Periodic Displacement Boundary Conditions Research Articles

Research into the thermal expansion behavior of spread tow woven pierced carbon/carbon composites at high temperature

Textile-reinforced carbon/carbon composites are frequently used for thermal safety due to their superb thermophysical properties. The coefficient of thermal expansion (CTE) is a fundamental performance metric of spread tow woven pierced carbon/carbon composites (STWPs). The multiscale representative volume element (RVE) models constructed as part of this work were used for investigating the CTEs of STWPs at high temperature. The temperature displacement coupling analysis step was established to predict the CTEs of STWPs considering the high-temperature environment. In addition, periodic displacement boundary conditions were adopted as node constraints with the spatial periodicity of RVE models. The influences of pore positions and configurations on the CTEs of the matrix were considered through two different matrix RVE model. The CTEs of the spread tow (ST) and fiber rod were computed using two microscale RVE models with an unequal fiber volume fraction. A novel modeling strategy for the mesoscale RVE model was put forth in order to calculate the CTEs of the STWPs due to the remarkable lightness and thinness of the ST. Only 9.64% and 7.92% errors in the in-plane and out-of-plane directions were found when the experimental findings were compared to those predicted by numerical models, demonstrating the accuracy and effectiveness of the multiscale RVE models. Moreover, the impacts of areal density of ST woven fabric on the CTEs of STWPs were discussed. The fundings demonstrated that the in-plane and out-of-plane CTEs both decreased as the areal density increased.

Numerical investigation on tensile behavior of three-dimensional six-directional braided composites

Based on the mesostructure, a parametric finite element (FE) model of the three-dimensional six-directional (3D6d) braided composites was developed considering the real cross-sectional shape of the yarn and its contact relationship. The 3D Hashin criterion and maximum stress criterion were used for failure determination and periodic displacement boundary conditions were imposed on the model to numerically simulate the initiation, propagation and final failure of yarns and matrix damage. The FE model accurately predicts the longitudinal tensile strength of 3D6d braided composites and simulates the progressive damage process associated with the stress-strain behavior. The longitudinal mechanical properties of the 3D6d braided composites decrease with increasing braiding angle, while increasing the fiber volume fraction leads to enhancement of these properties. Furthermore, the change rate of longitudinal mechanical properties with braiding angle is relatively stable, and the influence of fiber volume fraction on longitudinal properties decreases with the increase of braiding angle. For the damage mode, the increase of braiding angle makes the damage of braiding and sixth-directional yarns gradually change from single direction to multiple directions, and the decrease of fiber volume fraction makes the damage of braiding and fifth-directional yarns at the peak stress more serious.

Effective in-plane stiffness of unidirectional periodic nanoporous materials with surface elasticity

In this paper, the in-plane effective elastic properties of a porous material with periodic nanoscale holes of arbitrary shapes are investigated. A square representative unit cell (RUC) with a central hole is analysed for the original structure. On the edges of the RUC, proper periodic displacement boundary conditions are imposed. On the surfaces of the holes, the stress boundary condition is formulated through the Gurtin–Murdoch surface elasticity model. The problem is finally solved via the complex variable techniques, like superposition principle, conformal mapping, series expansion and collocation methods. Numerical examples for two common shapes, circle and square, of holes are presented. The results show that the in-plane effective properties of the structure are significantly influenced by the volume fraction (VF), size, shape of the holes, along with the surface elasticity. Specifically, a decrease in the VF or an increase in the size of the holes can lead to an increase in most of the effective moduli of the structure; a structure with circular holes has overall larger effective moduli than a structure with square holes; the surface elasticity can play a dominant role for certain effective moduli.

Predictions of transverse thermal conductivities for plain weave ceramic matrix composites under in-plane loading

A coupled temperature-displacement steady-state analysis of plain weave ceramic matrix composites along through-thickness direction was reported in this paper. Based on the formulation of Binary Model, a meso-scale 2 × 2 unit cell model of plain weave composites was established. The periodic displacement boundary conditions and through-thickness temperature gradient were imposed. The non-linear strain-dependent thermal properties of constituent materials have been discretised by multi-linear curves, which have been implemented by the user defined subroutine, USDFLD of the finite element package, Abaqus. The degradation of the composite through-thickness thermal conductivity with uni-axial straining has been predicted. The predictions considering tow waviness have a good agreement with experimental results. The analysis indicates that the degradation of through-thickness thermal conductivities is due to the combination of shear failure and wake debonding mechanisms. The matrix/medium played an important role in the through-thickness heat flow of plain weave ceramic matrix composites.

