Finite element analysis of viscoelastic composite structures based on a micromechanical material model

The stress and creep analysis of structures made of micro-heterogeneous composite materials is treated as a two-scale problem, defined as a mechanical investigation on different length scales. Reinforced composites show by definition a heterogeneous texture on the microlevel, determined by the constitutive behaviour of the matrix material and the embedded fibres as well as the characteristics of the bonding properties in the interphase. All these heterogeneities are neglected by the finite element analysis of structural elements on the macroscale, since a ficticious and homogeneous continuum with averaged properties is assumed. Therefore, the constitutive equations of the substitute material should well reflect the mechanical behaviour of the existing micro-heterogeneous composite in an average sense.The paper at hand starts with the brief outline of a micromechanical model, named generalized method of cells (GMC), which provides the macrostress responses due to macrostrain processes as well as the homogenised constitutive tensor of the substitute material. The macroscopic stresses and strains are obtained as volume averages of the corresponding microfields within a representative volume element. The effective material tensor constitutes the mapping between the macro-strains and the macro-stresses. The cells method is used for the homogenisation of the unidirectionally reinforced single layers of laminates made of viscoelastic resins and flexibly embedded elastic fibres. The algorithm for the homogenisation of the constitutive properties runs simultaneously to the finite element analysis at each point of numerical integration and provides the macro-stresses and the homogenised constitutive properties. The validity of the proposed two-scale simulation is investigated by solving boundary value problems and comparing the numerical results for the structures to the experimental data of creep and relaxation tests or analytical solutions.     

A micromechanical composite approach for finite element crashworthiness simulation

The present article deals with micromechanical composite modeling. Both analytical and computational micromechanics approaches are described as well as micromechanical modeling of damage. Based on micromechanics of failure theory, a user subroutine including a progressive damage algorithm is programmed for finite element analysis. Three theory-experiment correlations of tubes under a three-point bending test have been carried out using the bi-phase material model developed along with this project. These studies include three-ply schedules.     

Finite element analysis of damaged woven fabric composite materials

Since fiber reinforced composite materials have been used in main parts of structures, an accurate evaluation of their mechanical characteristics becomes very important. Due to their anisotropic nature and complicated architecture, it is very difficult to reveal the damage mechanisms of these materials from the results of mechanical tests. Therefore, there is a need to conduct reliable simulations and analytical evaluations. In this paper, the damage behavior of FRP is simulated by finite element analysis using an anisotropic damage model based on damage mechanics. The proposed procedure is applied to an example; the finite element analysis of microscopic damage propagation in woven fabric composites. Experimental tests have been conducted to evaluate the validity of the proposed method. It is recognized that there is a good agreement between the computational and experimental results, and that the proposed simulation method is very useful for the evaluation of damage mechanisms.     

A boundary element analysis of metal matrix composite materials

The numerical modelling of metal matrix composites is an important part of the research now being conducted on these materials. Due to the numerical complexity of a fully three-dimensional analysis, two-dimensional approximations are normally used with finite element methods. While these analyses are informative, they cannot treat complex particle shapes or examine three-dimensional effects in the composite. The use of boundary element methods in place of the more widely used finite element methods significantly reduces the computing power necessary to obtain a solution to a given problem, making it possible to simulate fully three-dimensional geometries. In the present paper a two-dimensional form of the BEM is applied to the study of metal matrix composite materials, and its performance compared with that of similar FEM stadies. We also compare the predicted composite properties with existing and new experimental results. We conclude that the BEM is an effective tool for the analysis of this class of problems.     

Nonlinear hygro-thermo-elastic vibration analysis of doubly curved composite shell panel using finite element micromechanical model

Nonlinear free vibration behavior of laminated composite curved panel under hygrothermal environment is investigated in this article. The mathematical model of the laminated panel is developed using Green–Lagrange-type geometrical nonlinearity in the framework of higher-order mid-plane kinematics. The corrugated composite properties are evaluated through the micromechanical model and all the nonlinear higher-order terms are included in the present model for the sake of generality. The equation of vibrated panel is obtained using Hamilton's principle and discretized with the help of the finite element steps. The solutions are computed numerically using the direct iterative method. The effect of parameters on the nonlinear vibration responses is examined thoroughly by solving the wide variety of numerical examples.     

