A numerical approach for determining the effective elastic symmetries of particulate-polymer composites

In this paper we deal with the problem of determining on the one hand the effective elastic properties of particulate-polymer composite materials and on the other hand the actual degree of symmetry of the resulting homogenised material. This twofold purpose has been accomplished by building a 2D as well as a 3D finite element model of the heterogeneous material and by using the strain-energy based numerical homogenisation technique. Both finite element models are able to reproduce with a good level of accuracy the real microstructure of the composite material by considering a random distribution of both particles and air bubbles (that are generated by the fabrication process). To assess the effectiveness of the proposed models, we present a numerical study to determine the effective elastic properties of the composite along with a comparison with the existing analytical and experimental results taken from literature and a sensitivity analysis in terms of the spatial distribution of the particles of the unit cell. Numerical results show that both models are able to provide the equivalent elastic properties with a very good level of accuracy when compared to experimental results and that the particulate-reinforced polymer composite could show, depending on the particles volume fraction and arrangement, an isotropic or a cubic elastic symmetry.     

On the capability of micromechanics models to capture the auxetic behavior of fibers/particles reinforced composite materials

This work investigates the possibility to predict the auxetic behavior of composites consisting of non-auxetic phases by means of micromechanical models based on Eshelby’s inclusion concept. Two specific microstructures have been considered: (i) the three-layered hollow-cored fibers-reinforced composite and (ii) a microstructure imitating the re-entrant honeycomb micro-architecture. The micromechanical analysis is based on kinematic integral equations as a formal solution of the inhomogeneous material problem. The interaction tensors between the inhomogeneities are computed thanks to the Fourier’s transform. The material anisotropy due to the morphological and topological textures of the inhomogeneities was taken into account thanks to the multi-site approximation of these tensors. In both cases, the numerical results show that auxetic behavior cannot be captured by such models at least in the case of elastic and isotropic phases. This conclusion is supported by corresponding finite element investigations of the second microstructure that indicate that auxetic behavior can be recovered by introducing joints between inclusions. Otherwise, favorable issues are only expected with auxetic components.     

On the capability of micromechanics models to capture the auxetic behavior of fibers/particles reinforced composite materials

This work investigates the possibility to predict the auxetic behavior of composites consisting of non-auxetic phases by means of micromechanical models based on Eshelby’s inclusion concept. Two specific microstructures have been considered: (i) the three-layered hollow-cored fibers-reinforced composite and (ii) a microstructure imitating the re-entrant honeycomb micro-architecture. The micromechanical analysis is based on kinematic integral equations as a formal solution of the inhomogeneous material problem. The interaction tensors between the inhomogeneities are computed thanks to the Fourier’s transform. The material anisotropy due to the morphological and topological textures of the inhomogeneities was taken into account thanks to the multi-site approximation of these tensors. In both cases, the numerical results show that auxetic behavior cannot be captured by such models at least in the case of elastic and isotropic phases. This conclusion is supported by corresponding finite element investigations of the second microstructure that indicate that auxetic behavior can be recovered by introducing joints between inclusions. Otherwise, favorable issues are only expected with auxetic components.     

Analytical and numerical analysis of 3D grid-reinforced orthotropic composite structures

A comprehensive micromechanical investigation of 3D periodic composite structures reinforced with a grid of orthotropic reinforcements is undertaken. Two different modeling techniques are presented; one is based on the asymptotic homogenization method and the other is a numerical model based on the finite element technique. The asymptotic homogenization model transforms the original boundary value problem into a simpler one characterized by effective coefficients which are shown to depend only on the geometric and material parameters of a periodicity cell. The model is applied to various 3D grid-reinforced structures with generally orthotropic constituent materials. Analytical formula for the effective elastic coefficients are derived, and it is shown that they converge to earlier published results in much simpler case of 2D grid reinforced structures with isotropic constituent materials. A finite element model is subsequently developed and used to examine the aforementioned periodic grid-reinforced orthotropic structures. The deformations from the finite element simulations are used to extract the elastic and shear moduli of the structures. The results of the asymptotic homogenization analysis are compared to those pertaining to their finite element counterparts and a very good agreement is shown between these two approaches. A comparison of the two modeling techniques readily reveals that the asymptotic homogenization model is appreciably faster in its implementation (without a significant loss of accuracy) and thus is readily amenable to preliminary design of a given 3D grid-reinforced composite structure. The finite element model however, is more accurate and predicts all of the effective elastic coefficients. Thus, the engineer facing a particular design application, could perform a preliminary design (selection of type, number and spatial orientation of the reinforcements) and then fine tune the final structure by using the finite element model.     

