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This paper aims to investigate the effect of viscoelastic behavior of polymer matrix of unidirectional fiber-reinforced laminated composite on stress distribution around the pin-loaded hole under tensile loading. The Laplace transform is used to prevent the integral form of matrix governing stress-strain relation. Applying a micromechanical model, all equilibrium equations for the fibers are written analytically in the Laplace domain. The numerical algorithm of Gaver–Stehfest is implemented, and the governing equations were solved at any given time to extract the concerned results in the time domain. The obtained results are validated against the Finite Element Method results obtained through ANSYS software. Moreover, a comparison of the results of this study at the time equal zero with elastic solutions of other references showed a good agreement. The results revealed that in the long term, the maximum tensile load in the intact fiber around the pinhole was enlarged and the tensile load in fibers far from the pinhole slightly was decreased. Moreover, the location of the maximum axial load that had occurred on pinhole edges was moved slightly toward the center over time.

The fracture strain of carbon fiber-reinforced plastics (CFRPs) within CFRP/steel hybrid laminate composites is reportedly higher than that of CFRPs due to transverse compressive stress induced by the steel lamina. A micromechanical model was developed to explain this phenomenon and also to predict the mechanical behavior of CFRP/steel hybrid laminate composites. First, the shear lag theory was extended to calculate stress distributions on fibers and matrix material in a CFRP under multiaxial stress condition, considering three deformation states of matrix (elastic and plastic deformation and fracture) and the transverse compressive stress. Then, the deformation behavior of CFRP was predicted using average stress in the ineffective region and the Weibull distribution of carbon fibers. Finally, the mechanical properties of CFRP/steel hybrid laminate composites were predicted by considering the thermal residual stress generated during the manufacturing process. The micromechanical model revealed that increased transverse compressive stress decreases the ineffective lengths of partially broken fibers in the CFRP and results in increased fracture strain of the CFRP, demonstrating the validity of the current micromechanical model.

Innovative pothole patching materials reinforced with a high-toughness, low-viscosity nanomolecular resin, dicyclopentadiene (DCPD, C10H12), have been experimentally proven to be effective in repairing cracked asphalt pavements and can significantly enhance their durability and service life. In this paper, a three-dimensional micromechanical framework is proposed based on the micromechanics and continuum damage mechanics to predict the effective elastic-damage behaviors of this innovative pothole patching material under the splitting tension test (ASTM D6931). In this micromechanical model, irregular coarse aggregates are approximated and simulated by randomly allocated multi-layer-coated spherical particles in certain representative sizes. Fine aggregates, asphalt binder (PG64-10), cured DCPD (p-DCPD), and air voids are formulated into an isotropic elastic asphalt mastic matrix based on the multilevel homogenization approach. The theoretical micromechanical elastic-damage predictions are then systemically compared with properly designed laboratory experiments as well as three-dimensional finite elements numerical simulations for the innovative pothole patching materials.

Magnetorheological (MR) fluid is a typical intelligent material which is widely adopted in the mitigation of civil engineering structures, and it is normally composed of nano-sized or micro-sized iron particles, carrier fluids and additives. Because of the complexity of its composition, it is one of the research hotspot to propose a micromechanical model which can effectively describe the micromorphological transformation as well as characteristics of MR fluids. In this study, a single-double chains micromechanical model of MR fluids is proposed by taking into consideration of the influence of volume fraction and magnetic induction on the microstructure evolution of MR fluids based on the coupled field as well as magnetic dipole theory. Additionally, the shear yield stress test of the self-prepared MR fluids with multi-wall carbon nanotubes(MWCNTs) and graphene oxide (GO) composites coated ferromagnetic particles is carried out by MCR302 rotational rheometer and the results have been compared with the theoretical values of the single-double chains micromechanical model to verify the effectiveness and accuracy of the proposed model.

The effect of NiTi alloy long wires on the viscoelastic behavior of epoxy resin was investigated by utilizing the dynamic mechanical analysis (DMA) and a novel micromechanical model. The present model is capable of predicting the viscoelastic properties of the shape-memory-alloy (SMA) reinforced polymer as a function of the SMA volume fraction, initial martensite volume fraction, pre-strain level in wires, and the temperature variations. The model was verified by conducting experiments. Good agreement between the theoretical and experimental results was achieved. A parametric study was also performed to investigate the effect of SMA parameters. According to the results, by the addition of a small volume fraction of SMA, the storage modulus of the composite increases significantly, especially at higher temperatures. Moreover, applying a 4% pre-strain caused a 10% increase in the maximum value of the loss factor of the SMA reinforced epoxy in comparison with the 0% pre-strained SMA reinforced epoxy.

The paper focuses on the nonlinear vibration of functionally graded graphene nanoplatelet reinforced composite doubly curved shallow shells resting on elastic foundations. The graphene nanoplatelet reinforced composites are assumed to be distributed uniformly and functionally graded through the thickness. The material properties are assumed to be temperature-dependent and are estimated through the Halpin–Tsai micromechanical model, while the Poisson’s ratio, density mass, and thermal expansion are implemented by the rule of mixtures. The mathematical formulation is developed based on the classical shell theory and Von Karman-Donnell geometrical nonlinearity assumption. The dynamical responses of a simply supported functionally graded-graphene nanoplatelet reinforced composite doubly curved shallow shells are obtained by employing the Airy’s stress function and the Galerkin’s method. The responses of nonlinear vibration as time history, frequency-amplitude curve, phase plane graphs, and Poincare maps are carried out in this paper. In addition, the effects of the environment, graphene nanoplatelets weight fraction, graphene nanoplatelets distribution patterns, and thickness-to-length ratio are scrutinized. The obtained results are also compared and validated with those of other studies.

