Concentric Cylinder Model Research Articles

Multi-Objective Robust Design Optimization for Crashworthiness Enhancement of Hybrid 2D Triaxially Braided Composite Tube Using Evolutionary Algorithms.

An innovative optimal design framework is developed aiming at enhancing the crashworthiness while ensuring the lightweight design of a hybrid two-dimensional triaxial braided composite (2DTBC) tube, drawing insights from the mesostructure of the composite material. To achieve these goals, we first compile the essential mechanical properties of the 2DTBC using a concentric cylinder model (CCM) and an analytical laminate model. Subsequently, a kriging surrogate model to elucidate the intricate relationship between design variables and macroscopic crashworthiness is developed and validated. Finally, employing multi-objective evolutionary optimization, we identify Pareto optimal solutions, highlighting that reducing the total fiber volume and increasing the glass fiber content in the total fiber volume are crucial for optimal crashworthiness and the lightweight design of the hybrid 2DTBC tube. By integrating advanced predictive modeling techniques with multi-objective evolutionary optimization, the proposed approach not only sheds light on the fundamental principles governing the crashworthiness of hybrid 2DTBC but also provides valuable insights for the design of robust and lightweight composite structures.

Multi Scale Modelling of the Hygro-Mechanical Behavior of Rhecktophyllum Camerunense Vegatable Fibers

The study of rhecktophyllum camerunense (RC) fibers as reinforcement of polymer matrix begin in 2008 and has already demonstrated their ability to replace the glass fibers. In this paper, the influence of humidity on the mechanical behavior of plant fiber is studied and a multiscale model is proposed. The moisture absorption of RC fibers is studied through a multi concentric cylinder model developed based on the work of Marklund. Using mechanical properties of the three main components of natural fibers; cellulose, hemicelluloses and lignines, the mechanical properties and hygroscopic coefficients of layers S1, S2 and S3 of RC fiber are calculated following the relative humidities of 23%, 54% and 75%. The results lead to the conclusion that there is an influence of relative humidity on the mechanical properties whether at the microscopic level of constituents or the mesoscopic scale of layers and the macroscopic scale of RC fiber structure. That influence is negative bacause it drops the mechanical properties of the fiber.

Closed-form asymptotic micromechanics model of fiber reinforced polymer and metal matrix composites

This work presents an analytical asymptotically-correct micromechanics model that helps to predict the effective material properties of a unidirectional composite material. The conventional and numerical approaches estimate the homogenized material properties of composites for their defined component volume fractions, their constituent properties and configurational geometry. Presently these approaches are based on kinematic assumptions such as having displacement or stress components vary through the cross section for beam like structures or through the thickness for plate like structures according to certain predefined functions that doesn’t always logically follow the 3D analysis. In the present formulation, the micromechanics model is developed by accommodating all possible deformations without assuming the displacement function or stress components. These are derived by minimizing the potential energy in terms of generalized strain measures. In the present formulation, Berdichevsky’s Variational Asymptotic Method (VAM) is employed as a mathematical tool to accomplish the homogenization procedure. The Hashin-Rosen model popularly referred to as the Concentric Cylinder Model (CCM) serves as the framework to estimate all the relevant homogenized elastic moduli and coupling coefficients. The derived quantities of interest are obtained as closed form expressions which are functions of the properties of the reinforcement material, the matrix material, their volumes fraction and the geometry of their relative arrangement. These expressions are arrived following the 3D elasticity governing rules by satisfying the interfacial displacement continuity and transverse stress equilibria conditions at the reinforcement and matrix materials interface. The developed expressions for the elastic moduli, shear moduli and Poisson’s ratios of few typical polymer and metal matrix composite materials are validated with some of the relevant results available in the literature.

A new progressive damage model for predicting the tensile behavior of the three-dimensional woven carbon/carbon composites using micromechanics method

A new progressive damage model for the three-dimensional (3 D) woven carbon/carbon (C/C) composites is developed at fiber-matrix level using the micromechanics method. A woven architecture based Representative Volume Element (RVE) model composed of yarns, matrix and yarn/matrix interface is constructed, in which the manufacturing void defects are accounted for. The fiber-matrix concentric cylinder model is employed as a repeating unit cell to represent the yarn, and the matrix micro strain field is computed analytically by the micromechanics method. The maximum stain criteria is utilized for fiber longitudinal breakage, and the Von-Mises criterion is applied for the damage initiation of matrix in both intra-yarns and inter-yarns. The damaged fiber and matrix are modeled by the stiffness degradation method combined with exponential damage evolution equations. The zero thickness cohesive elements governed by bilinear traction-separation constitutive are adopted for yarn/matrix interfacial debonding behavior. The micro progressive damage and failure behavior of the 3 D woven C/C composites subjected to tension is implemented through a developed user-defined material subroutine in commercial software ABAQUS. The predicted stress-strain response is in a good agreement with experimental results. In addition, the effect of manufacturing void defects is also examined by the developed model.