模糊结构有限元分析的一种新方法

本文利用信息熵的概念,将模糊变量转变为随机变量,将模糊结构视为随机结构进行处理,从而提出了模糊结构有限元分析的一种新方法。当模糊结构转换的随机变量处于小扰动情况下,利用摄动法得到有限元递归方程组,解之可以得到响应量的均值和方差。     

Reliability analysis of nonlinear laminated composite plate structures

A procedure for the reliability analysis of laminated composite plate structures subjected to large deflections under random static loads is presented. The nonlinear analysis of laminated composite plate structures is achieved via a corotational total Lagrangian finite element formulation which is based on the von Karman assumption and first order shear deformation theory. This formulation is applicable for the nonlinear analysis of plate structures with large rotations but moderate deformation and thus accurate enough to predict the behavior of the structures at the point of failure. The reliability assessment of laminated composite plate structures with random strength subjected to random loads is approached by the determination of limit state surfaces in load space. The limit space surfaces are obtained by performing a series of first ply failure analyses following different load paths in load space using the proposed nonlinear structural analysis technique and an appropriate failure criterion. A numerical technique is then proposed to evaluate the reliability of the plate structures. Examples of the reliability analyses of laminated plates with different layer orientations subject to random loads are given for illustration.     

Thermo-viscoelastic analysis of the integrated T-shaped composite structures

A thermo-viscoelastic finite element analysis is used to investigate the residual stresses and the curing deformation of the integrated T-shaped composite structure. First, a three dimensional (3D) incremental viscoelastic constitutive equation is established and implemented into the finite element software ABAQUS to predict the full field warpage profiles of the integrated T-shaped structures. These results are validated based on the measured data obtained from digital speckle correlation technology. Second, the effects of the cooling rate on the warpage deformation and the residual stresses of the integrated T-shaped composite structure are studied. Finally, the relationships between the different curing strategies and the corresponding residual stresses are studied, and it shows that the Outside-to-Inside curing strategy will develop the smallest residual stresses for the integrated T-shaped composite structures.     

Non-linear stress analysis of composite layered plates and shells using a mesh reduction method

This paper represents an attempt for reducing the dimensionality of the finite element method, based on applying a new concept to the finite strip method. Mindlin's plate-bending theory has been employed for the derivation of an efficient element for buckling and stress analysis of folded and stiffened plates made of composite layered materials. The plate midplane is to be discretized in one direction in terms of this new element, leading to a simple mesh reduced by one dimension as compared with standard finite element meshes. The interpolation in the other direction is achieved by employing independently a smooth polynomial over the plate width. An efficient modular programming package based on the new element has been designed, and a number of case studies have been employed for its validation. The package has proved to be an efficient tool for numerical modelling of trapezoidal and stiffened plates, and cylindrical shells, made of isotropic or composite layered materials.     

Analytical solution and finite element approach to the 3D re-entrant structures of auxetic materials

One of the methods in understanding the real microstructure of auxetic material is by separating it into several simplified structures that have distinct mechanisms. Among those simplified structures are chiral and re-entrant structures. This paper adapts a 2D re-entrant structure for a 3D auxetic structure. A re-entrant structure is chosen due to its fundamental characteristics underlying the main characteristics of auxetic materials. The energy methods of solid mechanics along with numerical methods are used to study the fundamental concept of auxetic materials. Understanding the characteristics of the re-entrant structure will lead to the better comprehension of other structures of auxetic materials, which will eventually contribute to the advance of research in this new class of materials.     

Numerical and exact models for free vibration analysis of cylindrical and spherical shell panels

The present paper shows a comparison between classical two-dimensional (2D) and three-dimensional (3D) finite elements (FEs), classical and refined 2D generalized differential quadrature (GDQ) methods and an exact three-dimensional solution. A free vibration analysis of one-layered and multilayered isotropic, composite and sandwich cylindrical and spherical shell panels is made. Low and high order frequencies are analyzed for thick and thin simply supported structures. Vibration modes are investigated to make a comparison between results obtained via the FE and GDQ methods (numerical solutions) and those obtained by means of the exact three-dimensional solution. The 3D exact solution is based on the differential equations of equilibrium written in general orthogonal curvilinear coordinates. This exact method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structure. The geometry for shells is considered without any simplifications. The 3D and 2D finite element results are obtained by means of a well-known commercial FE code. Classical and refined 2D GDQ models are based on a generalized unified approach which considers both equivalent single layer and layer-wise theories. The differences between 2D and 3D FE solutions, classical and refined 2D GDQ models and 3D exact solutions depend on several parameters. These include the considered mode, the order of frequency, the thickness ratio of the structure, the geometry, the embedded material and the lamination sequence.     

