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In this paper, a unit cell based micromechanical model is presented to predict the elastic-viscoplastic response of aligned short fiber titanium matrix composites subjected to combined axial loading in the presence of fiber/matrix interfacial damage. The effects of manufacturing process thermal Residual Stress (RS) are also included in the analysis. The representative volume element (RVE) of the short fiber composites consists of c×r×h cells in three dimensions in which a quarter of the short fiber is surrounded by matrix sub-cells. In order to obtain elastic-viscoplastic curves, the fiber is assumed to be linear elastic, while the matrix exhibits elastic-viscoplastic behavior. The Evolving Compliance Interface (ECI) model is employed to analysis interface damage. This model allows debonding to progress via unloading of interfacial stresses even as global loading of the composite continues. Results revealed that for more realistic predictions, in comparison with available experimental and the other models results, both interfacial damage and thermal residual stress effects should be considered in the analysis.

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The main purpose of the present research is analytical and numerical analyses of graphene/epoxy nanocomposites with a random distribution of nanoparticles. For this purpose, by combining the molecular dynamics and micromechanics methods, a new approach is presented. The molecular dynamics method is used to model the stiffness of the graphene/epoxy nanocomposites containing one layer of nano graphene embedded in epoxy resin. A multi-scale modeling strategy from macro to meso, then from meso to micro and finally from micro to nano scales is introduced. A representative volume element (RVE) is selected and for a nanocomposite having a single monolayer graphene embedded in epoxy resin, the longitudinal (E11), transverse (E22) and normal (E33) stiffnesses for three RVEs with arbitary graphene size are simulated. The best curve is fitted to each stiffness diagram and stiffnesses of the RVE in three directions with true graphene size are investigated. In order to consider the effect of randomly graphene sheets distribution in epoxy resin, micromechanical approach is used. Finally, the stiffness of the nanocomposites with randomly distributed graphene is calculated. For evaluation of the present approach in this research an experimental program is conducted. The result of the modeling is well agreed with the experimental data.

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In this study, a three-dimensional micromechanics-based analytical model is developed to study the effects of regular and random distribution of silica nanoparticles on the thermo-elastic and viscoelastic properties of polymer nanocomposites. The Representative Volume Element (RVE) of nanocomposites consists of three phases including silica nanoparticles, polyimide matrix and interphase. Since the polymer in the vicinity of the nanoparticles shows distinct properties from those of the bulk matrix, because of nanoparticle–polymer matrix interactions, this region as interphase is considered in micromechanical modeling with specific thickness and properties. In order to simulate random distribution of silica nanoparticles into polyimide matrix, the RVE is extended to c×r×h cubic nano-cells in three dimensions. Perfect bonding conditions are applied between the constituents of RVE. It is assumed that all three phases of the RVE to be homogeneous and isotropic to obtain the thermo-elastic response of nanocomposite. The extracted thermo-elastic properties by the micromechanical model with random distribution of silica nanoparticles are closer to the experimental data. To predict the effective viscoelastic properties of the nanocomposites, silica nanoparticles are modeled as a linear elastic material, while polyimide matrix and interphase are assumed to be as a linear viscoelastic material. The model is also used to examine the influence of varying interphase properties and silica nanoparticle size on the effective nanocomposite behavior. The overall creep behavior of the nanocomposite for several stress levels is also presented.

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In this paper, a 3D time dependent micromechanical model is presented to study the elastoviscoplastic behavior of aligned fiber reinforced composites in the presence of interfacial damage subjected to multi-axial loading. The representative volume element (RVE) of the composite consists of three phases including fiber, matrix and fiber/matrix interphase. The interphase is considered as a distinct phase with a definite thickness that covers the outer surface of fibers. The difference between of manufacturing process temperature to room temperature introducing thermal residual stresses is included in the analysis. The fiber and interphase are assumed to be elastic, while the matrix exhibits elastic-viscoplastic behavior with isotropic hardening. The Bodner-Partom viscoplatic theory is used to model the time dependent inelastic behavior of the matrix. The Needleman model is employed to analysis interphase damage. For metal matrix composites, it is shown that while predictions based on undamaged interphase are far from the reality, the predicted stress–strain behavior including interphase damage and thermal residual stresses demonstrate very good agreement with experimental data. Furthermore, the elastic properties of the composites with various aspect ratios are extracted by the micromechanical model. The elastic behavior predictions of the composite are also very close to experimental data and the other available model.

