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The editorial comments on the multi-scale predictive modelling of the composite materials' behavior. Transition of composite materials from nano to micron to meter-size is examined keeping in view the accuracy of computation and fabrication methods. The article probes the physical behavior of complex material systems under stress in terms of size, time and environment.

Polymer composite materials are being increasingly used in primary load-bearing structures in several advanced industrial fields such as aerospace vessels, railway wagons and mega-scaled wind turbines where detection of subcritical damage initiation can significantly reduce safety issues and maintenance costs. It is therefore crucial to inspect these composite structures in order to assess their structural health and to ensure their integrity. Non-destructive testing techniques (NDT) are used for this purpose, making it possible to monitor mechanical damage of composite materials under in situ or ex situ service conditions. This paper reviews the capabilities of the most common NDT techniques used to inspect the integrity of composite materials. Each technique has a detection potential and cannot allow a full diagnosis of the mechanical damage state of the material. Thus, depending on the occurring damage mechanism and the conditions of use, one technique will be preferred over another, or several techniques should be combined to improve the diagnosis of the damage state of the structures. [ABSTRACT FROM AUTHOR]

In this paper, an accurate formula for calculating the thermal residual stress field in a particle-reinforced composite are presented. Numerical examples are given to show r-variations of the thermal residual stresses. The increase in fracture toughness of matrix predicted by the thermal residual stress field is compared well with the experimentally measured increase. [ABSTRACT FROM AUTHOR]

Carbon nanotubes (CNTs) are expected to be ideal reinforcements of composite materials used in aircraft and sports industries due to their high modulus and low density. In the present paper, severe plastic deformation by high pressure torsion (HPT) of powders at elevated temperature (473 K) was employed to achieve both powder consolidation and grain refinement of aluminum-matrix nanocomposites reinforced by 5 vol% CNTs. Before the HPT, the powders were ball milled using planetary ball mill in order to achieve molecular level mixing. Aluminum was treated by the same process for a reference. The HPT processed disk were composed of considerably equilibrium grain boundaries with high misorientation angles. The CNT-reinforced ultrafine grained microstructural features resulted in high strength and good ductility. [ABSTRACT FROM AUTHOR]

Acid treatment and triethylene-tetramine (TETA) modification of multi-walled carbon nanotubes (MWCNTs) purposing to attain better dispersibility and stronger interfacial bonding between MWCNTs and epoxy matrix have been carried out in this paper. The epoxy and MWCNTs/epoxy composites were produced by cast molding method. Stress–strain curves show that TETA-MWCNTs/epoxy hold the greatest toughness of all samples with 0.5 wt.% nanoparticles. The Young’s modulus of TETA-MWCNTs/epoxy has a significant increase about 38% compared to the neat epoxy, while the Young’s modulus of unmodified MWCNTs/epoxy or acid-modified MWCNTs/epoxy has a bit of decrease. Tensile and impact strength tests reflect that TETA-MWCNTs reinforced epoxy composites have an obvious improvement of tensile strength about 30% and an enhancement of impact strength over 34% compared to the pure epoxy composites with only 0.5 wt.% loading of TETA-MWCNTs. Scanning electron microscopy images of fractured surface of MWCNTs/epoxy indicate homogeneous dispersibility of TETA-MWCNTs and strong interfacial adhesion between the TETA-MWCNTs and the epoxy in the MWCNTs/epoxy composite. [ABSTRACT FROM AUTHOR]

The fracture process of composite laminates subjected to static or fatigue tensile loading involves sequential accumulation of intra- and interlaminar damage, in the form of transverse cracking, splitting and delamination, prior to catastrophic failure. Matrix cracking parallel to the fibres in the off-axis plies is the first damage mode observed. Since a damaged lamina within the laminate retains certain amount of its load-carrying capacity, it is important to predict accurately the stiffness properties of the laminate as a function of damage as well as progression of damage with the strain state. In this paper, theoretical modelling of matrix cracking in the off-axis plies of unbalanced symmetric composite laminates subjected to in-plane tensile loading is presented and discussed. A 2-D shear-lag analysis is used to determine ply stresses in a representative segment and the equivalent laminate concept is applied to derive expressions for Mode I, Mode II and the total strain energy release rate associated with off-axis ply cracking. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed. [ABSTRACT FROM AUTHOR]