Determination of thermo-elastic parameters for dynamical modeling of 2.5D C/SiC braided composites

An approach on determining elastic parameters and Coefficient of thermal expansion (CTE) of a 2.5-dimensional (2.5D) braided composites is proposed in this paper, by adopting mesoscopic mechanics integrated Finite element (FE) modeling. According to the geometric features of meso-structure, Representative volume cell (RVC) models of composite for predicting thermo-elastic parameters are established. On the basis of the models, homogenized parameter prediction is carried out in three steps: Firstly, equivalent elastic properties is predicted subject to periodic displacement boundary conditions; secondly, the equivalent thermal modulus is determined by using the periodic non-adiabatic temperature boundary conditions; thirdly, using the obtained elastic parameters and thermal modulus to calculate the equivalent coefficient of thermal expansion. A multiscale finite element analysis is conducted: The thermo-elastic parameters of yarn is calculated using the RVC model; subsequently, the equivalent parameters of the yarn are substituted into the RVC of 2.5D braided C/SiC composites, to predict the thermo-elastic parameters. Results indicate that the CTE determined by homogenized parameter prediction of 2.5D C/SiC composites shows good agreements with the experimental results. At last, the refined FE model and the equivalent homogeneous model are employed to verify the effectiveness of the predicted parameters in terms of effective modeling. After the comparative analysis on thermal modal data between refined model and equivalent model, the acquired results demonstrate the effectiveness of the proposed method in determining thermo-elastic parameters.

Theoretical aspects of selecting repeated unit cell model in micromechanical analysis using displacement-based finite element method

Repeated Unit Cell (RUC) is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element (DFE) method, and merely applying Periodic Displacement Boundary Conditions (PDBCs) to RUC is almost a standard practice to conduct such analysis. Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions (PTBCs, also known as traction continuity conditions) are guaranteed and whether the solution is independent of selection of RUCs. This paper presents the theoretical aspects to tackle these questions, which unify the strong form, weak form and DFE method of the micromechanical problem together. Specifically, the solution’s independence of selection of RUCs is dealt with on the strong form side, PTBCs are derived from the weak form as natural boundary conditions, and the validity of merely applying PDBCs in micromechanical Finite Element (FE) analysis is proved by referring to its intrinsic connection to the strong form and weak form. Key points in the theoretical aspects are demonstrated by illustrative examples, and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for UniDirectional (UD) fiber-reinforced composites.

Effect of the Orientation of Hexagonal Fibers on the Effective Elastic Properties of Unidirectional Composites

AbstractExisting studies reveal that the shape corners of hexagonal fiber affect the degree of constraint on the matrix material. However, none of these studies included the effect of orientation of hexagonal fibers. In this study, a computational micromechanics model of oriented hexagonal fibers in periodic unidirectional composite materials is established for the determination of effective orthotropic elastic properties of the composite. In the present numerical modeling, the representative unit composite cell including the matrix material and the single oriented hexagonal fiber or random oriented hexagonal fibers is solved by micro-scale finite element analysis with different stress loads and periodic displacement boundary conditions, which are applied along the cell boundary to meet the requirement of straight-line constraint during deformation of the cell. Subsequently, the effective elastic properties of the composite are evaluated for periodic regular packing and random packing using the homogenization approach for investigating the influence of unified orientation and random orientation of the hexagonal fibers on the overall elastic properties of the fiber-reinforced composites. The numerical results are verified by comparing with other available results.

Micromechanical properties of unidirectional composites filled with single and clustered shaped fibers

Abstract Computational micromechanics provides an efficient strategy to optimize composite materials by addressing the effect of different material and geometric parameters involved. In the present paper, the effective transverse elastic properties for periodic composite materials reinforced with single and clustered polygonal fibers are evaluated using the micromechanical finite element formulation subject to periodic displacement boundary conditions. The cross-sectional shapes of polygonal fibers are assumed to be triangular, square, pentagonal, hexagonal, octagonal, and circular to perform comprehensive investigation. By applying a periodic displacement constraint along the boundary of the representative unit cell of the composite to meet the requirement of straight-line constraint during the deformation of the unit cell, the computational micromechanical modeling based on homogenization technology is established for evaluating the effects of fiber shape and cluster on the overall properties. Subsequently, the micromechanical model is divided into four submodels, which are solved by means of the finite element analysis for determining the traction distributions along the cell boundary. Finally, the effective orthotropic elastic constants of composites are obtained using the solutions of the linear system of equations involving traction integrations to investigate the effects of fiber shape and cluster on the overall properties.