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Establishing accurate structure–property relationships for three-phase composites is a fundamental task about a reliable design of such materials. In this study, a three-dimensional micromechanics-based analytical model is presented to evaluate the effects of interphase on the mechanical properties of three-phase fibrous composites under off-axis loading. The representative volume element of composites consists of three phases including reinforcement (long fiber), matrix and interphase which all of three phases are assumed to be isotropic and linear elastic. The state of arrangement of fiber within the matrix materials is assumed to be random with uniform distribution and fibers are surrounded by the interphase. The effects of interphase such as its thickness and stiffness on the mechanical properties of fibrous composites under off-axis loading are investigated. Moreover, the influences of fiber volume fraction with and without considering interphase on the response of composite materials are examined. By introducing a parameter which is called the interphase reinforcement ratio, the results demonstrate that the intensity of interphase effects on Young’s modulus of composites increases from 0 degree (longitudinal loading) to 90 degree (transverse loading). The obtained results by the present micromechanical model could be useful to optimal design of composite materials with superior mechanical properties.

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Significant improvements in mechanical properties of polymers reinforced with nanoparticles at relatively low volume fractions, is caused that the use of polymer nanocomposites increase. The main reason for the increase in mechanical properties of nanocomposites is the presence of an interphase region between the nanoparticles and polymer matrix. In this work using a unit cell-based micromechanical model, the percolation behavior of the mechanical properties of nanoparticle reinforced polymer nanocomposites is investigated. The Representative Volume Element (RVE) of nanocomposites consists of three phases including nanoparticles, polymer matrix and interphase. The RVE is extended to c×r×h nano-cells in three dimensions and the state of dispersion of nanoparticles into matrix is random. Effects of interphase region including its thickness and elastic modulus and nanoparticle geometry on the percolation behavior of the nanocomposite are studied. Results show that with decreasing the nanoparticle size or increasing aspect ratio of nanoparticle, critical volume fractions decreases. The predicted results of the present micromechanical model are in good agreements when compared with results of the other micromechanical model. The herein reported results could be useful to guide the modeling and optimal design of nanocomposite reinforced by nanoparticles with the highest economic interest.

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Mechanical properties of polymeric materials are significantly sensitive to the loading rate. Therefore, it is necessary to develop a dynamic constitutive model to investigate their strain rate dependent mechanical behavior. In this study, first by conducting torsion experiments the shear behavior of neat and reinforced epoxy with carbon nano-fibers (CNFs) was studied experimentally. Then, the Johnson-Cook (J-C) model has been modified to be able to model the shear behavior of neat polymers. The strain rate effects on elastic behavior of polymers were considered by introducing a material equation. Then, by combining the modified Johnson-Cook (MJ-C) model with a micromechanical model (Halpin-Tsai model) and using pure polymer experimental tesults and mechanical properties of carbon nano fiber, the strain rate dependent mechanical behavior of polymers reinforced with CNFs at arbitrary strain rates and volume farction of carbon nanofiber has been predicted. The new model presented in this research is called as the dynamic-micromechanical constitutive model. The predicted results for the neat and nano-phased polymers were compared with conducted and available experimental results. It has been shown that the present dynamic constitutive model can predict the strain rate dependent mechanical behavior of polymeric materials with a good accuracy.

