含界面相Voronoi单元的等效弹性常数的计算

采用含界面相Voronoi单元有限元法,根据广义胡克定律,计算了在给定边界条件下,颗粒增强复合材料的等效弹性常数。建立了含多个随机分布的椭圆形夹杂及界面相的VCFEM模型,分析了夹杂体分比,界面相厚度和界面相弹性模量等因素对颗粒增强复合材料等效弹性常数的影响,并利用普通有限元方法对比验证。结果表明,当界面相弹性模量小于基体与夹杂时,材料的等效弹性模量会随着界面相厚度的增大而减小,随着夹杂体分比的增大而减小,并且界面过薄时,材料的等效弹性模量会随着夹杂体分比的增大而增大;当界面相弹性模量大于基体或夹杂时,材料的等效弹性模量会随着夹杂体分比和界面相厚度的增大而增大。而界面相的厚度和弹性模量对材料的等效泊松比的影响较小,材料的等效泊松比主要受夹杂体分比的影响,与其呈反比关系。     

基于整体位移模式的平面孔洞结构数值模拟方法

针对平面孔洞问题提出了一种新的数值模拟方法。本文通过水平集方法引入孔洞边界、力边界和位移边界水平集函数,利用边界水平集函数来构造边界试探项,将试探空间表示为二元幂级数与边界试探项的线性组合;同时提出一种基于水平集方法的位移边界条件施加方法,利用位移边界水平集函数来构造满足位移边界条件的近似位移场,并给出了相应的刚度矩阵和载荷矩阵表达式。与FEM、XFEM、无网格法等方法相比,该方法无需将求解域离散,具有较低的计算成本、特性良好的刚度矩阵和较为广泛的适用性。数值算例验证了该方法的有效性。     

Computational studies on high-stiffness,high-damping SiC–InSn particulate reinforced composites

With the objective of achieving composite material systems that feature high stiffness and high mechanical damping, consideration is given here to unit cell analysis of particulate composites with high volume fraction of inclusions. Effective elastic properties of the composite are computed with computational homogenization based on unit cell analysis. The correspondence principle together with the viscoelastic properties of the indium–tin eutectic matrix are then used to compute the effective viscoelastic properties of the composite. Comparison is made with parallel experiments upon composites with an indium–tin eutectic matrix and high volume fractions of silicon-carbide reinforcement. The analytical techniques indicate that combinations of relatively high stiffness and high damping can be achieved in particulate composites with high SiC volume fractions. Based on analysis, the tradeoffs between stiffness and damping characteristics are assessed by changing the volume fraction, size, packing, and gradation of the particulate reinforcement phases. Practical considerations associated with realization of such composites based on the surface energy between the SiC and the InSn are discussed.     

General mean-field homogenization schemes for viscoelastic composites containing multiple phases of coated inclusions

We consider matrix materials reinforced with multiple phases of coated inclusions. All materials are linear viscoelastic. We present general schemes for the prediction of the effective properties based on mean-field homogenization. There are four contributions in this work. First, we present a two-step homogenization procedure in a general setting which besides the usual assumptions of Eshelby-based models, does not suffer any restriction in terms of material properties, aspect ratio or orientation. Second, for a matrix reinforced with coated inclusions, we propose two general homogenization schemes, a two-step method and a two-level recursive scheme. We develop and compare the mathematical expressions obtained by the two schemes and a generalized Mori–Tanaka (M–T) model. Third, for a two-phase composite, either standalone or stemming from two-step or two-level schemes, we use a double-inclusion model based on a closed-form but non-trivial interpolation between M–T and inverse M–T estimates. Fourth, we conduct an extensive validation of the proposed schemes as well as others against experimental data and unit cell finite element simulations for a variety of viscoelastic composite materials. Under severe conditions, the proposed schemes perform much better than other existing homogenization methods.     

A micromechanical study of drying and carbonation effects in cement-based materials

This paper is devoted to a micromechanical study of mechanical properties of cement-based materials by taking into account effects of water saturation degree and carbonation process. To this end, the cement-based materials are considered as a composite material constituted with a cement matrix and aggregates (inclusions). Further, the cement matrix is seen as a porous medium with a solid phase (CSH) and pores. Using a two-step homogenization procedure, a closed-form micromechanical model is first formulated to describe the basic mechanical behavior of materials. This model is then extended to partially saturated materials in order to account for the effects of water saturation degree on the mechanical properties. Finally, considering the solid phase change and porosity variation related to the carbonation process, the micromechanical model is coupled with the chemical reaction and is able to describe the consequences of carbonation on the macroscopic mechanical properties of material. Some comparisons between numerical results and experimental data are presented.     

