit cell geometries using high-resolution μCT data.