The very complex, multi-level hierarchical construction of textile composites and their structural components commonly manifests via significant property variation even at the macro-level. The concept of a “meso-volume” (introduced by this author in early 1990s) is consistently applied in this work to 3-D stress/strain and failure analyses of 3-D woven composites at several levels of structural hierarchy. The meso-volume is defined as homogeneous, anisotropic block of composite material with effective elastic properties determined through volumetrically averaged 3-D stress and strain fields computed at a lower (“finer”) level of structural hierarchy and application of generalized Hooke’s law to the averaged fields. The meso-volume can represent a relatively large, homogenized section of a composite structural component, a lamina in laminated composite structure, a homogenized assembly of several textile composite unit cells, a single homogenized unit cell, a resin-impregnated yarn, a single carbon fiber, even a carbon nanotube assembly. When composed together, distinct meso-volumes constitute a 3-D Mosaic model at the respective hierarchy level. A multi-scale methodology presented in this paper first illustrates 3-D stress/strain analysis of the Mosaic unidirectional composite, computation of its effective elastic properties and their further use in 3-D stress/strain analysis of the Mosaic model of 3-D woven composite Unit Cell. The obtained 3-D stress/strain fields are then volumetrically averaged within the Unit Cell, and its effective elastic properties are computed. The predicted effective elastic properties of 3-D woven composite are compared with experimental data and show very good agreement. Further, those effective elastic properties are used in 3-D simulations of three-point bending tests of 3-D woven composite; theoretical predictions for central deflection show excellent agreement with experimental data. Finally, a 3-D progressive failure analysis of generic 3-D Mosaic structure is developed using ultimate strain criterion and illustrated on the 3-D woven composite Unit Cell. The predicted strength values are compared to experimental results. The presented comparisons of theoretical and experimental results validate the adequacy and accuracy of the developed material models, mathematical algorithms, and computational tools. [ABSTRACT FROM AUTHOR]

In this paper the creep crack propagation in a short glass fibre reinforced polypropylene composite has been investigated at various temperatures in the range from 32 to 60°C. Creep crack speed ( da/ dt) resulted initially decreasing till a minimum value, and then gradually increasing up to instability and fracture. Both initial and minimum crack speed values were found to strongly increase as test temperature increased. Moreover, isothermal curves of the applied stress intensity factor Kappl as a function of the crack speed ( da/ dt) were obtained at various temperatures. Portions of these curves in the stable crack acceleration region were hence shifted along the da/ dt, axis according to a time-temperature reduction scheme, thus allowing the construction of a creep crack propagation master curve. The shift factor values, aT for the creep crack propagation master curve appeared to be higher than those obtained, in the same temperature range, from dynamic mechanical measurements in a linear viscoelastic regime. [ABSTRACT FROM AUTHOR]

Discusses the tensile behavior of silicon carbide/aluminum composites subjected to quasi-static and high strain-rate loading. Metal matrix composites; Dynamic tension tests; Powder metallurgy aluminum alloy; Tensile impact loading-unloading-reloading stress-strain results at high strain rate; Isothermal stress-strain curve; Adiabatic stress-strain curve; Phenomenologically-based constitutive model.

ZrO2 porous nanosolid has been successfully prepared by a novel hydrothermal hot-press (HHP) method, using ZrO2 nanoparticles as the starting material. Furthermore, a kind of O, O-donating chelating regent, morin was assembled into the pores of ZrO2 porous nanosolids, and a morin/ZrO2 porous nanocomposite was obtained. Because of the interaction between morin molecules and the surface of ZrO2 porous nanosolid, a blue-shift of the photoluminescence (PL) peak was observed in ZrO2/morin nanocomposite by comparing with that of morin. [ABSTRACT FROM AUTHOR]

The capability to assess microstructural details in a polymer matrix composite is important in addressing composite design for engineering applications. The generation of three-dimensional microstructure using a non-invasive high-resolution experimental diagnostics method will advance our knowledge within this field. An inert composite has been studied, and both X-ray microtomography (XRT) for microstructural investigation in 3D and a parallel series of shock experiments (with associated modelling) have been conducted. The experimental aims of this study lay in several areas: firstly, to adequately define the bulk morphology; secondly, to determine the geometry of defects within the material; and finally, to demonstrate a direct linkage with the mechanical response determined by finite element analysis. This work is the first step in finding a way to non-invasively link 3D microstructural invesigation and numerical simulation to predict the shock performance of a composite material. [ABSTRACT FROM AUTHOR]