In the present research, a novel rate-dependent micromechanical model was presented to predict the stiffness and strength of unidirectional glass/epoxy composites. To predict the strain-rate dependent stress–strain behavior of glass fibers, using the Maxwell model with the aid of semi-empirical relations, a new viscoelastic constitutive model was proposed. Moreover, to predict the strain-rate dependent ultimate strength of brittle glass fibers, the elasto-plastic strain-rate dependent Cowper-Symonds material model was simplified by deleting the plastic terms. The strain-rate dependent mechanical properties of the polymer were also investigated by using the modified Goldberg model. Then, by modifying the Mori-Tanaka micromechanical model, a rate dependent micromechanical model was developed to predict the effective elastic properties (stiffness and strength) of unidirectional fibrous composites at arbitrary strain rates. The present model was called the strain-rate dependent Mori-Tanaka micromechanical model. As inputs, the present model just needs the viscoelastic and viscoplastic properties of fibers and polymer. Therefore, the present model reduces the necessary experimental data to predict the rate-dependent mechanical properties of unidirectional composites. For verification of the present model, the results were compared with experimental data and very good consistency in predicting the rate-dependent behavior of unidirectional composites was observed.

A nested analytical method, a product of combining two micromechanical models is developed in this study. The proposed micromechanical method predicts the relaxation properties of polymer hybrid nanocomposites containing linearly visco-elastic matrix, transversely isotropic elastic carbon fibers, and graphene nanoplatelets. Calculations performed in this model are of two scales. The small scale, which is the domain of epoxy resin and graphene nanoplatelet interactions, and the large scale, which assumes the small scale as a homogenized isotropic matrix. In the large scale, the prescribed matrix is then reinforced by the unidirectional CFs. Each scale calculation gives the properties of the underlying material. Secant moduli and the field fluctuation techniques are adopted in this study. Resulting explicit formulae allows one to calculate the overall relaxation moduli of the graphene nanoplatelet/carbon fiber-reinforced polymer hybrid nanocomposites. By comparing the data obtained by experiments and the results extracted by the proposed micromechanical approach, the accuracy of the model becomes apparent. Addition of graphene nanoplatelets into the fibrous composites leads to an improvement in the relaxation properties of the hybrid nanocomposites. Also, the elastic properties of graphene nanoplatelet/carbon fiber-reinforced epoxy hybrid nanocomposites are reported. The role of graphene nanoplatelet agglomeration, frequently encountered in real engineering situations, in the mechanical response of unidirectional hybrid nanocomposites is examined. The effects of volume fraction of graphene nanoplatelets and CFs on the overall mechanical properties are investigated.

Unsuitable surface quality is frequently observed in the machining of composites due to their heterogeneity and anisotropic properties. Thus, minimizing the machining damages requires a thorough understanding of the machining process. In this study, two different finite element models were developed using Abaqus/Explicit to simulate the cutting process of unidirectional carbon fiber-reinforced polymer: (i) a macromechanical model based on the homogenization approach and (ii) a micromechanical model in which the composite constituents were treated separately. The effects of CFRP mechanical properties, the energy of breaking and hourglass control were analyzed using a macromechanical model. The results revealed that CFRP properties and the numerical parameters highly influenced the cutting process. A comparative study was also performed between the macromechanical and the micromechanical models to study the mechanisms of chip formation. It was demonstrated that the material removal mechanisms for both models are in good agreement with the experimental observations for different fiber orientation angles.

A micromechanical model for short fiber-reinforced composites (SFRCs) with functionally graded interphases and a systematic prediction scheme to determine the effective properties are presented. The matrix and the fibers are regarded to be linear elastic, isotropic, and homogeneous. Fibers are assumed to be ellipsoids coated perfectly by functionally graded interphases, which is supposed to be formed chemically or physically by the constituents near the interface. First, to analyze the grading interphase effect, layer-wise concept is followed to divide the functionally graded interphases into multi-homogeneous sub-layers. Next, to take the effect of functionally graded interphases into account, a combination of multi-inclusion method and Mori–Tanaka method is applied to predict effective elastic properties of this unidirectional SFRCs with respect to the content and aspect ratio of the inclusions. By employing coordinate transformation, spatially elastic moduli are obtained. Finally, Voigt homogenization scheme is used to obtain the overall, averaged, symmetrical elastic properties of the SFRCs. Numerical examples and analyses demonstrate the applicability of the proposed method and indicate the influences of graded interphase, orientation, and aspect ratio of inclusions as well as properties and contents of the constituents on the overall properties of SFRCs.

This paper introduces a new method of determining the mechanical properties of carbon nanotube-polymer composites using a multi-inclusion micromechanical model with functionally graded phases. The nanocomposite was divided into four regions of distinct mechanical properties; the carbon nanotube, the interface, the interphase and bulk polymer. The carbon nanotube and the interface were later combined into one effective fiber using a finite element model. The interphase was modelled in a functionally graded manner to reflect the true nature of the portion of the polymer surrounding the carbon nanotube. The three phases of effective fiber, interphase and bulk polymer were then used in the micromechanical model to arrive at the mechanical properties of the nanocomposite. An orientation averaging integration was then applied on the results to better reflect macroscopic response of nanocomposites with randomly oriented nanotubes. The results were compared to other numerical and experimental findings in the literature.