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In this paper, by applying a new programming mode, thermomechanical behavior of activated composite with shape memory alloy fiber is extracted subjected to cyclic off axis loading using a 3D analytical micromechanical model. Object-orientation and its applied principles are implemented on the micromechanical model and response of the composite is determined by Newton - Raphson nonlinear numerical solution method at different thermal interval. In order to achieve an optimal response, a factor as convergence coefficient in the Newton - Raphson nonlinear solution method is employed. Representative volume element of the composite consists of two-phases including shape memory alloy fiber and metal matrix. behavior of the metallic matrix is considered as viscoplastic while shape memory alloys is assumed nonlinear inelastic based on Lagoudas model which is able to model phase transformation and superelastic behavior of the shape memory alloys. Moreover, arrangement of fibers within the matrix is considered randomly. Thermomechanical responses of composite at different temperature ranges are investigated to display the shape memory effect and superelasticity properties of shape memory fiber. In this regard, at the first, the composite system is exposed to cyclic mechanical loading and unloading and then exposed to thermal loading. Shape memory effect property of shape memory wire and composite are compared and the effects of forces within the active composite induced via axially constraining of the composite are investigated. Furthermore, the effect of fiber orientation is illustrated. Comparison between the present research results and previous available researches shows good agreement.

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Research on microstructure of main engineering materials revealed that some of these materials exhibit similar microstructure patterns at different length scales. Since these patterns are replicated at different length scales the whole microstructure can be viewed as a set of periodic substructures. Homogenization technique for periodic microstructures has found many applications in simulation of composite materials by considering the geometry of fibers distribution. In this study a homogenization technique for periodic microstructures is developed. In this generalization a multi-step homogenization is being used. In each step of homogenization the geometry which is coincident with the true microstructure is produced to maintain the properties of the mechanical properties of the related cell. By using the presented method effect of size and grading of each of reinforcing phases and the interaction between fibers is taken into account. The results of the presented theory are compared with the existing experimental data on the particle reinforced composites. Good agreement between the presented theory and experimental data is found.

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A three-dimensional analytical micromechanical model based on unit cell is extended and presented to extract the electro-thermo-mechanical properties of short Carbon Nano-Tube (CNT) reinforced piezo-polymeric composite. Representative volume element (RVE) of the piezonanocomposite consists of three phases including CNT, piezo-polymeric matrix and interphase region. The presented model considers the CNT as a transversely isotropic solid fiber and CNT/matrix interphase region possessing van der Waals’ interaction as an isotropic hollow cylindrical solid that its mechanical properties are derived using the equivalent continuum model. Both phases are considered linear elastic. Also, the matrix is a piezoelectric material that is mechanically isotropic and elastic, and polarized along the perpendicular direction to CNT axis. The state of CNT arrangement within the matrix is assumed to be regular and square. First, the results obtained from the model are compared with available researches. Then, the effects of CNT volume fraction and aspect ratio and interphase effective thickness on the overall properties of the nanocomposite are investigated. In this study, despite the prior works, all the piezo-electro-thermo-mechanical properties of the nanocomposite are studied. The results show that even small amount of FVF has significant effect on improving the composite properties. Furthermore modeling of interphase region includes a great effect on the most of the composite properties, thus its modeling is necessary for more actual prediction about the nanocompite response.

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The application of woven fabrics in composites manufacturing has been increased because of their special mechanical behavior. Due to the complexity of modeling and simulation of these composites, in this research a micromechanics based analytical model has been developed to predict the elastic properties of woven fabric composites. The present model is simple to use and has a high accuracy in predicting the elastic properties of woven fabric composites. One of the most important effective factors on the modeling accuracy is utilizing a proper homogenization method. Therefore, a new homogenization method has been developed by using a laminate analogy based method for the woven 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. Then, the proposed homogenization model has been combined with a micromechanical model to propose the new micromechanical model. The applied assumptions improve the prediction of mechanical properties of woven fabrics composites, especially the out of plane elastic properties. The proposed model has been evaluated by comparing the predicted results with four available experimental results available in the literature, and the accuracy of the present model has been shown.