A micromechanical analysis of fiber crack propagation in composite materials due to transverse tensile loads

The fiber crack propagation in composites due to transverse tensile loads is studied using a micromechanical model and Linear Elastic Fracture Mechanics. To approach the problem, a three domain cylindrical model is introduced to simulate the fiber cracking. The model problem is then solved by the dislocation and singular integral equation techniques. The stress intensity factors of the fiber crack are calculated for various situations. It is found that fiber anisotropy has hardly any effect on the fiber crack propagation; “reverse composites” (composites in which fiber is less stiff than the matrix, such as Nicalon/SiC ceramic composite) virtually eliminate fiber crack propagation.     

On the representative volume element of asphalt concrete at low temperature

The feasibility of characterizing asphalt mixtures’ rheological and failure properties at low temperatures by means of the Bending Beam Rheometer (BBR) is investigated in this paper. The main issue is the use of thin beams of asphalt mixture in experimental procedures that may not capture the true behavior of the material used to construct an asphalt pavement.For the rheological characterization, three-point bending creep tests are performed on beams of different sizes. The beams are also analyzed using digital image analysis to obtain volumetric fraction, average size distribution, and spatial correlation functions. Based on the experimental results and analyses, it is concluded that representative creep stiffness values of asphalt mixtures can be obtained from testing at least three replicates of the thin (BBR) mixture beams.Failure properties are investigated by performing strength tests using a modified Bending Beam Rheometer (BBR), capable of applying loads at different loading rates. Histogram testing of BBR mixture beams and of larger beams is performed and the failure distribution is analyzed based on the size effect theory for quasibrittle materials. Different Weibull moduli are obtained from the two specimens sizes, which indicates that BBR beams do not capture the representative volume element (RVE) of the material.     

Combined loading micromechanical analysis of a unidirectional composite

A microscopic region of a unidirectional composite is modelled by a finite element micromechanical analysis using a generalized plane strain formulation, but including longitudinal shear loading. The analysis is capable of treating elastic, transversely isotropic fibre materials, as well as isotropic, elastoplastic matrix materials. Matrix material properties are considered to be temperature- and/or moisture-dependent. The longitudinal shear loading capability permits the analysis of the shear response of unidirectional composites in the fibre direction. In conjunction with a laminated plate point stress analysis, the present micromechanical analysis has been used to predict the stress/strain response into the inelastic range of a graphite/epoxy [±45]_4s laminate. Available experimental data for various environmental conditions indicate excellent agreement with the analytical predictions.     

A micromechanical analysis to predict the cord-rubber composite properties

Both three- and two-dimensional generalized plane strain finite element analyses based on a micromechanics approach were carried out to investigate the linear and nonlinear effective composite properties as well as the stress fields. A unit cell model of cord-rubber composite subjected to different loadings was studied to predict the effective composite properties. The numerical results of effective composite properties obtained from 2D and 3D finite element analyses were compared with experimental data and other finite element results available in the literature. The effects of rubber material nonlinearity and large deformation on the effective composite properties and interface stress distributions are presented and discussed.     