A multi-scale micromechanical model is proposed to predict the damage degree of hybrid fiber-reinforced concrete under or after high temperatures. The thermal degradation of hybrid fiber-reinforced concrete is generally composed of the damage of the cement paste caused by thermal decomposition and thermal incompatibility, the deterioration of aggregates and fibers, and the interfacial damage between aggregates and the matrix. In this multi-scale model, four levels of hybrid fiber-reinforced concrete structures are considered when the thermal damage degree is derived; namely, the equivalent calcium silicate hydrate (C–S–H) product level, the cement paste level, the concrete level, and the hybrid fiber-reinforced concrete level. At the cement paste level, thermal decompositions of C–S–H product and calcium hydroxide are taken into account. In addition, a dimensionless parameter of the crack density is introduced to represent the thermal cracking of the matrix. At the concrete level, the interfacial damage of aggregates is simulated by a spring–interface model, in which the interfacial parameters are assumed to be functions of temperature. Moreover, at the cement paste level and the hybrid fiber-reinforced concrete level, a sub-stepping homogenization method is proposed to determine the effective properties. Comparisons between previously published experimental data and predictions and discussions illustrate the feasibility of the proposed multi-scale model in predicting thermal damage of concrete and hybrid fiber-reinforced concrete.

The effect of fiber distribution, in glass/carbon hybrid fiber composites, on the compressive kinking strength is studied using a 3D finite element-based micromechanical model. Existing experimental data from literature have indicated negative effects of hybridizing glass to carbon on the compressive strength. In this study a micromechanical modeling approach has been adopted to study the role of relative locations of glass and carbon fibers and their distributions on the predicted peak compressive strength. In the micromechanical model, the hybridization ratio was varied by changing the number of glass fibers relative to the number of carbon fibers. The effect of fiber distribution was studied by changing the interfiber spacing and location. Results obtained from the analysis indicate the importance of symmetric fiber distribution. It was found that the distribution with glass fiber in the center with a distribution of carbon fibers on the exterior is able to enhance the compressive strength as compared to an unsymmetrical arrangement of fibers in the model.

This study examines the effects of temperature and fiber and matrix diffusivities on the diffusion of fluid in glass fiber-reinforced polymer composites. Glass fiber-reinforced polymer thin plates were immersed in deionized water at two temperatures: room temperature and 50℃. During the diffusion process, the overall mass changes and dimension changes were recorded, which relate to the volumetric change and the through-the-thickness strain. Different constitutive models are considered in order to understand the diffusion of fluid through the glass fiber-reinforced polymer plates. The macroscopic models of this work, Fickian and Gurtin coupled deformation–diffusion, are first considered in order to describe the macroscopic diffusion behaviors. Two microscopic models that include fiber volume contents and diffusivities of the constituents (fiber and matrix) are then considered in order to gain fundamental insight into the effects of microstructural morphologies and constituents' diffusivities on the diffusion process in the glass fiber-reinforced polymer specimens.

Electroactive polymers with time-dependent behavior are considered in the present paper by way of a new physics-based micromechanical model; such viscoelastic response is described by the internal evolution of the polymer network, providing a new viewpoint on the stress relaxation occurring in elastomers. The main peculiarity of such internally rearranging materials is their capacity to locally reset their reference stress-free state, leading to a mechanical behavior that relaxes out (eases off) an induced stress state and that can thus be assimilated to a sort of internal self-healing process. Such high deformability and recoverability displayed by dynamically cross-linked polymers can be conveniently exploited when they are coupled in electromechanical problems; the deformation induced by an electric field can be easily tuned by the intensity of the electric field itself and the obtained shape can be maintained without any electric influence once the material microstructure has rearranged after a sufficient curing time. In the present paper, both features of the polymeric material, that is, internal remodeling and electromechanical coupled response, are considered and a theoretical framework is established to simulate representative boundary value problems.

Most concrete structures repaired by the electrochemical deposition method are not fully saturated and the healing interfaces are not always perfect in reality. To demonstrate these issues, micromechanical models are presented for unsaturated concrete repaired by electrochemical deposition method with the healing interfacial transition zone based on our latest work. The repaired unsaturated concrete is represented as a multiphase composite made up of the water, unsaturated pores, intrinsic concrete, deposition products and the healing interfacial transition zone between the latter two components. The equivalent particle, matrix and composite for repaired unsaturated concrete are obtained by modifying the differential-scheme and the generalized self-consistent method. Modifications are utilized to rationalize the differential-scheme based estimations by taking into the water (including further hydration and viscosity effects), interfacial transition zone and the shapes of the pores into considerations. Furthermore, our predictions are compared with those of the existing models and available experimental results, thus illustrating the feasibility and capability of the proposed micromechanical framework.