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The aim of this paper is investigation of progressive damage in a metal matrix composite lamina using coupling of micromechanical method and continuum damage mechanics viewpoint. The micromechanical method is a representative volume element based method known simplified unit cell method which possesses the capability of investigating of progressive damage and plastic behavior in the representative volume elements. The studied damage is isotropic and anisotropic based on continuum damage mechanics viewpoint. Under investigation composite system is Carbon/Aluminum composite. The matrix behavior is considered as isotropic and elastoplastic and the fiber behavior is transversely isotropic and elastic. The fiber arrangement within the matrix is regular. The matrix elastoplastic behavior model is included as bi-linear behavior and solution method is successive approximation method. According to available previous studies, Siliconcarbide/Titinium composite system is noticed for validation and comparison with experimental data. Also the effect of fiber volume fraction on the damage progression routine is studied. The results show that by increasing the longitudinal and transverse loadings, the damage variable grows in the fiber direction and perpendicular to the fiber direction and the axial and transverse Young's modulus decrease subsequently. Also the results prove that in longitudinal loading, considering anisotropic damage, damage progression in the fiber direction is more than its growth in perpendicular to the fiber direction. Whereas, under transverse loading, damage growth in perpendicular to the fiber direction is faster.

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In this research, a three dimensional analytical method is presented for predicting the dynamic properties of polymer nanocomposites. In the present method elastic-viscoelastic correspondence principle is applied on the simplified method of cell, and loss modulus, storage modulus, loss factor and Hysteresis loop are obtained using energy method as well as force balance method. The considered nanocomposite possesses Polypropylene as a matrix reinforced by vapor grown carbon fibers. The rrepresentative volume element consists of three isotropic phases including fiber, interphase and matrix with linear viscoelastic behavior based on Zener model. Furthermore the nanocomposite constituents dynamic properties are extracted in frequency domain by employing Fourier transform method and Schapery model First to assure the validation of the model, the results are compared with experimental results. Parametric studies such as the effects of number of subcells, fibers volume fraction (FVF) and aspect ratio, matrix/fiber link strength factor and interphase loss factor on the nanocomposite dynamic properties are investigated.. Obtained results reveal that the presented method has acceptable speed and accuracy. Moreover fiber aspect ratio and FVF increasing leads to decrease the nanocomposite hysteresis loop area, subsequently its damping capacity reduces. Interphase also contains considerable effects on the nanocomposite dynamic properties, so its modeling has a great importance.

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In this work, the effect of carbon nanotube (CNT) size on the effective elastic properties of a hybrid composite reinforced by fuzzy fiber is investigated using a unit cell-based micromechanical approach. This hybrid nanocomposite is composed of the CNT, carbon fiber, polymer matrix and interphase created due to the non-bonded van der Waals interactions between the CNTs and polymer. The novel constructional feature of this hybrid nanocomposite is that the uniformly aligned CNTs are radially grown on the surface of the horizontal carbon fibers. The CNT and carbon fiber are modeled as a transverse isotropic solid, while the interphase and polymer matrix are assumed to be isotropic. The influence of CNT size on the overall behavior of polymer matrix nanocomposite (PMNC), composite fuzzy fiber (CFF) and hybrid composite reinforced with fuzzy fiber is examined. Results show that size of CNT is more significant for the transverse effective properties of the hybrid nanocomposites reinforced with fuzzy fiber. It has been found that the transverse effective properties of hybrid nanocomposite are improved with increasing the CNT size. The micromechanical model is also used to examine the influence of interphase on the overall behavior of the PMNC, CFF and hybrid composite reinforced with fuzzy fiber. The effective elastic properties of the hybrid composite obtained by the present micromechanical model demonstrate very good agreement with those predicted by the other researches.