A combined experimental and numerical study has been carried out in order to predict initial failure in transversely loaded carbon fibre/epoxy composites. Three-point bending experiments on macroscopic composite specimens with special laminate lay-ups were carried out in a scanning electron microscope (SEM). The in-situ experiments allow observing the onset of microscopic composite failure under transverse loading and measurement of the global applied load at onset of failure. The experimental results show that interfacial failure was the dominating failure mechanism. The interfacial stresses at initiation of failure were determined successfully by a non-linear micro/macro FE-Analysis and compared with experimental results obtained from 3-point bending tests of standard composite specimens. The results show that the interfacial normal strength (INS) governs the failure process. [ABSTRACT FROM AUTHOR]

The article discusses a study on matrix fracture strength in a bonded brittle composites. It indicates that crack-tip transverse tensile stress often leads to the problem of matrix cracking modeling for bonded fibers. As the matrix crack continuously propagating, the crack-tip transverse tensile stress is assumed and separated the debonded length. To include the effect of crack-wake debonding for the bonded brittle composites, elastic response above the slipping region is extended.

A SiCw/6061Al composite was fabricated through a squeeze-casting route and hot extruded to obtain a composite with directionally aligned whiskers. Based on observed changes in whisker orientation and length before and after deformation, compressive deformation behaviour of the directionally aligned SiCw/Al composite was investigated. It is found that when the compressive temperature is much lower than the solidus of the matrix alloy, the compressive flow stress of the directionally aligned composite is increased with compressive strain first and then decreased. When the compressive temperature equals the solidus of the matrix, however, the compressive flow stress of the directionally aligned composite is increased monotonously with compression strain. During compression, whisker rotation and breakage occurred, and the higher the compressive temperature, the easier the whisker rotation and hence the smaller the degree of whisker breakage. When the compressive strain was quite high, the degree of whisker breakage was serious even at the temperature as high as the solidus of the matrix. Analyzing changes in whisker orientation and breakage before and after compression indicates that the decreased compressive flow stress with compressive strain is the result of the decreased load carrying ability of whiskers caused by whisker rotation and breakage. Compared with whisker rotation, whisker breakage has a bigger contribution to the decreased compressive flow stress. No strain softening in the composite compressed at 580°C can be thought to be a result of the very low strengthening effect of whiskers at such a high temperature. From the point of view of whisker breakage, to get higher properties of SiCw/Al composite parts made by means of plastic forming, too high plastic strain should not be suffered by SiCw/Al composites during the plastic forming. [ABSTRACT FROM AUTHOR]

This study outlines the mechanical properties of an explosive material tested at AWE Plc, Aldermaston, Reading, Berkshire, UK. The material is a composite polymer bonded explosive of energetic binder and HMX crystals, referred to as EDC37. An understanding of material deformation under a range of conditions and age, along with damage quantification, is required to predict mechanical behaviour throughout service life. The mechanical testing of EDC37 was performed alongside simultaneous recording of Acoustic Emission (AE) data at static strain rates and temperatures. The simultaneous testing was intended to focus on the link between mechanical properties and damage evolution. Forty tests were performed in various configurations, consisting of live explosive material and an inert simulant. Evaluation of the Acoustic Emissions was performed and data grouped into categories of activity. It was concluded that AE confirms mechanical behaviour associated with damage accumulation in compression (crack initiation and growth, crack closure and/or HMX twinning) and crack damage (binder HMX debonding and coalescence) above a threshold stress or time in tension. The activity seen is different between tensile and compressive modes and needs to be taken into consideration in Finite Element Models. [ABSTRACT FROM AUTHOR]