In this research, the effects of multi-walled carbon nanotubes on the distribution of long-term creep strains in thick-walled multi-walled carbon nanotube/fiber/polymer three-phase laminated composites are studied. In the first step, micromechanical models are developed to calculate the elastic properties of multi-walled carbon nanotube/vinylester and multi-walled carbon nanotube/E-glass fiber/vinylester composites. Using classical lamination plate theory, equilibrium and compatibility equations and strain–displacement relations, the distribution of effective stresses is considered. Moreover, utilizing Schapery single-integral model for nonlinear viscoelastic materials, Prandtl–Reuss relations and Mendelson’s approximation method, not only the distribution of circumferential and radial strains is investigated but also the effects of fiber orientation and weight fraction (wt.%) of the multi-walled carbon nanotubes on the way of distribution are studied. The results demonstrated that the addition of the multi-walled carbon nanotube to the vinylester can reduce absolute values of the radial and circumferential creep strains and dimensionless effective stresses. Moreover, most reduction occurred in the inner wall of the cylindrical shell when fiber orientation was α = 90°.

In quasi-brittle polycrystalline materials, damage by cracking or cleavage dominates plastic and viscous deformation. This paper proposes a micromechanical model for rock-like materials, incorporating the elastic-damage accommodation of the material matrix, and presents an original method to solve the system of implicit equations involved in the formulation. A self-consistent micromechanical approach is used to predict the anisotropic behavior of a polycrystal in which grain inclusions undergo intragranular damage. Crack propagation along planes of weakness with various orientation distributions at the mineral scale is modeled by a softening damage law and results in mechanical anisotropy at the macroscopic scale. One original aspect of the formulated inclusion–matrix model is the use of an explicit expression of Hill’s tensor to account for matrix ellipsoidal anisotropy. To illustrate the model capabilities, a uniaxial compression test was simulated for a variety of polycrystals made of two types of mineral inclusions with each containing only one plane of weakness. Damage always occurred in only one mineral type: the damaging mineral was that with a smaller shear modulus (respectively higher bulk modulus) when bulk modulus (respectively shear modulus) was the same. For two minerals with the same shear moduli but different bulk moduli, the maximum damage in the polycrystal under a given load was obtained at equal mineral fractions. However, for two minerals with different shear moduli, the macroscopic damage was not always maximum when the volume fraction of two minerals was the same. When the weakness planes’ orientations in the damaging mineral laid within a narrow interval close to the loading direction, the macroscopic damage behavior was more brittle than when the orientations were distributed over a wider interval. Parametric studies show that upon proper calibration, the proposed model can be extended to understand and predict the micro–macro behavior of different types of quasi-brittle materials.

In the present research, a micromechanical-analytical model was developed to predict the elastic properties and strength of balanced plain weave fabric composites. In this way, a new homogenization method has been developed by using a laminate analogy method for the balanced plain weave fabric composites. The proposed homogenization method is a multi-scale homogenization procedure. This model divides the representative volume element to several sub-elements, in a way that the combination of the sub-elements can be considered as a laminated composite. To determine the mechanical properties of laminates, instead of using an iso-strain assumption, the assumptions of constant in-plane strains and constant out-of-plane stress have been considered. The applied assumptions improve the accuracy of prediction of mechanical properties of balanced plain weave fabrics composites, especially the out-of-plane elastic properties. Also, the stress analysis for prediction of strain–stress behavior and strength has been implemented in a similar manner. In addition, the nonlinear mechanical behavior of balanced plain weave composite is studied by considering the inelastic mechanical behavior of its polymeric matrix. To assess the accuracy of the present model, the results were compared with available results in the literature. The results, including of engineering constants (elastic modulus and Poisson’s ratio) and stress–strain behavior show the accuracy of the present model.

A fully micromechanical model is developed for estimating the effective coupled thermo-electro-elastic material coefficients of three-phase piezoelectric structural fiber composites. The implicit f...

This article presents a new micromechanical model to predict biaxial tensile moduli of plain weave fabric composites by considering the interaction between the orthogonal interlacing strands. The two orthogonal yarns in micromechanical unit cell were idealized as curved beams with a path depicted using sinusoidal shape functions. The biaxial tensile moduli of plain weave fabric composites were derived by means of the minimum total complementary potential energy principle founded on micromechanics. Biaxial tensile tests were conducted on the resin transfer molding–made EW220/5284 plain weave fabric composites at five biaxial loading ratios of 0, 1, 2, 3 and ∞ to validate the new model. Predictions from the new model were compared with experimental data. Good correlation was achieved between the predictions and actual experiments, demonstrating the practical and effective use of the proposed model. Using the new model, the biaxial tensile moduli of plain weave fabric composites can be predicted based only on the properties of basic woven fabric.

The electrical conductivity of carbon nanotube–epoxy composites is investigated analytically and experimentally. The theoretical predictions of the effective electrical conductivity of carbon nanotube–epoxy composites were performed by the analytical approach based on a micromechanical model of composites. The parametric analysis carried out revealed an influence of geometrical and electrical parameters of the micromechanical model on the effective electrical conductivity of carbon nanotube–epoxy nanocomposite. The nanocomposites made from the DGEBA-based and RTM6 epoxy resins filled with different weight content of Baytubes C150P and N7000 multi-walled carbon nanotubes were prepared. The experimental values of the electrical conductivity of the nanocomposites were compared with those calculated by means of the analytical model.

This study introduces a unit cell-based finite element micromechanical model that accounts for correct post cure fabric geometry, in situ material properties and void content within the composite to accurately predict the effective elastic orthotropic properties of 8-harness satin weave glass fiber-reinforced phenolic composites. The micromechanical model utilizes a correct post cure internal architecture of weave, which was obtained through X-ray microtomography tests. Moreover, it utilizes an analytical expression to update the input material properties to account for in situ effects of resin distribution within yarn (the yarn volume fraction) and void content on yarn and matrix properties. This is generally not considered in modeling approaches available in literature and in particular, it has not been demonstrated before for finite element micromechanics models of 8-harness satin weave composites. The unit cell method is used to obtain the effective responses by applying periodic boundary conditions. The outcome of the analysis based on the proposed model is validated through experiments. After validation, the micromechanical model was further utilized to predict the unknown effective properties of the same composite.

