Effective Properties Of Composites Research Articles

Numerical predictions for the effective properties of flexoelectric composites with spherical inclusion

Numerical predictions for the effective properties of flexoelectric composites with spherical inclusion

Multiscale and multiphysics FEA simulation and materials optimization for laser ultrasound transducers

The relationship between the nanocomposite design and the laser ultrasound transducer (LUT) characteristics was investigated through simulations in multiple scale levels for material behavior, device response, and acoustic wave propagation in media. First, the effects of the nanoparticle size and concentration on the effective properties of composites were quantitatively investigated with the finite element analysis (FEA) method. Second, the effective properties of the nanocomposite were assigned to the layer, which is modeled as a homogeneous material, in the FEA for the LUT simulating the energy conversion from the incident laser to the acoustic wave. Finally, the ultrasound propagation in the water was calculated by a theoretical wave propagation model. The FEA-based prediction was compared with the experimental data in the literature and a theoretical analysis for LUT based on Thermal-Acoustic coupling. As a result, the ultrasound waves on the transducer surface and at a distance in the water could be predicted. Based on the hierarchically integrated prediction procedure, the optimal conditions of the photoacoustic nanocomposites were investigated through the parametric study with the particle size and concentration as variables. The results guide the material designs optimized for different device characteristics, such as high pressure and broad bandwidth.

Critical investigation on the effect of fiber geometry and orientation on the effective mechanical properties of fiber-reinforced polymer composites

In this study, finite element method is used to investigate the effect of combined geometry and orientation of the fiber on the elastic properties of fiber-reinforced composites. The finite element models were developed using COMSOL Multiphysics. Representative volume elements consisting of circular, square and elliptical cross-section of fibers were used in the case of combined geometry while 0°, 15°, 30°, 45°,60°, 75°, 90° and 135° were angles considered for the fiber orientation. Results from the study show that the combined geometry and fiber orientation angle has significant effect on the performance of fiber reinforced composites.

Self-consistent assessments for the effective properties of two-phase composites within strain gradient elasticity

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 explicit relations between the Eshelby-like tensors and corresponding concentration tensors that are used to define the averaged field variables inside the inclusions. Obtained analytical solutions allow to evaluate the effective classical and gradient elastic moduli of composite materials accounting for the phases properties, volume fraction, shape and size of inclusions. Presented solution for the effective gradient moduli covers the full range of volume fraction and correctly predicts the absence of gradient effects for the homogeneous classical Cauchy medium. Examples of calculations for the composites with spherical inclusions are given. Micro-scale definition of the well-known simplified strain gradient elasticity theory is provided. Namely, it is shown that this theory is the phenomenological continuum model for the composites with isotropic matrix and with the small volume fraction of stiff isotropic spherical inclusions, which have the same Poisson’s ratio to those one of matrix phase.

Systematic Approach for Finite Element Analysis of Thermoplastic Impregnated 3D Filament Winding Structures—Advancements and Validation

This work aims to enhance and validate a systematic approach for the structural finite element (FE) analysis of thermoplastic impregnated 3D filament winding structures (fiber skeletons). The idealized modeling of geometrically complex fiber skeletons used in previous publications is refined by considering additional characteristic dimensions and investigating their mechanical influence. Moreover, the modeling approach is transferred from the meso- to the macro-level in order to reduce modeling and computational effort. The properties of meso- and macro-level FE models are compared using the example of simple loop specimens. Based on the results, respective application fields are defined. In the next step, the same modeling approach is applied to a more complex, three-dimensional specimen—the inclined loop. For its macro-level FE model, additional material characterization and modeling, as well as enhancements in the modeling of the geometry, are proposed. Together with previously determined effective composite properties of fiber skeletons, these results are validated in experimental tensile tests on inclined loop specimens.

Effective properties of two-dimensional dispersed composites. Part I. Schwarz's alternating method

The generalized alternating method of Schwarz can be presented as an infinite sequence of all the mutual interactions between inclusions in the boundary value problem stated for a composite. Schwarz's method for overlapping domains has been assigned to decomposition methods widely used in pure numerical computations. In the same time, the generalized alternating method for non-overlapping inclusions is convenient in symbolic-numerical computations described in this paper. Implementation of the explicit and implicit schemes yields new approximate analytical formulas for the effective properties of dispersed composites. Moreover, the exactly derived precision of their validity in concentration and in contrast parameter is established. The first order iteration corresponds to the famous Maxwell's self-consistent approach.