The mechanical behavior of open-cell foams may be modeled either on a microscopic or a macroscopic scale. In the first case, the behavior of the individual cell walls is described by beam models, while in the second case a continuum mechanical approach is applied. Both approaches have different advantages: On the one hand, the microscopic approach allows for a simple formulation of the constitutive equations but requires detailed knowledge of the heterogeneous microstructure, e.g. geometrical data of the beams and of the topology, and becomes numerically expensive for large structures. On the other hand, the macroscopic approach leads to efficient computations but requires more complicated constitutive equations, if e.g. anisotropy is taken into account. In the present contribution the advantages of the microscopic and macroscopic descriptions are combined by a numerical so-called second order homogenization scheme. Therefore, a small but representative element of the microstructure consisting of a few beam elements is chosen and attached to the quadrature points of the macroscopic finite element model. The macroscopic model is formulated in the framework of a Cosserat continuum, which allows to take care of size effects. The macroscopic strain and curvature tensors are projected onto the microstructure leading to a deformation mode of the beam ensemble. The resulting forces and moments in the beams are homogenized by an appropriate averaging procedure defining the corresponding stresses and couple stresses on the macroscale. In this approach, anisotropy is included in a natural way choosing an anisotropic distribution of the beams in the testing volume element (TVE). In addition, damage is described on the microscopic level of the individual beams. [ABSTRACT FROM AUTHOR]

Studies the microstructures and mechanical properties of three-dimensional C[sub f]/silicon-oxygen-carbon composites fabricated by polysiloxane pyrolysis. Interfacial structure and density; Flexural strength; Fracture toughness.

Precise estimation of local stress profiles in individual phases of a fiber reinforced metal matrix composite is a crucial concern for design of composites. Stress profiles are significantly affected by plastic relaxation of soft matrix. In this work, an analytical model was developed to compute local stress profiles in individual phases of fibrous metal matrix composites. To this end, embedded cell cylindrical composite model was applied in which a layered concentric cylinder consisting of a fiber-, matrix- and homogenized composite layers was used. Mean field micromechanics was integrated into the conventional elasticity solution process so that micro-macro dual scale analysis could be performed. The algorithm was formulated in an iterative incremental structure which was able to perform plastic analysis. This also allows temperature dependence of flow stress to be considered. Taking copper-SiC system as a reference composite, stress profiles were obtained for mechanical and thermal loading cases. For comparison, independent finite element analyses were carried out for two different unit cell models. Excellent agreement between analytical and numerical solutions was found for the mechanical loading case even for plastic range. In the case of thermal loading, however, plastic solutions revealed notable difference in quantity, especially for the axial stress component. [ABSTRACT FROM AUTHOR]

The fatigue performance of Kaowool fiber reinforced 339 aluminum composites at 300°C is limited by spherical thin walled hollow Kaowool shot particles. These act as crack initiation sites particularly when located at the surface. This problem does not occur for thick walled particles or particles filled with the aluminum matrix. The effect of wall thickness (t) is evaluated from finite element analysis of both 2D and 3D models, with and without plasticity. Both models predict that hollow thin walled particles act as defects, while thick walled particles act as reinforcements, this transition being defined by a critical wall thickness (tc). The 3D model is preferred in that it predicts more accurate and smaller values of tc. Specifically, the 3D elastic/plastic model predicts that the largest stress concentration occurs for a fractional surface particle and that in this condition tc = 0.18a, where a is the particle radius. This value agrees with our experimental observation that particles with t > 0.2a do not initiate failures. [ABSTRACT FROM AUTHOR]

The effect of glass-fiber epoxy interface in cross-ply reinforced composites on the fatigue behavior is studied by using load-increasing fatigue test. The damage as measured by stiffness reduction is more significant for the composites with poor bonded fibers as was found for EP sized ones, dependent on test conditions. Energy loss is shown to be a sensitive tool to characterize the nature of fiber matrix adhesion. The energy loss for composites with poor adhesion between fiber and matrix results in significantly higher amounts of consumed energy during a single stress-strain loop than those composites containing well-bonded fibers. [ABSTRACT FROM AUTHOR]

The reinforced and toughened PP/PA66 in situ composites were prepared via extrusion-drawing-injection method. The relationship among composition, phase morphology and mechanical properties, together with their functional mechanism, was investigated. The results show that in the range of PA66 weight fraction (fw) from 0 to 20% and under the experimental processing conditions, the main changes in phase morphology of the composites with fw are that the number of in situ formed PA66 microfibers and remained PA66 particles increases with fw whereas the fiber transverse size and its dispersity decrease till fw = 15% and then increase. This can be attributed to the combined effect of break-up, coalescence and deformation of the PA66 phase in the PP phase in the course of extrusion and drawing. The tensile strength of composites has a maximum value at fw of 15% and Young's modulus increases with fw up to a plateau level, while impact strength continuously rises with fw, an effect which can be ascribed to the distinct dependence of these properties on the phase-morphological factors mentioned above. [ABSTRACT FROM AUTHOR]