In this article, the free vibration behavior of functionally graded carbon nanotube reinforced composite plate is investigated under elevated thermal environment. The carbon nanotube reinforced composite plate has been modeled mathematically using higher order shear deformation theory. The material properties of carbon nanotube reinforced composite plate are assumed to be temperature dependent and graded in the thickness direction using different grading rules. The effective material properties of the functionally graded plate are introduced in the present model through a micromechanical model under temperature load. The governing differential equation of the functionally graded carbon nanotube reinforced composite plate is obtained using Hamilton’s principle. The domain is discretized using the suitable isoparametric finite element steps and solved numerically through a computer code developed in MATLAB environment. The validity and the convergence behavior of the present numerical results have been checked and a simulation model is also developed in commercial finite element package (ANSYS) using ANSYS parametric design language code. The effect of various geometrical parameters (aspect ratios, support conditions, and thickness ratios), the grading effect, and the temperature variation on the free vibration behavior of functionally graded carbon nanotube reinforced composite are examined and discussed in detail.

The present study introduces a progressive fatigue damage model within a multiscale framework by incorporating a Simplified Unit Cell Micromechanical model into a Finite Element program. The use of micromechanics will allow the study of damage at the micro-scale which can therefore identify modes of failure in each of the composite’s constituents, separately. The use of finite element method at the macro-scale enables the model to capture the geometric complexities including regions of stress concentration, which expedites the failure of the material. Damage progression is modeled through the degradation of the material property corresponding to the failure mode detected by the micromechanical model. The results of the model are in good agreement with the experimental data for both unidirectional and multidirectional laminates. The present approach is capable of predicting the fatigue life of composite laminates of any arbitrary geometry and lay-up configuration with minimum dependence on empirical parameters.

A micromechanical model using properties of both polymer and filler is proposed to address creep response in case of nanocomposites consisting of graphite nanoparticles embedded in a polymer matrix. Empirical creep models like Burgers and Findley models have been frequently used for creep simulation of polymeric-based nanocomposites. An elastic stiffness model has been established first to simulate stiffness property of nanocomposites with emphasis on filler distribution conditions. Creep stiffness is then predicted from the outstanding stiffness model based on the linear elastic–viscoelastic principle. In the model development, a parameter termed as additional constraint stiffness factor has been defined in the model to account for the constraining effect played by nanoparticles on the polymer chains. Magnitude of constraint factor indicates performance of nanoparticles in preventing polymer chains motion under creep loading of the nanocomposite. Creep predictions of the model with and without effect of the additional constraint stiffness factor are compared with experimental results obtained for vinyl ester reinforced nanocomposites. Predictions of the model disregarding the additional constraint stiffness factor overestimate the experimental results and do not provide good agreement. For each of the studied nanocomposites, the present model was able to provide creep response according to different filler percentage and different temperature along with the same stiffness function and similar constraint factors, in each case.

A finite element micromechanical model of a high strength composite material is subjected to a range of loading conditions to demonstrate its ability to predict failure. An investigation into the relative magnitude and distribution of the normal and shear stresses within the interface region of a single fibre embedded in a matrix region is compared to that of a multi-fibre representative volume element, where the fibre placement is statistically equivalent to that of a real material. A study is subsequently undertaken in which the relative magnitudes of the shear and normal strengths of the fibre–matrix interface are varied under transverse tension and shear. The results are interpreted with relation to the yield strength of the matrix. The predicted performance of the composite is shown to compare well with published experimental data, under transverse tension and in-plane shear. It is concluded that a single set of interface strength parameters can be used to represent the behaviour of the composite material. The results also show that interfacial shear strengths are expected to be equal, and higher than the interfacial normal strength.

In this study, the authors present a micromechanical finite element modelling approach to the analysis of a set of ultrafine-grained polycrystalline copper structures. The models take into account both realistic grain distribution and the number of refinement passes of the microstructure. The grain size effect is successfully predicted, with non-uniform deformation and shear localization reproduced during global plastic flow in agreement with experimental observations. The models provide a useful tool with which to interpret damage and fracture mechanisms occurring in ultrafine-grained structures.

Polymer nanocomposites offer remarkable enhancement in properties compared to pristine polymers, and also compared to conventional micro- and macro-composites. The present study is focused on the preparation of nanocomposites by the usage of ultrasound. Polystyrene/alumina nanocomposites were synthesized using commercial alumina nanoparticles of approximately 200 nm size. These particles were dispersed in polystyrene solution by subjecting to ultrasound. Composites were synthesized at different filler loadings varying from 0.2% to 1% by weight. Dispersion characterization of these composites was carried out using scanning electron microscopy and X-ray diffraction. X-ray diffraction data revealed the incorporation of the filler into the polymer matrix. The mechanical properties, mainly tensile and impact properties, of the composites were studied to analyse the effect of nanofillers on the enhancement in functional properties compared to the neat polymer. Tensile strength and modulus varied with the filler loading in the polymer matrix. Theoretical prediction of the composite modulus was done using existing micromechanical models such as Halpin–Tsai and Mori–Tanaka. A comparison was made between the experimental moduli and the predicted values. Cavitation erosion studies were conducted on the composites and the mass eroded was quantified.