Adaptive periodical representative volume element for simulating periodical postbuckling behavior

Finite element method (FEM) with fixed representative volume element (RVE) encounters some difficulties in simulating the periodical postbuckling behaviors of infinite long beam or infinite large film on soft substrate under compression, because the wavelength and pattern of buckling are not known before simulation and will change with the increase of compression strain. In this paper, an adaptive periodical RVE is constructed in a mapping space to avoid remeshing in the real space, and the mapping coefficients, that is, the dimension and shape of RVE in real space, are treated as variables in average energy density minimization to obtain correct postbuckling configurations. The validness and efficiency of the proposed algorithm have been demonstrated by our numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Material spatial randomness: From statistical to representative volume element

The material spatial randomness forces one to re-examine various basic concepts of continuum solid mechanics. In this paper we focus on the Representative Volume Element (RVE) that is commonly taken for granted in most of deterministic as well as in stochastic solid mechanics, although in the latter case it is called the Statistical Volume Element (SVE). The key issue is the scale over which homogenization is being carried out—it is called the mesoscale, separating the microscale (level of microheterogeneities) from the macroscale (level of RVE). As the mesoscale grows, the SVE tends to become the RVE. This occurs in terms of two hierarchies of bounds stemming from Dirichlet and Neumann boundary value problems on the mesoscale, respectively. Since generally there is no periodicity in real random media, the RVE can only be approached approximately on finite scales. We review results on this subject in the settings of linear elasticity, finite elasticity, plasticity, viscoelasticity, thermoelasticity, and permeability.     

Investigating the micromechanical evolutions within inherently anisotropic granular materials using discrete element method

This paper investigates the mechanical behavior of inherently-anisotropic granular materials from macroscopic and microscopic points of view. The study is achieved by simulating biaxial compression tests performed on granular assemblies by using numerical discrete element method. In the same category of numerical studies found in the literature, the simulations were performed by considering elliptical/oval particles. In the present study, however, the shape of particles is considered as convex polygons, which mostly resembles real sand grains. Particle assemblies with four different bedding angles were tested. Similar to what observed in experiment, inherent anisotropy has a significant effect on macroscopic mechanical behavior of granular materials. The shear strength and dilative behavior of assemblies were found to decrease as the bedding angle increases. Evolution of the microstructure of all samples and the influence of bedding angle on the fabric and force anisotropy during loading process were investigated. It is seen that the microscopic evolutions in the fabric can justify well the macroscopic behavior of granular assemblies. It is found that the long axis of particles tend to be inclined perpendicular to the loading axis, which results in generating more stable column-like microstructures in order to transfer the applied load. Moreover, the number of contacts as well as the magnitude of forces among particles varies in different directions during the loading process and the initial anisotropy condition totally evolves due to the induced anisotropy within samples.     

Determining a representative volume element capturing the morphology of fibre reinforced polymer composites

Production parameters have been found to influence the morphology of microstructure and damage behaviour in composite materials. To model the effects of this microstructural inhomogeneity, it is necessary, for practical purposes, to consider a limited, representative microstructure. A method to find a representative volume element (RVE) is investigated in which the Kolmogorov goodness-of-fit test is applied to a spatial distribution statistic, local population density, which is defined as a ratio between the fibre diameter and the area of that fibre’s enclosing Voronoi polygon. The method is applied to actual spatial distribution data recorded for a crossply composite laminate manufactured from 3M scotchply 1003 prepreg. For the composite laminate studied, a representative volume element size is determined through applying the Kolmogorov goodness-of-fit test at significance levels 0.05 and 0.10, resulting in sizes of approximately 300 × 300 μm.     

The Linear Matching Method applied to composite materials: A micromechanical approach

The paper considers a Direct Method for the evaluation of the maximum load corresponding to pre-assigned limits on the non-linear behaviour of the matrix and fibres in a laminate structure. This is achieved by combining a consistent micro-macro model for linear behaviour with an extension of the Linear Matching Method (LMM), previously extensively applied to Direct Methods in plasticity. The method is developed with assumptions that allow the methodology to be displayed in its simplest form. Applications to examples of laminate elements and a laminate plate containing a hole are described, assuming a matrix with a limit on ductility.     