This study has successfully incorporated Al2O3, SiC particulates into the 7005Al alloy matrix by using a drag-push method. The reinforced particulates are uniformly distributed in the matrix. This study also discusses the influence of aging treatment on the friction welding properties of 7005Al/10 wt%, 15 μm and 6 μm SiC(p) composites and 7005Al/10 wt%, 15 μm Al2O3(p) composites joint system. Experimental results show that after peak aging treatment was performed, if SiC particulates were used in the strengthening phase, the heat-affected zone (HAZ) had higher density of strengthening particulate, this resulted an increase in the hardness and stress concentration at the fully plasticized zone (Zpl) of the HAZ region, but a decrease in the width of the Zpl zone and the welding strength. And the welded fracture surface morphology had a low-ductile fracture. [ABSTRACT FROM AUTHOR]

Environment-friendly fiber-reinforced composites were fabricated using ramie fibers and soy protein isolate (SPI) and were characterized for their interfacial and mechanical properties. Ramie fibers were characterized for their tensile properties and the parameters for the Weibull distribution were estimated. Effect of glycerol content on the tensile properties of SPI was studied. Interfacial shear strength (IFSS) was determined using the microbond technique. Based on the IFSS results and fiber strength distribution, three different fiber lengths and fiber weight contents (FWC) were chosen to fabricate short fiber-reinforced composites. The results indicate that the fracture stress increases with increase in fiber length and fiber weight content. Glycerol was found to increase the fracture strain and reduce the resin fracture stress and modulus as a result of plasticization. For 10% (w/w) of 5 mm long fibers, no significant reinforcement effect was observed. In fact the short fibers acted as flaws and led to reduction in the tensile properties. On further increasing the fiber length and FWC, a significant increase in the Young's modulus and fracture stress and decrease in fracture strain was observed as the fibers started to control the tensile properties of the composites. The experimental data were compared to the theoretical predictions made using Zweben's model. The experimental results are lower than the predicted values for a variety of reasons. However, the two values get closer with increasing fiber length and FWC. [ABSTRACT FROM AUTHOR]

Finite element (FE) micro-models have been developed in order to determine contact, stress and strain conditions produced by a steel asperity sliding on the surface of a fibre-reinforced polymer composite. Two cases were studied, i.e. a parallel and an anti-parallel fibre orientation relative to the sliding direction. In order to get more realistic simulation results relating to the failure conditions in the composite structure, FE contact macro/micro-models were used, contrary to the so far widely applied anisotropic analytical or numerical macro-models. To model a “micro-environment” as part of a “macro-environment”, the displacement coupling technique was introduced. The contact analysis operates on both the macro- and the micro-level, applying node-to-node contact elements. The contact results, especially the contact pressure distribution, can characterize the real fibre/matrix micro-system. Displacement and strain results lead to explanations of fibre related phenomena, matrix shear effects, and fibre/matrix debonding events. On the basis of the stress results, conclusions were drawn on the possible wear mechanisms of the fibre-reinforced polymer composite. For parallel fibre orientation, fibre/matrix debonding as a result of shear stresses at the interface, matrix shear type failure and fibre thinning are the dominant sliding wear mechanisms. If an anti-parallel fibre orientation is considered, matrix shear, tension/compression type fibre/matrix debonding and fibre thinning, associated with fibre cracking events, are the most dominant wear mechanisms. To study the wear mechanisms experimentally, diamond tip scratch tests were carried out, showing that the predicted failure events occur also in reality. [ABSTRACT FROM AUTHOR]

Many applications of structural materials involving composites include impact or dynamic loading in a humid environment. Composite materials are known to degrade when subjected to humid conditions, and therefore the humidity confounds the difficulty of determining the high strain rate behavior of composites. Several researchers have found that water absorption by composites causes degradation of matrix dominated quasi-static properties. However, very little is known of the effect of absorbed moisture on the high strain rate properties of polymer matrix composites, that are useful in the automotive, aerospace, and naval applications of composite structures. A Split-Hopkinson Pressure Bar facility is used herein to study the effect of absorbed moisture in high strain rate tests (200–1200/s) of a unidirectional IM7/8551-7 graphite/epoxy composite. The study includes dry, medium, and saturated moisture conditions. The tests show significant variation of high strain rate properties from static properties, and the reasons are identified. In addition, a better understanding of the effect of the matrix and fiber/matrix interface on the high strain rate properties of composites is achieved. [ABSTRACT FROM AUTHOR]