A mesh-free Galerkin approach for modeling damage in plain woven fabric composite is presented. The model is based on the continuum damage mechanics and is applied to both mosaic and smooth fabric idealizations of the plain woven composite. A mesh-free Galerkin method is formulated for the first time to include the continuum damage mechanics for micromechanics model of woven fabric composites. An incremental technique of applied displacement/strain is developed to obtain the relationship between the representative volume cell stresses and strains. Also presented for the first time is an analytical formulation for damage in the mosaic unit cell representation of the woven fabric composite. Several examples are presented to demonstrate the application of the proposed methods and comparisons are made between the newly developed analytical formulation and the proposed mesh-free method.

Since pullout behaviors of fibers intersecting a fracture plane of cementitious composite are similar to those in a single-fiber pullout test, micromechanical model of fracture energy for hooked-end steel fiber-reinforced cementitious composite (HSFRCC) is developed on the basis of single hooked-end steel fiber pullout test. The hooked-ends of steel fibers intersecting a fracture plane have various deformations which can be generally classified into hooked-end total deformation, partial deformation, and nondeformation. The pullout energy of steel fiber with deformed hooked-end is significantly different from that with nondeformed one; derivations of pullout energies of hooked-end steel fibers with deformed/nondeformed hooked-ends are carried out first. The fracture energy model of HSFRCC is proposed using probabilistic method accounting for energy contributions from all steel fibers intersecting the fracture plane. Experimental validation of the proposed micromechanical model is performed, and excellent agreements are observed in comparison with experimental data from uniaxial tensile tests. As the proposed fracture energy model is a function of physical and micro-geometric properties of hooked-end steel fibers and cementitious matrix, it can guide optimal design of HSFRCC.

A progressive micromechanical damage-plasticity formulation is proposed to analyze the single hooked-end steel fiber pullout energy from the surrounding cement-based matrix within the context of hooked-end steel fiber-reinforced cementitious composites (HSFRCC). As the hooked-end steel fiber has a unique fiber geometry, its fiber pullout energy from the cement-based matrix consists of the interfacial fiber-matrix debonding, the frictional sliding and pullout energy, and the elastoplastic deformation energy of the steel fiber hooked end. The aforementioned energy components are analytically derived first, and the superposition principle is subsequently employed to obtain the total energy dissipation during the fiber pullout process. Good agreement is obtained for comparisons between the experimental results of single hooked-end steel fiber pullout tests and the proposed analytical predictions. This satisfactory verification supports the validity and applicability of the proposed damage-plasticity energy prediction formulation, and suggests the applicability of this methodology to further investigation on micromechanical fracture energy prediction of HSFRCC during flexural macro-cracking.

Based on a well-established micromechanical model of damage initiation in low-cycle fatigue (LCF) already developed in Abdul-Latif (1994), a new extension is proposed for describing the damage deactivation effect. With a small strain assumption, it is assumed that the local damage variables initiate at the crystallographic slip system level. It is considered that the damage is active only if micro-cracks (MC) are open, while damage affects differently the mechanical properties of polycrystals during its closure (inactive phase). The anisotropic damaged (activation and deactivation) behavior concept is adopted only at the macroscopic level. With a fourth-order damage tensor, the deactivation damage effect under multiaxial cyclic loadings is modeled describing the related phenomenon of the induced-oriented anisotropy. Several numerical simulations are conducted describing the overall damaged behavior of polycrystals in biaxial LCF. The responses of a given grains aggregate are recorded and then discussed. As a conclusion, the model describes fairly well the damage activation and deactivation effect in plastic fatigue, notably under multiaxial complex loading paths.

A three-dimensional micromechanical model based on the assumptions of simplified unit cell method (SUCM) is presented to obtain the closed-form solution for overall behavior of a unidirectional polymer matrix composite. The composite system consists of nonlinear viscoelastic matrix reinforced by transversely isotropic elastic fibers. The Schapery single integral viscoelastic constitutive equation in multiaxial stress state is used to model the nonlinear viscoelastic matrix. The presented analytical formulation is able to predict the effective response of the composite in any combination of normal and shear loading conditions. In particular, the effective creep response of the material in the off-axis loading is investigated. Prediction of the presented analytical model for the creep response of glassy amorphous polymer PMMA material shows good agreement with available experimental data. Furthermore, the predicted overall creep behavior of 10 and 908 off-axis coupons of graphite/epoxy composite demonstrate close agreement with experimental and other numerical results available in the literature. The overall creep-recovery of the graphite/epoxy composite in various off-axis loading conditions for several stress levels is also presented.

A micromechanical model is developed to characterize the constitutive behavior of stretch broken carbon fiber (SBCF) materials. The model takes into account the characteristics of the viscous resin materials and the effect of randomly distributed discontinuous fibers. The predicted force-to-stretch (FTS) values for uniaxial stretching of SBCF prepreg tapes favorably compare with experimental data.