Wave propagation analysis of sandwich plates with graphite particles filled viscoelastic material core in hygrothermal environments

In the present work, the wave propagation behavior of sandwich plates with graphite particles filled viscoelastic material core under the hygrothermal environments is investigated. A four-variable integral higher-order shear deformation theory (HSDT) and the Hamilton’s principle are applied to derive the equations of motion and the corresponding wave dispersion relations. The accuracy and effectiveness of the present model are verified by comparison with previous research. The effective properties of the particulate composite are accurately determined by a differential scheme with consideration of the particle interactions. Results imply that increased effective moduli are obtained through incorporating the graphite particles, or decreasing the temperature or increasing the moisture. Influences of the volume fraction of graphite particle, the core-to-face layer thickness ratio, temperature and moisture on the wave dispersion responses are quantitatively analyzed and qualitatively assessed. It has been found that the hygrothermal environments play a significant role in the wave propagation characteristics.

Design of multiphase auxetic metamaterials by a parametric color level set method

This paper presents a systematic optimization design method for the multiphase auxetic metamaterials with different deformation mechanisms in both 2D and 3D scenarios. In this method, the parametric color level set (PCLS) is developed to describe different material phases in the microstructures, in which at most 2L materials phases can be precisely represented by only L description functions without any overlaps. Furthermore, clear and smooth material interfaces can be guaranteed in the design, and multiple material usage constraints can be efficiently handled by the well-established gradient-based algorithm. The shape derivative theory is introduced to analyze the design sensitivities for the optimization problem. The effective elasticity properties of the multiphase composites are evaluated by the numerical homogenization method under periodic boundary conditions. Various symmetric conditions are defined and enforced to induce the re-entrant and chiral patterns in both 2D and 3D metamaterials. Several numerical examples are provided to demonstrate the features of the proposed method in tailoring different types of multiphase auxetics. The multiphase metamaterials with two and more material phases are discussed. It is shown that the presented design method can be used to devise both the re-entrant and chiral auxetic metamaterials with excellent auxetic and stiffness properties.

Dynamic Effective Properties of Lead-Reinforced Epoxy Resin Composites with Differential Method

In this paper, the quasi-P wave propagation in epoxy/lead composites is studied by the differential method with polarization stress and polarization momentum. The corresponding differential equations are numerically solved by the fourth-order Runge–Kutta method, and the dynamic effective modulus and density are obtained. Correctness of the results obtained by the differential method is verified by comparing with the results obtained by the self-consistent method as well as experiments. Results show that the dynamic effective modulus L 1133 and L 3333 increase with the increase of aspect ratio δ , whereas L 1111 and L 1122 decrease with the increase of δ . The phase velocity ratio of the quasi-P wave propagation in the composites tends to 1 when the dimensionless wave number is large, and the dynamic effective density and modulus obtained are not isotropic when δ ≠ 1 . It is believed that the differential method can be a choice for solving dynamic effective properties of heterogeneous composites.

Concurrent Topology Optimization of Composite Plates for Minimum Dynamic Compliance.

This paper proposes a novel density-based concurrent topology optimization method to support the two-scale design of composite plates for vibration mitigation. To have exceptional damping performance, dynamic compliance of the composite plate is taken as the objective function. The complex stiffness model is used to describe the material damping and accurately consider the variation of structural response due to the change of damping composite material configurations. The mode superposition method is used to calculate the complex frequency response of the composite plates to reduce the heavy computational burden caused by a large number of sample points in the frequency range during each iteration. Both microstructural configurations and macroscopic distribution are optimized in an integrated manner. At the microscale, the damping layer consists of periodic composites with distinct damping and stiffness. The effective properties of the periodic composites are homogenized and then are fed into the complex frequency response analysis at the macroscale. To implement the concurrent topology optimization at two different scales, the design variables are assigned for both macro- and micro-scales. The adjoint sensitivity analysis is presented to compute the derivatives of dynamic compliance of composite plates with respect to the micro and macro design variables. Several numerical examples with different excitation inputs and boundary conditions are presented to confirm the validity of the proposed methodologies. This paper represents a first step towards designing two-scale composite plates with optional dynamic performance under harmonic loading using an inverse design method.

Incremental sequential homogenization on effective elastoplastic properties of composites with functionally graded interphase

Based on a novel incremental sequential homogenization scheme, this paper investigates elastoplastic behavior of composite with functionally graded interphase. The scheme aims to obtain effective consistent tangent moduli of composites under infinitesimal strain load. The effective moduli in each load step is investigated via two procedures. Firstly, a multi-coated model is established to represent the functionally graded interphase. Phases of the model are virtually added from outside to inside. Then homogenization is applied with help of the temporary effective properties obtained in virtually adding. During homogenization, phases obey classical J2 plasticity and their plastic operators are implemented to acquire effective elastoplastic responses of composite. Validation of present method is conducted by available models and experimental results. In the end, influences of thickness/yield stress of interphase and aspect ratio/volume fraction of reinforcement on elastoplastic behavior of composite are studied. Based on present model, interphase and reinforcement enhance load capacity of composite by changing elastic and plastic strain distributions within each phase.