A macroscopic model for materials reinforced by flexible membranes

A macroscopic model is presented aimed at assessing the macroscopic elastic behaviour of materials reinforced by periodically distributed flexible membranes. According to this model, called multiphase model, the reinforced material is described not as a single homogenized continuum as in the classical homogenization approach, but as the superposition of two mutually interacting continuous media, namely the matrix phase and the reinforcement phase. It is shown in particular how such a model allows to capture both scale and boundary effects, which cannot be accounted for in a classical homogenization procedure.     

Solutions for effective shear properties in three phase sphere and cylinder models

Solutions are presented for the effective shear modulus of two types of composite material models. The first type is that of a macroscopically isotropic composite medium containing spherical inclusions. The corresponding model employed is that involving three phases: the spherical inclusion, a spherical annulus of matrix material and an outer region of equivalent homogeneous material of unlimited extent. The corresponding two-dimensional, polar model is used to represent a transversely isotropic, fiber reinforced medium. In the latter case only the transverse effective shear modulus is obtained. The relative volumes of the inclusion phase to the matrix annulus phase in the three phase models are taken to be the given volume fractions of the inclusion phases in the composite materials at large. The results are found to differ from those of the well-known Kerner and Hermans formulae for the same models. The latter works are now understood to violate a continuity condition at the matrix to equivalent homogeneous medium interface. The present results are compared extensively with results from other related models. Conditions of linear elasticity are assumed.     

Prediction of tension–compression cycles in multiphase steel using a modified incremental mean-field model

A micromechanical model is proposed for multiphase metals consisting of a ductile matrix reinforced by hard, equiaxed inclusions. The model belongs to a class of incremental mean-field theories of the first order and is suitable for general, non-monotonic loading paths. This paper specifically addresses the definition of the effective, instantaneous shear modulus of the isotropic comparison materials which intervene in the solution of the linearized, homogenisation problem. Time integration of the composite response is calculated using a Newton–Raphson scheme and a consistent tangent operator is derived. Predictions of the phase stresses developed under various loading modes and for a wide range of volume fractions of inclusions are assessed by a comparison with finite element simulations of periodic unit cells. It is argued that the latter predictions depend dramatically on the topological arrangement of the inclusions. Considering a cubic ordering of inclusions, it is possible to reproduce FE predictions with the mean-field model on the condition that the comparison materials are stiffer than the real phases during the first few percent of plastic strain. The mean-field model provides an accurate prediction of the average stress developed within individual phases.     

A micromechanically based couple-stress model of an elastic orthotropic two-phase composite

We determine couple-stress moduli and characteristic lengths of a two-dimensional matrix-inclusion composite, with inclusions arranged in a periodic square array and both constituents linear elastic of Cauchy type. In the analysis we replace this composite by a homogeneous planar, orthotropic, couple-stress continuum. A generalization of the original Mindlin's (1963) derivation of field equations for such a continuum results in two (not just one!) characteristic lengths. We evaluate the couple-stress properties from the response of a unit cell under several types of boundary conditions: displacement, displacement-periodic, periodic and mixed, and traction controlled. In the parametric study we vary the stiffness ratio of both phases to cover a range of different media from nearly porous materials through composites with very stiff inclusions. We find that the aforementioned boundary conditions result in hierarchies of orthotropic couple-stress moduli, whereas both characteristic lengths are fairly insensitive to boundary conditions, and fall between 0.12% and 0.22% of the unit cell size for the inclusions' volume fraction of 18%.     

A two-phase elastoplastic model for unidirectionally-reinforced materials

A complete analytical formulation for the elastoplastic behaviour of a composite material comprising one single array of reinforcing inclusions perfectly bonded to the matrix is developed in this paper. Fundamental relationships establish the link between the total stress and strain variables, and those pertaining to the individual constituents (matrix and reinforcement) regarded as superposed continuous phases. Assuming that each constituent behaves as an elastic perfectly plastic material, the constitutive equations governing the evolution of the reinforced material as a whole are derived. They reveal a hardening phenomenon arising from the non-compatibility between matrix and reinforcement plastic strains. It is shown in particular that the obtained constitutive law falls within the formalism of generalized standard plasticity: the reinforcement residual stress plays the role of a hardening parameter which controls the evolution of the yield surface, while the associated kinematic variable is the plastic strain discrepancy between matrix and reinforcement phases.Owing to its inherent simplicity, the model is easily amenable to a numerical treatment for structural analysis. It is shown in particular how the classical iterative algorithm can be modified accordingly, and an illustrative application is finally presented in the field of civil engineering.     