This paper explores the use of both macroscale and microscale modelling for the analysis of extrusion of an AA2009 + 25%SiCp metal matrix composite (MMC). The performance of a micromechanical model, where the heterogeneous microstructure of the MMC is explicitly modelled, in predicting the tensile stress—strain behaviour of an AA2009 + 25% SiCp MMC is examined. A macroscale modelling approach is used to simulate extrusion of the MMC through two different die designs, where the MMC is modelled as a homogeneous continuum. Firstly, the extrusion results are used to compare the two die designs, to determine which is the more favourable. Secondly, the predicted macroscale plastic strain distributions and pressures are used with the micromechanical model to assess microscale stress states in the material during extrusion with a view to gaining insights into the risk of damage in the material. In this context, pressure is shown to be hugely important in controlling tensile stress magnitude and in reducing microscale damage risk, and essentially ensuring that extrusion can be achieved in practice. However, the results reveal that damage risk is not totally eliminated and that there may still be locations where the material may rupture.

A simple micromechanical model for the deformation of an isolated fiber fragment embedded within a bundle of continuous filaments is used to study progressive fragmentation of the low elongation-to-break (LE) fiber component during extension of a model two-component fibrous structure. The model structure, representing a blended yarn or cord, is realized in experimental specimens by helically wrapping a number of high elongation-to-break (HE) components around a straight central LE component; polyester sewing thread and cotton sewing thread are used is this work as the HE and LE components, respectively. The concept of a characteristic fragment length, involving the failure statistics of a fragment as influenced by the interaction forces between the fragment and the surrounding fibrous medium, is used to interpret the fragmentation experiments and calibrate a dimensionless parameter in the micromechanical model. The calibrated model is shown to provide insight into force interactions between the fragment and the surrounding structure. Bounds are established on the force interaction behavior associated with possible variations in the value of a constitutive parameter.

Nonwoven structures have a range of applications which include geotextiles, interlinings, carpet backing and as reinforcements in composites. In this study, the tensile behavior of nonwoven structures including needlepunched and thermal bonded has been predicted by modifying the micromechanical model based upon the geometrical and mechanical properties of the constituent fibers (Adanur, S. and Liao, T. (1999). Fiber Arrangements Characteristics and Their Effects on Nonwoven Tensile Behavior, Textile Research Journal, 69(11): 816-824). In the modified model, the effects of fiber orientation in addition to the fiber curl factor are incorporated. The theoretical models have been validated with experimental results. The effects of lapping angle and curl factor have also been investigated on the thermal bonded nonwoven structures. Furthermore, the distribution of fiber orientation within a nonwoven structure is related to the lapping and fiber orientation angles using Fourier series.

In this study nanocomposites consisting of an epoxy matrix filled with silicate clay particles are investigated. Recent and ongoing research has shown that dramatic enhancements can be achieved in stiffness and thermal properties in these nanocomposites with small amounts of particle concentration. The resulting properties of nanocomposites are intimately related to the microstructure achieved in processing these materials. However, the ideal situation of full exfoliation, dispersion, and orientation is not usually achieved. A more common case is the partial exfoliation and intercalation. The latter is a process whereby the polymer penetrates the interlayer spaces of clay particles, causing an increase in the layer spacing (d-spacing). The region consisting of a matrix with exfoliated clay nanolayers or platelets is analyzed by assuming a near uniform-dispersion and a random orientation. The properties of intercalated clusters of clay platelets are calculated by a rule of mixtures based on a parallel platelet system. The modified composite theory of Halpin—Tsai is applied to calculate the modulus of the nanocomposite as a function of the clay concentration for various parametric variations, including the exfoliation ratio, the particle/matrix stiffness ratio Ef/Em, the particle volume fraction f, and the particle aspect ratio L/t. The modified composite theory satisfactorily captures the stiffness behavior of the polymer/clay composites.

A micro-electro-mechanical model of the behavior of piezoelectric ceramics including thermal effects is presented and compared to experimental data. Results include analytical and numerical investigations of the behavior of piezoelectric ceramics. The model is based on physical mechanisms and includes elastic, dielectric, and piezoelectric anisotropy. Moreover, the model is based on an internal energy approach so that work-energy relations may be directly applied. Results from the model give insight into material behavior.

A previously developed micromechanical model is used to formulate the problem of a blended yarn, consisting of low elongation (LE) and high elongation (HE) fibers undergoing axial extension, with a fiber break in the central region of the hybrid fiber array. A hybrid parameter R, which is the ratio of the axial stiffness of the HE fibers to that of the LE fibers, is shown to have an important effect on the intact fiber stress concentration factor (SCF), and the broken fiber slip extent at the fiber break. While the SCF increases for HE fibers adjacent to broken LE fibers, it decreases for LE fibers adjacent to broken HE fibers as R takes on values away from unity (homogeneous yarn). Higher loading can therefore be sustained by the LE fibers, and a beneficial hybrid effect can be realized.

This paper deals with the static strength of mechanically tightened joints augmented with anaerobic adhesives. Tests were performed on a variety of specimens distinguished by fairly homogeneous (annular butt joint) or realistically inhomogeneous (threaded, cylindrical and double lap joints) working conditions over the bondline. For each geometry, the strength of the dry (unbonded) joint was compared with the strength of the joint bonded with an assortment of anaerobics. The results indicate that the strength of all joints (bonded and unbonded) increases with the contact force. When strong adhesives (retainers) are used, the overall strength approximately equals the sum of friction and adhesive strengths, taken separately. When weak adhesives (threadlockers) are adopted, the superimposition of effects grossly overestimates the measured strength. A micromechanical model is proposed that explains the observed macroscopic behaviour.