The Interface Model and the Interphase Model for Predicting the Effective Elastic Properties of Nano-Fiber Composites

The effective bulk modulus and the effective in-plane shear modulus of nano-fiber composites are investigated using interface model and interphase model based on the generalized self-consistent method, the closed-form analytical solutions of effective bulk modulus and all equations for predicting effective in-plane shear modulus by numerical method based on the two models are presented. Using the interface model, interface effects of the effective bulk modulus and the effective in-plane shear modulus are discussed by use of numerical examples. Further research demonstrates that the analytical formula of the effective bulk modulus and the numerical results of the effective in-plane shear modulus derived from the interface model can be obtained again from the interphase model. An example of aluminium containing nano voids shows that the effective bulk modulus and the effective in-plane shear modulus predicted by the interface model have large deviations from that of the interphase model when the void radius is small, however for larger void radius, the difference is small.

Simplified micromechanics approach to analysis the performance of UD composites

A simplified micromechanical approach is used for the modelling and analysis of unidirectional (UD) compositeperformance. In this paper, the influence of volume fraction and constituent properties on the effective longitudinal,transverse, and shear properties of unidirectional composites are investigated. These effective properties are determinedusing the micromechanical approach, which is based on mathematical modelling using the rule of mixtures. Four differenttypes of unidirectional composites such as T300/BSL914C, IM7/8511-7, T300/PR319, and S2-Glass/epoxy were used foranalysis purposes. The method was validated with existing experimental results. The response is dependent on an array ofparameters, such as the orientation of fibers, the volume fractions of fibers, array of fibers and the material properties oftheir constituents. Further, this micromechanical method might be used with other reinforcing fibers for the prediction ofproperties of UD, hybrid and other composites architectures.

Analysis of the Effective Dynamic Properties of Particulate Composites with Respect to Constituent Properties

The propagation of longitudinal and shear elastic waves through a multi-phase material was studied and the effective elastic properties of the medium were evaluated. The distribution of the reinforcing inclusions was considered random throughout the matrix. The effective dynamic properties of the composites, including their effective bulk and shear moduli and effective densities, were examined along with the effective phase velocity and attenuation of the incident P and S waves. The Sabina–Willis model was employed to study the wave propagation behavior, and the model performance was analyzed through comparison with experimental data from the literature. The results indicated that wave propagation significantly depended on the physical and mechanical properties of inclusions relative to those of the matrix and the normalized wave number of the propagated elastic wave. Moreover, despite the fact that the elastic properties of the incidence in the P and S waves exhibited a similar trend, their values differed significantly. The results can serve as a design criterion for composite materials under dynamic loading.

A Two-Level Homogenization Approach for Polymer Nanocomposites with Coated Inclusions

In polymer nanocomposites, other than the matrix and inclusion, a third phase so-called interphase, is commonly observed. Inter-phase properties affect the overall macroscopic mechanical behavior. It is crucial to model the interphase and obtain the effective composite properties accordingly. Homogenization theory is very useful and powerful; however, many of the homogenization-based techniques have deficiencies. The goal of the study is to combine two very well-known homogenization techniques to model the polymer nanocomposites with coated inclusions. One of the goals of the study is to demonstrate the deficiency that originated from the interphase modeling and overcome this problem by the proposed two-level homogenization method. This method aims to model load transfer between the matrix and the reinforcement element through the interphase in a correctly. For this purpose, first, an effective inclusion is formed using finite element homogenization, then the effective inclusion and the matrix are homogenized using micromechanics-based Double Inclusion method. The proposed method provides a remarkable improvement compared to the micromechanics-based method for the soft interphase case.

Smart damping of a simply supported laminated CNT-based hybrid composite plate using FE approach

We present the finite element (FE) model using the first-order shear deformation theory (FSDT) to investigate the damping performance of laminated hybrid fiber-reinforced composite (HFRC) smart plates via the active constrained layer damping (ACLD) treatment. A unique feature of the HFRC is that the nanoscale carbon nanotubes (CNTs) are embedded in the matrix phase of carbon fiber composite to improve the overall properties, especially the damping characteristics of the resulting HFRC. Two- and three-phase micromechanical models are employed to determine the effective elastic properties of the base composite and HFRC respectively. The constraining layer of the ACLD treatment is considered to be made of vertically reinforced 1–3 piezoelectric composite (PZC) material. The system consists of a laminated HFRC plate integrated with the two patches of ACLD treatment and the numerical results are computed for three cases: symmetric and anti-symmetric cross-ply, and anti-symmetric angle-ply. The damping performance of the laminated HFRC square plate is significantly enhanced over the laminated base composite plate due to the incorporation of a small amount of CNTs. In particular, the anti-symmetric angle-ply case provides better damping than symmetric/anti-symmetric cross-ply cases. Analysis of the HFRC plate showed that its vibration amplitudes can be attenuated from ∼8 to ∼16% by adding a small amount CNTs. The effect of in-plane and transverse actuation of 1–3 PZC on the damping characteristics of the overall plate was also studied. We found that the transverse actuation significantly influences the damping performance of the overall plate. The outcomes of our study provide substantial evidence that the addition of a small amount of CNTs in the conventional composite structure can improve its damping performance significantly. This is practically possible in view of the recent research activities in the field of fabrication of large-scale CNT-based hybrid composite structures.