Cross-property relations for two-phase planar composites

The overall property of a composite material is dictated by parameters that characterize its microstructure. Theoretically, cross-links between different physical properties of the same material have been established by eliminating all or partially these microstructural parameters. Practically, such a correlation may be used to determine one property from another once the latter is measured or calculated: the success of this approach depends on whether the correlation is insensitive to the detailed material microstructure. In the present paper, cross-property relations for planar two-phase composites are examined using both analytical approaches and the digital-based finite element method. Both isotropic and transversely isotropic two-phase planar composites are studied. Focus is placed on studying how the microstructure (e.g., shape, size, distribution and volume fraction of inclusions) affects the correlation between two different overall properties of the composite. At a fixed volume fraction, questions on whether the correlation is one-to-one and whether it is sensitive to large material contrast (e.g., voids or rigid inclusions) or how the inclusions are distributed in the matrix will be answered.     

Some aspects of numerical simulation for Lamb wave propagation in composite laminates

Some aspects of numerical simulation of Lamb wave propagation in composite laminates using the finite element models with explicit dynamic analysis are addressed in this study. To correctly and efficiently describe the guided-wave excited/received by piezoelectric actuators/sensors, effective models of surface-bounded flat PZT disks based on effective force, moment and displacement are developed. Different finite element models for Lamb wave excitation, collection and propagation in isotropic plate and quasi-isotropic laminated composite are evaluated using continuum elements (3-D solid element) and structural elements (3-D shell element), to elaborate the validity and versatility of the proposed actuator/sensor models.     

High performance 3D-analysis of thermo-mechanically loaded composite structures

This paper considers the analysis of composite structures, simultaneously loaded by mechanical and thermal loads, as often found in aerospace applications. Typically a thermal analysis providing the temperature field must precede the stress analysis, which has to account for thermal as well as for additional mechanical loads. Presently, thermal analyses are mostly carried out by finite difference methods or by 3D finite elements, whereas the stress analysis is usually performed by the use of shell elements. Thus, the temperature field has to be transferred from a finite difference or 3D finite element model to a shell finite element model. This process often requires lots of manual user interaction and can get very time consuming. The paper suggests an integrated analysis process which uses a shell finite element model throughout. Thermal lamination theories and related finite elements developed by the first author are used for the 3D thermal analysis. This leads to a reduction of the computing time by two orders of magnitude as compared to 3D finite elements whereas the accuracy of the results is nearly unaffected. The stress analysis is carried out using the same geometry model but with different mesh density. Interpolation between the different meshes can be accomplished automatically since both discretizations are defined on the same geometry. Standard shell elements based on the First order shear deformation theory (FSDT) provide the three in-plane stress components. A novel postprocessing scheme is adopted for determining all transverse stress components from the in-plane stresses and the temperature field. The postprocessing methodology is based on the extended 2D-method which utilizes the material law for transverse shear and the 3D equilibrium conditions. It is computationally very efficient and can be applied in conjunction with any standard finite element package. The interaction of thermal and stress analysis is demonstrated by the example of a composite wing box for a future large airliner.     

Shape optimization of bonded patch to cylindrical shell structures

Adhesive bonding has been widely used to join or repair metallic and composite structural components to achieve or restore their designated structural stiffness and strengths. However, current analysis methods and empirical databases for composite bonded patch repairs or joints are limited to flat structures, and there exists a very limited knowledge on the effect of curvature on the performance and durability of composite bonded joints and repairs. Recently, a novel finite element formulation was presented for developing adhesive elements for conducting 2.5‐D simplified stress analysis of bonded repairs to curved structures. This paper presents the work on optimal shape design of a bonded curved composite patch using the newly developed adhesive element. The Sequential Linear Programming (SLP) method is employed as the optimization algorithm in conjunction with a fully implemented mesh generation algorithm into which new features have been incorporated. The objective of shape optimization is to minimize the maximum stress in the entire adhesive layer to ensure that the bonded patch effectively works together with the parent structure in service. Several different objective functions, related to possible failure mechanisms of the adhesive layer, are proposed to optimize the shape of a bonded patch. Copyright © 2003 John Wiley & Sons, Ltd.     