Elastic properties of CNT- and graphene-reinforced nanocomposites using RVE

The present paper is aimed to evaluate and compare the effective elastic properties of CNT- and graphene-based nanocomposites using 3-D nanoscale representative volume element (RVE) based on continuum mechanics using finite element method (FEM). Different periodic displacement boundary conditions are applied to the FEM model of the RVE to evaluate various elastic constants. The effects of the matrix material, the volume fraction and the length of reinforcements on the elastic properties are also studied. Results predicted are validated with the analytical and/or semiempirical results and the available results in the literature. Although all elastic stiffness properties of CNT- and graphene-based nanocomposites are found to be improved compared to the matrix material, but out-of-plane and in-plane stiffness properties are better improved in CNT- and graphene-based nanocomposites, respectively. It is also concluded that long nanofillers (graphene as well as CNT) are more effective in increasing the normal elastic moduli of the resulting nanocomposites as compared to the short length, but the values of shear moduli, except G23 of CNT nanocomposite, of nanocomposites are slightly improved in the case of short length nanofillers (i.e., CNT and graphene).

Numerical predictions of the mechanical properties of NT-ZnOw reinforced composites

A new method to generate a three-dimensional (3D) nanoscale tetrapod-shaped zinc oxide whisker (NT-ZnOw) with spatial random distribution is proposed, and a corresponding program is developed. A whisker-generating program is combined with finite element method to build a 3D finite element model that can predict the mechanical properties of NT-ZnOw/resin composites. A 3D finite-element unit cell is adopted and subjected to periodic displacement boundary conditions to explore the equivalent mechanical properties of the NT-ZnOw/resin composites. A micromechanics finite element model of the NT-ZnOw reinforced composites containing various volume fractions of NT-ZnOw is also developed. Effects of different volume fractions and aspect ratios of the whisker on the stiffness of the composites are investigated. These parameters can be used in the microscopic prediction and analysis to determine the mechanical properties of whisker-reinforced composites with multivariate and random distribution of the whiskers. The numerical and theoretical predictions are in good concordance.

XFEM Modelling of Inelastic Material Behaviour and Interface Failure in Textile-Reinforced Composites

This paper addresses the multiscale simulation of heterogeneous materials. The considered composite materials exhibit a hierarchical material structure with three distinct length scales - micro, meso and macro. This feature of the morphology allows for the application of homogenisation techniques based on a representative volume element (RVE) which is entirely typical for the local, periodic material structure.The heterogeneous material structure in an RVE is modelled by the extended finite element method (XFEM) Suitable material models account for the deformation behaviour of the constituents in the generated RVE models. The combination of XFEM and a cohesive zone model is used to represent discrete failure processes in the local material structure. This multiscale approach is applied to predict the effective material behaviour of fibre reinforced polymers. Using periodic displacement boundary conditions, effective stress-strain curves are computed for glass fibre reinforced polypropylene with unidirectional and woven arrangements of the reinforcing fibres.

Multiscale XFEM‐modelling and simulation of the inelastic material behaviour of textile‐reinforced polymers

AbstractThis paper addresses the multiscale simulation of fibre‐reinforced polymers. The considered composite materials exhibit a hierarchical material structure with three distinct length scales—micro, meso and macro. This feature of the morphology allows for the application of homogenization techniques based on a representative volume element (RVE) that is entirely typical for the local, periodic material structure. The effective macroscopic material behaviour of the composite can be predicted from the properties of the individual constituents and the geometric arrangement of the reinforcing fibres based on the simulation of the material behaviour in the RVE.The heterogeneous material structure in an RVE is modelled by the eXtended finite element method (XFEM). To this, two special element types, called X‐element and 2X‐element, are derived. They can represent one or two material interfaces within the element domain. For an efficient modelling process, an automated model generation procedure that determines the required element types, locates the material interfaces and performs the subdivision of the X‐elements into tetrahedral integration domains has been developed. Problems related to a consistent interface approximation and a continuous displacement field are discussed.In the generated RVE models, a viscoplastic material model accounts for the inelastic material behaviour of the polymeric matrix, whereas the glass‐fibres are assumed to have a linear elastic stress–strain behaviour. Using periodic displacement boundary conditions, effective stress–strain curves are computed for glass‐fibre‐reinforced polypropylene with unidirectional and woven arrangements of the reinforcing fibres. Copyright © 2010 John Wiley & Sons, Ltd.

Periodic three‐dimensional mesh‐generation for Voronoi tessellations with application to cubic crystal aggregates

AbstractWe present a technique for the generation of unstructured periodic spatial discretizations of three–dimensional Voronoi tessellations. These define model microstructures for various polycrystalline aggregates. The elastic properties of cubic crystal aggregates are examined numerically using periodic displacement boundary conditions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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