Unidirectionally solidified Al2O3/Y3Al5O12 (YAG) or Al2O3/Er3Al5O12 (EAG) eutectic composites, which are named as Melt Growth Composites (MGCs) has recently been fabricated by unidirectional solidification. The MGCs have a new microstructure, in which continuous networks of single-crystal Al2O3 phases and single-crystal oxide compounds (YAG or EAG) interpenetrate without grain boundaries. The MGCs fabricated are thermally stable and has the following properties: 1) the flexural strength at room temperature can be maintained up to 2073 K (just below its melting point), 2) a fracture manner from room temperature to 2073 K is an intergranular fracture different from a transgranular fracture of sintered composite with the same composition, 3) the compressive creep strength at 1873 K and a strain rate of 10−4/sec is 7–13 times higher than that of sintered composites, 4) the mechanism of creep deformation is based on the dislocation creep models completely different from the Nabarro-Herring or Coble creep models of the sintered composites, and 5) it shows neither weight gain nor grain growth, even upon heating at 1973 K in an air atmosphere for 1000 hours. The above superior high-temperature characteristics are caused by such factor as the MGCs having a single-crystal Al2O3/single-cryatal oxide compounds without grain boundaries and colonies, and the formation of the thermodynamically stable and compatible interface without amorphous phase. [ABSTRACT FROM AUTHOR]

During fatigue of Kaowool fiber reinforced aluminum composites at 20°C, cracks are initiated at hollow Kaowool particles. The stress concentrations associated with these particles arise from two sources: (i) residual stresses due to differential thermal contraction of the Kaowool and aluminum and (ii) the applied cyclic fatigue stress. These stresses are calculated from a finite element model which incorporates plasticity of the aluminum matrix. In general, the mechanical stresses are considerably larger than the thermal stresses. The total stress, in both the aluminum matrix and the Kaowool particle, increases with decreasing particle wall thickness and the proximity of the particle to the surface. In general, the stress concentrations in the aluminum matrix are more critical than those in the Kaowool particles, and are predicted to exceed locally the yield strength of 339 aluminum for all values of wall thickness. The particles observed experimentally at the fatigue fracture origins are thin walled and close to the surface, in quantitative agreement with the predictions of the finite element model. [ABSTRACT FROM AUTHOR]

The effect of static and cyclic loading conditions on the stress corrosion cracking of unidirectional glass reinforced polymer (GRP) rods used in composite high voltage insulator has been investigated. A series of stress corrosion experiments have been performed on unidirectional E-glass/modified polyester composite rods. The rods have been subjected to mechanical tensile static and cyclic stresses in the presence of a nitric acid solution. The stress corrosion fracture process in the rods was monitored using acoustic emission techniques. The experimental loading conditions simulated possible in-service loadis for composite suspension insulators. The results obtained in this study showed that the brittle fracture process can be generated in the rods when subjected to relatively low tensile stresses in the presence of a nitric acid solution. The morphology of the experimentally generated brittle fracture cracks in the rods closely resemble those from in-service failed composite suspension. It has also been shown in this research that low frequency, low amplitude vibrations in tensile loads can significantly accelerate the fracture process. It appears that the brittle fracture cracks in the rods generated under cyclic loads are less planar in nature in comparison with the cracks formed under static conditions. It has also been found that the acoustic emission generated during the stress corrosion fracture process in the rods is sensitive to the placement of the transducers. However, reasonably good correlation between the stress corrosion crack growth rates and acoustic emission has been attained. [ABSTRACT FROM AUTHOR]

Using a new quasi-sphere model, an analytical method is presented to determine the material properties and stress concentration factors of rubber-toughened polymers. The calculation is simple and the closed form results fit quite well with experimental data and various results using the finite element method. This simple and efficient method can be easily used to calculate a huge amount of results to fit the requirement of engineering. Also, this type of modeling can provide a better understanding of deformation mechanisms for development of this important composite material. [ABSTRACT FROM AUTHOR]