Cracks and re-entrant corners in functionally graded materials

Functionally graded materials (FGMs) are special composites in which the volume fractions of constituent materials vary gradually, giving continuously graded mechanical properties. The aim of this paper is the evaluation of the strength of structures composed by FGMs incorporating re-entrant corners - tending to the more common crack for vanishing corner angle. The end result is useful in engineering applications predicting the strength of the element corresponding to the unstable brittle crack propagation in such innovative materials. To show the general validity of the method, heterogeneous plates under tension and beam under bending containing re-entrant corners and by varying corner angle, depth and grading of the FGM are considered. Ad hoc performed numerical finite element simulations, by using the FRANC2D code, agree with the theoretical predictions.     

Isogeometric analysis for flexural behavior of composite plates considering large deformation with small rotations

A large deformation theory, so-called Green strains with small rotations, is proposed and employed for flexural analysis of composite plates. Isogeometric analysis cooperated with first-order shear deformation theory is used to derive finite element models. Strain-displacement relations in the sense of von-Kármán theory and the proposed theory are formulated. Shear locking phenomenon is avoided by using reduced integration technique. Newton–Raphson method is employed for nonlinear analysis procedure. Numerical examples, including isotropic and laminated composite plates under different boundary conditions, are investigated. The results have been verified with those available in the literature and show the advantages of the proposed strain theory.     

A circular inclusion in a finite domain I. The Dirichlet-Eshelby problem

Summary This is the first paper in a series concerned with the precise characterization of the elastic fields due to inclusions embedded in a finite elastic medium. A novel solution procedure has been developed to systematically solve a type of Fredholm integral equations based on symmetry, self-similarity, and invariant group arguments. In this paper, we consider a two-dimensional (2D) circular inclusion within a finite, circular representative volume element (RVE). The RVE is considered isotropic, linear elastic and is subjected to a displacement (Dirichlet) boundary condition. Starting from the 2D plane strain Navier equation and by using our new solution technique, we obtain the exact disturbance displacement and strain fields due to a prescribed constant eigenstrain field within the inclusion. The solution is characterized by the so-called Dirichlet-Eshelby tensor, which is provided in closed form for both the exterior and interior region of the inclusion. Some immediate applications of the Dirichlet-Eshelby tensor are discussed briefly.     

Influence of rotation on vibration characteristics of thick composite disks

Abstract

Thick composite disks are utilized in fast-rotating machines, including turbine disks and flywheels. Dynamic equations of motion for a rotating composite disk have been formulated in a polar coordinate system using Hamilton’s principle, and numerical analysis has been performed by finite element interpolation. The natural frequencies of isotropic and laminated composite disks have been obtained when the rotational speed changes. The effects of transverse shear and rotary inertia on the vibration characteristics of rotating disks have also been investigated.     

Modeling of inclusions with interphases in heterogeneous material using the infinite element method

A two-dimensional heterogeneous infinite element method (HIEM) for modeling heterogeneous materials, like imbedded inclusions with surrounding interphases, is proposed in this paper. The special element, called heterogeneous infinite element (HIE), was formulated based on the conventional finite element method (FEM) using the similarity stiffness property and matrix condensing operations. An HIE-FE coupling scheme was also developed and implemented using the commercial software ABAQUS to conduct a complete elastostatic analysis.

The proposed approach was first validated so that heterogeneous material containing circular inclusions can be studied. The displacement and stress distribution around the inclusions were accurately captured. The approach was then applied to analyze the effective modulus of the single-cell and 2 × 2-cell square models with the presence of interphases. The effects of varying the modulus and thickness of the interphases were also examined. Finally, the influences of the shape and orientation of the inclusions are investigated. Results show that different arrangements in the model can have marked influences on the evaluation of the effective elastic modulus for periodic fiber-reinforced composites.     

Towards the design of sandwich panel composites with enhanced mechanical and thermal properties by variation of the in-plane Poisson's ratios

The finite element (FE) method has been used to study the mechanical and thermal properties of both conventional and re-entrant (i.e. negative Poisson's ratio) honeycombs, which may be used as the cores of sandwich panel composites. Failure of the honeycomb structures was simulated using a crack propagation method developed in-house. The cell-wall stress build up in the conventional honeycomb was calculated to be significantly reduced relative to the re-entrant honeycomb under (2D) hydrostatic loading, implying that the conventional core will undergo significantly less internal damage than the re-entrant core. Conversely, the re-entrant honeycomb performs better than the conventional honeycomb under thermal loading conditions. The size and pathway of the crack formed during the simulation is dependent on the failure stress distribution used in the crack propagation routine.