The effect of interfacial properties on the cohesion of highly filled composite materials

It has long been recognized that the cohesion of composite materials, in low confinement, is strongly affected by the properties of the interfacial transition zone (ITZ) between inclusions and matrix. While the effect of the ITZ on the elasticity properties of composites has been studied by many authors in the context of linear homogenization methods, the upscaling of the cohesion strength of highly filled composite materials has not been addressed. This is the focus of the non-linear homogenization procedure developed in this paper, which is based on the separation of the heterogeneous material system in phases of constant strength properties, a non-linear elastic representation of the limit stress state in each phase, and the definition of appropriate effective strain quantities that capture the morphological features of the microstructure. Applied to a three phase composite model composed of rigid inclusion, interface zone and matrix, the model provides a quantitative means of studying the effect of the interface cohesion and the interface volume fraction on the composite cohesion. In particular, we identify a critical interface-to-matrix cohesion ratio, below which the composite cohesion is smaller than the one of the matrix. Furthermore, the model lends itself readily to the study of the degradation of the interfacial properties in composite materials. This is shown for non-degraded and chemically softened cement-based materials, for which we provide conclusive evidence (1) that the interface strength properties of mortar are far more affected by chemical degradation than the one of the cement paste matrix; and (2) that chemical degradation does affect the mechanical strength performance of the cement paste not only through a change of volume proportions (i.e. increase of porosity), but as well through a pure chemical softening of the solid’s cohesion.     

On the Size of RVE in Finite Elasticity of Random Composites

This paper presents a quantitative study of the size of representative volume element (RVE) of random matrix-inclusion composites based on a scale-dependent homogenization method. In particular, mesoscale bounds defined under essential or natural boundary conditions are computed for several nonlinear elastic, planar composites, in which the matrix and inclusions differ not only in their material parameters but also in their strain energy function representations. Various combinations of matrix and inclusion phases described by either neo-Hookean or Ogden function are examined, and these are compared to those of linear elastic types.     

A micromechanical iterative approach for the behavior of polydispersed composites

In this paper, an iterative homogenization method is proposed in order to predict the behavior of polydispersed materials. Various families of heterogeneities according to their geometrical or mechanical properties are progressively introduced into a volume of matrix. At each step, the behavior of intermediate medium is obtained by any analytical homogenization method and is used as matrix of the following step. All homogenization methods, like dilute strain or stress approximations, Hashin’s bounds, three phases method, Mori–Tanaka’s approach or for example the N-layered inclusions method lead to the same effective behavior for the polydispersed material after convergence of the iterative process. Moreover, this convergence is obtained even for significant fractions of heterogeneities and for highly contrasted or polydispersed materials. This method is applied to various composites and validated by comparison with other modellings and experimental results.     

A local finite element implementation for imposing periodic boundary conditions on composite micromechanical models

Recent advances in computational speed have resulted in the ability to model composite materials using larger representative volume elements (RVEs) with greater numbers of inclusions than have been previously studied. Imposing periodic boundary conditions on very large RVEs can mean enforcing thousands of constraint equations. In addition, a periodic mesh is essential for enforcing the constraints. The present study investigates a method that uses a local implementation of the constraints that does not adversely affect the computational speed. The present study demonstrates the method for two-dimensional triangular and square RVEs of periodically-spaced regular hexagonal and square arrays of composite material containing fibers of equal radii. To impose the boundary conditions along the edges, this study utilizes a cubic interpolant to model the displacement field along the matrix edges and a linear interpolant to model the field along the fiber edges. It is shown that the method eliminates the need for the conventional node-coupling scheme for imposing periodic boundary conditions, consequently reducing the number of unknowns to the interior degrees of freedom of the RVE along with a small number of global parameters. The method is demonstrated for periodic and non-periodic mesh designs.     

NUMERICAL SIMULATION OF 2D FIBER-REINFORCED COMPOSITES USING BOUNDARY ELEMENT METHOD

Introduction Withthedevelopmentofmodernindustry,compositesareincreasinglybeingappliedto agreatnumberofimportantstructures.Todeterminethemacroscopicaleffective characteristicsofcompositesisanessentialprobleminmanyengineeringapplications.The macroscopicalef…     

Multiphase approach as a generalized homogenization procedure for modelling the macroscopic behaviour of soils reinforced by linear inclusions

This paper examines the possibility of applying a homogenization procedure to soils reinforced by linear inclusions, regarded as elastic periodic composites for which scale effects have to be considered, as shown by the preliminary numerical analysis of two illustrative problems. A so-called multiphase model is developed for this purpose, aimed at improving the classical homogenization method on two decisive points. First, by modelling the reinforced soil at the macroscopic scale as the superposition of two mutually interacting continuous phases, describing the soil and the reinforcement network, respectively. Second, by assuming that the reinforcements display a shear and flexural behaviour, in addition to the axial one, so that the corresponding phase may be described as a micropolar continuum. Its is shown that such a multiphase approach can be interpreted as an extension of the homogenization procedure, making it thus possible to capture the previously mentioned scale effects, provided that the constitutive parameters of the model can be properly identified from the reinforced soil characteristics.     