Finite element micromechanical modelling of a unidirectional composite subjected to axial shear loading

A micromechanical model is presented which predicts the behaviour of a unidirectional composite subjected to axial shear load using standard finite elements. Only a three-dimensional model can handle the necessary shear loading boundary conditions when using such elements. These boundary conditions give shear stress components but no direct stress components within the composite. A parametric study is carried out on unidirectional carbon fibre/epoxy within the linear elastic regime of both constituents. The study reveals that the most critical parameters controlling the axial shear modulus of the composite are matrix modulus and fibre volume fraction whilst the stress state in the composite is mainly controlled by geometrical features of the composite, i.e., fibre volume fraction and fibre spacing. Comparison between the predicted axial shear modulus based on the concentric cylinder model and the current finite element model shows good agreement for low and intermediate fibre volume fractions. Both predictions lie within the Hashin bounds and the finite element prediction tends to be closer to the upper Hashin bound for fibre volume fractions greater than 60%. The initial tangent shear modulus predicted with the finite element model and that measured differ by less than 2.5%. The non-linear shear stress/strain response of the composite material is also predicted and agreement with the experimental results is good.     

A meshless grain element for micromechanical analysis with crystal plasticity

This study concerns the development of a 2‐D meshless grain element for elasto‐plastic deformation and intergranular damage initiation and propagation in polycrystalline fcc metals under static loading. The crystallographic material behaviour of the grains is represented by a rate‐independent single‐crystal plasticity model while including material orthotropy. The two slip planes are arbitrarily located with respect to the crystallographic axis of the grain. A non‐linear constitutive model known as the cohesive zone model is employed to represent the inelastic interaction between the grain boundaries, thus permitting grain boundary opening and sliding. The cohesive model describes the deformation characteristics of the grain boundaries through a non‐linear relation between the effective grain boundary tractions and displacements. Because of the presence of non‐linear material behaviour both inside the grain and along the cohesive grain boundaries, the method utilizes the principle of virtual work in conjunction with the meshless formulation in the derivation of the system of non‐linear incremental equilibrium equations. The solution is obtained via an incremental procedure based on the Taylor series expansion about the current equilibrium configuration. The fidelity of the present approach is verified by considering simple polycrystalline metals of only a few grains. Copyright © 2006 John Wiley & Sons, Ltd.     

Microstructure-based simulation of thermomechanical behavior of composite materials by object-oriented finite element analysis

While it is well recognized that microstructure controls the physical and mechanical properties of a material, the complexity of the microstructure often makes it difficult to simulate by analytical or numerical techniques. In this paper we present a relatively new approach to incorporate microstructures into finite element modeling using an object-oriented finite element technique. This technique combines microstructural data in the form of experimental or simulated microstructures, with fundamental material data (such as elastic modulus or coefficient of thermal expansion of the constituent phases) as a basis for understanding material behavior. The object-oriented technique is a radical departure from conventional finite element analysis, where a “unit-cell” model is used as the basis for predicting material behavior. Instead, the starting point of object-oriented finite element analysis is the actual microstructure of the material being investigated. In this paper, an introduction to the object-oriented finite element approach to microstructure-based modeling is provided with two examples: SiC particle-reinforced Al matrix composites and double-cemented WC particle-reinforced Co matrix composites. It will be shown that object-oriented finite element analysis is a unique tool that can be used to predict elastic and thermal constants of the composites, as well as salient effects of the microstructure on local stress state.     

Computational analysis of mixed-mode fatigue crack growth in quasi-brittle materials using extended finite element methods

In the present paper an extended finite element method (XFEM) containing strong discontinuity within elements is introduced and implemented in the commercial general purpose software ABAQUS. The algorithm allows introducing a new crack surface at arbitrary locations and directions in elements. To consider fatigue crack nucleation and propagation in quasi-brittle materials the XFEM is combined with a cyclic cohesive model. Accumulative material damage is described by separate evolution equations. The crack path is completely independent of the mesh structure but determined by the mixed-mode loading cases. Numerical simulations illustrate the ability of this method to simulate fracture with unstructured meshes. The computational results agree with known fracture experiment data. Known fatigue observations can be predicted using the present model.