A micromechanical model was established based on the fluid dynamics theory. This model could be used to calculate several kinds of data when the asphalt pavement under the influence of traffic loading is in water-saturated condition. The results showed that the maximum pressure inside the effective pore was located at the junction between exit slits and the pore wall. There was a positive correlation between the pressure and the vehicle speed. Therefore, the repeated traffic loading could cause emulsification, shift and even peeling of the asphalt membrane. Moreover, the bigger size of the exit slit is, the higher velocity of the fluid has. The high velocity flow keeps scouring both the exit slit and the lower boundary of pore wall. It will cause a bigger slit. Pressure distribution inside the effective pore is related to the number of the exit slit which connect with the pore. More exit slits means bigger pressure inside the effective pore. In addition, if asphalt membranes at exit slits have micro-cracking, the cumulative damage could appear easily and asphalt membranes could be peeled easily. Finally, a test was conducted so as to obtain the bonding strength and adhesion strength between asphalt and aggregate. Then, we can get accurate damage form and position during the scour process by comparing the numerical simulation results with experiment results.

This work presents a new micromechanical model to describe the 3-D elastic and damaged behaviour of randomly oriented fibre composite. The damage mechanisms are described by the progressive introduction of oriented microcracks in a random discontinuous fibre composite. In this work, the homogenisation is performed using a Mori-Tanaka scheme. Whereas, symmetry is not obtained in estimates of the overall stiffness for multiphase systems with heterogeneity of different shapes or orientations. For this reason, in this work two levels of homogenisation are considered. The Mori-Tanaka method is applied on the matrix with microcracks to give an equivalent damaged matrix, which can be anisotropic. The Mori-Tanaka scheme is used for the second time to homogenise fibres embedded in the new equivalent damage matrix. Generally, this new matrix is anisotropic and for this case no explicit formula for the Eshelby tensor ( S) has been obtained. Thus, it is necessary to compute numerically the components of this fourth order tensor. Moreover damage mechanisms can be modelled using statistical considerations. The damage onset and growth can appear in the matrix, fibres or interface. Hence, overall damaged behaviour can be modelled and predicted as well as the microscopic damage accumulation process.

The numerical aspects of a micromechanical model for a viscoelastic cohesive zone are discussed herein. The cohesive forces encountered in the region ahead of a crack tip are represented by a damage dependent traction-displacement law which is both history dependent as well as internal variable-type. An incrementalized form of this traction-displacement law has been integrated numerically, and an example problem has been solved to demonstrate the efficacy of the model.

Based on the slip theory, a micromechanical model of damaged-inelastic behavior, which was recently proposed for metallic polycrystalline structures (FCC), is extended in order to describe the unilateral effect in low-cycle fatigue with a small strain assumption. In this micromechanical model, the micro-damage variables initiate and then evolve on the activated crystallographic slip systems. These variables are coupled with micro-macro constitutive equations. The formulation of the unilateral character of the damage (activation and deactivation) is limited only to the macroscopic level using the isotropic damaged concept. At this point, the unilateral effect is introduced with the help of a simple phenomenological constant. It allows to appropriately describe the macro-damage parameter evolution during the closure of defects (inactive phase) with the continuity of the stress-strain response.

This work takes a micromechanical approach to fabric tensile modeling. The entire uniaxial tensile stress-strain behavior of the fabric is modeled from the constitutive yarn properties (tensile, bending, flattening, and consolidation behavior) and the original fabric geometry. Techniques for measuring these yarn properties are described. In most cases, there is good agreement between the theoretical and experimental results for several fabrics of differing weave and yarn construction. Modified approaches are suggested for those cases where prediction of fabric stress-strain behavior deviates from the experimental data.

A theoretical micromechanical model is proposed to describe the damaged behavior of polycrystalline metals. Based on the slip theory, a local micro-damage variable representing the transgranular damage is introduced and fully coupled with micro-macro anelastic constitutive equations for FCC polycrystals proposed by Cailletaud (1987, 1992). The micro-damage is supposed to be initiated and then evolved on the activated crystallo graphic slip systems to define isotropic damage at the macroscopic level (i.e., in the Repre sentative Volume Element RVE). The coupling between damage and the behavior at both microscopic and macroscopic levels is carefully discussed. The obtained model is applied and discussed in the case of uniaxial monotonic and cyclic loading, neglecting the quasi- unilateral effect as well as the localization of the fatigue micro-cracks on the surface of the loaded medium.

The present work studies the overall (effective) thermal conductivity in solid media with a variable microcrack density. For a solid undergoing continuous straining, the self-consistent model is used to describe the evolution of microcrack density in the strain history. While the model established by Budiansky and O'Connell is implemented for the degradation of the load-bearing capacity due to microcracks, the micromechanical model established by Tzou and Chen is used to relate the microcrack density to strains. Degradation of thermal conductivity is then obtained by the analytical result obtained by Tzou in the same self-consistent framework.

A micromechanical model of the large displacement behavior of a sliver of oriented helical fibers has produced algorithms for predicting and updating all five independent mechanical constants. The incorporation of the micromechanics in a finite-element model of a uniform rope of initially untwisted fibrous material is described. The response of the whole model to combined external and torsional stresses such as occur during twist insertion is then described. A detailed analysis of the stresses and strains in the deformed model shows that fiber packing in the yarn is predicted to quickly become non-uniform. The inner regions become most densely packed, and fibers there are subject to the highest stress levels. Fibers further from the center largely avoid being stressed by moving toward the yarn axis.