Meso-scale approach to modelling the fracture process zone of concrete subjected to uniaxial tension

A meso-scale analysis is performed to determine the fracture process zone of concrete subjected to uniaxial tension. The meso-structure of concrete is idealised as stiff aggregates embedded in a soft matrix and separated by weak interfaces. The mechanical response of the matrix, the inclusions and the interface between the matrix and the inclusions is modelled by a discrete lattice approach. The inelastic response of the lattice elements is described by a damage approach, which corresponds to a continuous reduction of the stiffness of the springs. The fracture process in uniaxial tension is approximated by an analysis of a two-dimensional cell with periodic boundary conditions. The spatial distribution of dissipated energy density at the meso-scale of concrete is determined. The size and shape of the deterministic FPZ is obtained as the average of random meso-scale analyses. Additionally, periodicity of the discretisation is prescribed to avoid influences of the boundaries of the periodic cell on fracture patterns. The results of these analyses are then used to calibrate an integral-type nonlocal model.     

Strength homogenization of matrix-inclusion composites using the linear comparison composite approach

A homogenization procedure to estimate the macroscopic strength of nonlinear matrix-inclusion composites with different strength characteristics of the matrix and inclusions, respectively, is presented in this paper. The strength up-scaling is formulated within the framework of the yield design theory and the linear comparison composite (LCC) approach, introduced by Ponte Castaneda (2002) and extended to frictional models by Ortega et al. (2011), which estimates the macroscopic strength of composite materials in terms of an optimally chosen linear thermo–elastic comparison composite with a similar underlying microstructure. In the paper various combinations for the underlying material behavior for the individual phases of the composite are considered: The matrix phase can be a quasi frictional material characterized either by a Drucker–Prager-type (hyperbolic) or an elliptical strength criterion, which predicts a strength limit also in hydrostatic compression, while the inclusion phase either may represent empty pores, pore voids filled with a pore fluid, rigid inclusions, or solid inclusions, whose strength characteristics also maybe described by a Drucker–Prager-type or an elliptical strength criterion. For generating the homogenized strength criterion efficiently in such general cases of matrix-inclusion composites, a novel algorithm is proposed in the paper. The validation of the proposed strength homogenization procedure for selected combinations of strength characteristics of the matrix material and the inclusions is conducted by comparisons with experimental results and alternative existing strength homogenization models.     

双周期圆柱形压电夹杂反平面问题的精确解及其应用

研究无限压电介质中双周期圆柱形压电夹杂的反平面问题.借鉴Eshelby等效夹杂原理,通过引入双周期非均匀本征应变和本征电场,构造了一个与原问题等价的均匀介质双周期本征应变和本征电场问题.利用双准周期Riemann边值问题理论,获得了夹杂内外严格的电弹性解.作为压电纤维复合材料的一个重要模型,预测了压电纤维复合材料的有效电弹性模量.     

A theoretical model for the prediction of thermal expansion behaviour of particulate composites

The thermal expansion coefficient of particle-reinforced polymers was evaluated using a theoretical model which takes into account the adhesion efficiency between the inclusions and the matrix — an important factor affecting the thermomechanical properties of a composite. To measure the adhesion efficiency a boundary interphase, i.e. a layer between the matrix and the fillers having a structure and properties different from those of the constituent phases, was considered. This layer is assumed to have varying properties.To obtain information concerning the properties and extent of the interphase, an experimental study of the thermal behaviour of aluminium-epoxy composites was undertaken. Differential Scanning Calorimetry (DSC) measurements were performed to evaluate heat capacity with respect to temperature. In addition, the effects of different factors, such as heating rate and filler concentration on the glass transition temperature of the composite, were examined. The sudden changes in heat capacity values in the glass transition region were used to estimate the extent of the boundary interphase according to an existing theory.Finally, the values of the thermal expansion coefficient, predicted by this model, were compared with theoretical results obtained by other authors and with experimental results.