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In this work, an elastoplastic constitutive model is planned to analyze the effects of adding silica nanoparticles on the overall elastic-plastic stress-strain curves of the polymer matrix nanocomposites. The elastic modulus of the nanocomposites are evaluated by the combination of the Mori-Tanaka and Eshelby micromechanical models considering interphase region formed due to the interaction between silica nanoparticles and the polymer matrix. Then, the elastic-plastic stress-strain curves of nanocomposites are extracted by employing a micromechanics-based ensemble-volume averaged homogenization procedure. To prove the validity of the developed method, the predictions are compared to the experimental data existing in the literature. The effects of volume fraction and diameter of silica nanoparticles, thickness and adhesion exponent of the interphase on the polymeric nanocomposite elastic-plastic stress-strain curves are extensively examined. Stiffer elastoplastic behavior is found in the presence of interphase region. The results clearly indicate that the strengthening of the silica nanoparticle-reinforced polymer nanocomposites is improved with (1) increasing nanoparticle volume fraction, (2), decreasing the nanoparticle diameter, (3) increasing the interphase thickness and (4) decreasing the interphase adhesion exponent. Finally, the elastic-plastic stress-strain curves of silica nanoparticle/polymer nanocomposites under biaxial loading is achieved.

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Studying the behavior of composite materials reveals that various types of failure modes occur when material experiences different loading conditions, which may have a significant impact on performance and properties of a structure. In this research, we study the mechanical response of orthogonal multi-layers by considering different failure modes at micro-scale and their development in macro-scale. For this purpose, the effect of the emergence and growth of fiber separation and subsequent formation of matrix cracks are investigated in the micro-scale. Furthermore, interlayer separation caused by leaving the matrix are studied in macro-scale. To model the separation of fiber matrix which is the first dominant failure mode, the sticky area method is used. The model verification and obtained results are compared with the previous research. Then, XFEM method is used to take into account the failure mode of matrix. Finally, using of the sticky area method, we are able to simulate the separation of matrix layers. The FE-program Abaqus via its user scripting interface (Python) are employed in this research for modeling of fibers embedded into matrix.

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In this research, an analytical method is presented for predicting the viscoelastic and dynamic behavior of polymer nanocomposite. The analytical model is achieved by coupling the SUC micromechanical model with standard linear solid model. Boltzmann superposition principle is used to develop the constitutive equations. First, the strain associated with a relaxation experiment is considered, and then by using the idea of linearity as embodied in the Boltzmann superposition principle, the resulting stress history is predicted. Eventually, the creep function corresponding to the relaxation modulus is obtained and the hysteresis loop for nanocomposite material is represented. Creep response is sinusoidal in time and a function of stress history. Loss and storage modulus and material behavior in Laplace domain are obtained using standard linear solid model and SUC micromechanical model, respectively. Standard linear solid model is achieved by paralleling the Kelvin model with Maxwell model. The model is validated with experimental results. Effects of different interphase thickness, CNT volume fraction and phase angle on hysteresis loop is studied. Obtained results reveal that increasing the CNT volume fraction and phase angle leads to decreasing and increasing the nanocomposite hysteresis loop area, respectively. Also, Interphase thickness contains considerable effects on the nanocomposite dynamic behavior.

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Once a composite laminate is subjected to quasi-static tensile or fatigue loading, some damage modes initiate and propagate in the laminate. The first damage mode is the matrix crack that forms in the layers with an angle to the loading direction. Although not leading to breakage, these cracks reduce the equivalent mechanical properties of the composite laminate. In this paper, a new nonlinear analytical model is presented and used to predict the stiffness degradation of the cross-ply composite laminates. For this purpose, a new third-order polynomial function is proposed as the Helmholtz free energy of the composite, and the appropriate equations are derived. A microscopic experimental test is designed and accompanied by the analytical model to investigate the damage progression in a glass/epoxy cross-ply laminate. Also, finite-element micromechanical models with periodic boundary conditions (PBC) are proposed and used to determine the damage constants. The model is validated against the 3D micromechanical models and the quasi-static uniaxial loading-unloading experimental tests. The validation shows a very good agreement between the model and the experiments.
 

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In the present research, classic micromechanical methods and their application as constitutive models in conjugation with incremental theory were developed. Using the modified Eshelby model, the Eigen strain concept in polymeric composite, and a modified form of self-consistent model the elastic properties of nanocomposites were predicted. Also, the stress-strain behavior of elastomer nanocomposites was calculated and validated by the experimentally determined ones. The results showed that the new model can predict the stress-strain behavior of elastomer nanocomposite at different particle volume fractions.