Effective in-plane elastic properties of honeycomb-polymer composites

Honeycomb composites are now common materials in applications where high specific stiffness is required. Previous research has found that honeycombs with polymer infills in their cells, here referred to as honeycomb-polymer composites (HPCs), exhibit effective stiffnesses greater than the honeycomb or polymer alone. Currently, the state of analytic models for predicting the elastic properties of these composites is limited, and further research is needed to better characterize the behavior of these materials. In this research, a nonlinear finite element analysis was employed to perfor2m parametric studies of a filled honeycomb unit cell with isotropic wall and infill materials. A rigid wall model was created as an upper bound on the deformable wall model’s performance, and an empty honeycomb model was employed to better understand the mechanisms of stiffness amplification. Parametric studies were completed for infill material properties and cell geometry, with the effective Young’s modulus studied in two in-plane material directions. The mechanisms by which the stiffness amplification occurs are studied, and comparisons to existing analytic models are made. It has been observed that both the volume change within the honeycomb cell under deformation and the mismatch in Poisson’s ratios between the honeycomb and infill influence the effective properties. Stiffness amplifications of over 4000 have been observed, with auxetic behavior achieved by tailoring of the HPC geometry. Additionally, the effect of large effective strains up to 10% is explored, where the cell geometry changes significantly. This research provides an important step toward understanding the design space and benefits of HPCs.

Microstructural integrity characterization of cement-based construction materials

In this paper, a new micromechanical framework to characterize the microstructural integrity and predict the effective properties of multi-phase particulate composites is presented. Within the framework, a new scalar micromechanical parameter is identified and used to derive new expressions for the effective elastic properties of particulate composites using the mean-field homogenization technique. The derived equations are then generalized for composites with multiple phase constituents. The generality of the proposed framework is demonstrated by combining the derived equations with the existing homogenization techniques such as the Mori–Tanaka method and the Generalized Maxwell’s Approach (GMA). The results show that the theory delivers consistent estimates of the effective properties of two-phase elastic composite materials. The new scalar micromechanical parameter is also used to characterize the microstructural integrity of both asphalt mixtures and Portland cement concrete. The results show that the new scalar micromechanical parameter correlates well with multiple key fundamental properties of asphalt concrete mixture, including the creep rate, the fracture energy density, the endurance limit, and the damage rate parameters. The results also show that the new micromechanical framework can be used to accurately predict the effective modulus properties of Portland cement concrete mixtures.

Stabilization of the extended finite element method for stiff embedded interfaces and inclusions

AbstractThis article investigates the performance of the XFEM for stiff embedded interfaces and inclusions. It is known that the XFEM may lead to ill‐conditioned stiffness matrices and oscillations in the interface traction field, the severity of which depends on the underlying basis functions, as well as on the orientation of the interface. The jumps at the discontinuity are shown to contain quadratic bubble residuals that can introduce oscillatory behavior. Those residuals are worsened by the ill‐conditioning of the system with very stiff interfaces. A variationally consistent method is proposed to overcome the oscillatory behavior and ill‐conditioning, in which the assumed strain method is developed to directly eliminate bubble residuals and deploy Legendre polynomials and explore their orthogonality properties to improve the conditioning of the stiffness matrices. Numerical examples illustrate the efficiency and generality of the proposed approach at both element and structural levels. The new approach is shown to be robust for imposing Dirichlet type boundary conditions at the crack interface, such as crack closure and initially rigid cohesive laws. The effects of numerical oscillations on the prediction of effective properties of composites in XFEM‐based computational homogenization procedures are also discussed.

Effective elastic properties of one-dimensional hexagonal quasicrystal composites

The explicit expression of Eshelby tensors for one-dimensional (1D) hexagonal quasicrystal composites is presented by using Green’s function method. The closed forms of Eshelby tensors in the special cases of spheroid, elliptic cylinder, ribbon-like, penny-shaped, and rod-shaped inclusions embedded in 1D hexagonal quasicrystal matrices are given. As an application of Eshelby tensors, the analytical expressions for the effective properties of the 1D hexagonal quasicrystal composites are derived based on the Mori-Tanaka method. The effects of the volume fraction of the inclusion on the elastic properties of the composite materials are discussed.