Theoretical "t-z" Curves for Piles in Radially Inhomogeneous Soil

Accurate estimates of pile settlement are key for efficient design of axially loaded piles. Calculations of pile settlement can be simplified using one-dimensional “t-z” curves describing pile settlement at a certain depth as a function of side friction. In the realm of this simplified framework, theoretical “t-z” curves can be derived by substituting an attenuation function describing the variation of shear stress with distance from the pile, into a soil constitutive model relating shear strain to shear stress, then integrating with respect to distance to get the settlement at the pile circumference due to an applied shear stress. A handful of analytical “t-z” curves are available in the literature using the concentric cylinder model to define an attenuation function; these include solutions for linear-elastic, power-law and hyperbolic constitutive models. However, radially homogeneous soil has often been assumed, ignoring the effect of the pile installation resulting in unconservative calculations of pile settlement. This paper considers the installation of the pile, resulting in a radially variable shear modulus distribution in the surrounding soil. A radial inhomogeneity correction factor has been developed for selected constitutive models based on two simplified functions for the soil inhomogeneity, which can be applied to the previously derived “t-z” curves produced assuming radially homogeneous soil. The performance of this simplified method is investigated.

Micromechanical analysis of longitudinal and shear strength of composite laminae

The analysis of several micromechanical models for estimating strength of composite laminae is presented. Longitudinal tensile, compressive and in-plane onset shear strengths are analytically estimated and compared with experimental data available in the literature. The tensile longitudinal load predominantly induces rupture of fibers. On the other hand, the compressive strength is highly influenced by fiber misalignment, inducing a wide range of failure mechanisms. The material response to in-plane shear presents a strong nonlinear response. The estimation of longitudinal tensile strength based on the rule of mixture approaches is compared with 27 experimental data. A novel improvement is proposed assuming that in situ strength of fiber is smaller than fiber strength measured individually due to manufacturing induced damage. For the in-plane shear, 6 models are compared with 10 experimental stress-strain curves, including a novel closed-form expression based on the concentric cylinders model. Finally, for the longitudinal compressive strength, 8 micromechanical models, including a novel model to estimate misalignment effect in fiber crushing, are compared with 61 experimental data are analyzed. Results indicate that the minimal average error for the longitudinal tensile strength is 12.4% while for the compressive strength it is 15%. For the shear strength, the closest prediction depends on the strength definition and the proposed damage onset strength presents the best predictions. In general, the newly proposed models present the best estimations compared with the other models.

Occlusion culling for computer-generated cylindrical holograms based on a horizontal optical-path-limit function.

Recently, great progress has been made in the research of cylindrical holography as a promising technique of 360° display. However, there is an unsolved issue of occlusion culling, which is critical to cylindrical holography and degrades the reconstructed images due to overlapping. To our knowledge, the occlusion issue in cylindrical holography has never been deeply discussed. In this paper, a method of occlusion culling is proposed for computer-generated cylindrical holograms based on a horizontal optical-path-limit function. In cylindrical diffraction, the propagation characteristics of light waves can be described by the point spread function, which is mainly obtained by analyzing the meaning of the obliquity factor in the concentric cylinder model. Different from the planar diffraction, the diffraction area of each source point is limited within the tangents in cylindrical diffraction. Therefore, a horizontal optical path limit function that acts directly on the point spread function for occlusion culling is established. Besides, the proposed method can be applied to the three-dimensional object by using the layer-oriented method. Moreover, the effectiveness of the proposed occlusion culling method is verified by the numerical simulation results and error analysis of the reconstructed images.

Slit Aspect Ratio Effect on Flow Instability and Heat Transfer Characteristics of Wavy Vortex Flow

The slit aspect ratio effect on the flow distribution, shear stress at the cylinder and heat transfer characteristics of wavy vortex flow under variable conditions was investigated by changing the rotating Reynolds number of the inner cylinder and temperature gradient between the inner and outer cylinder walls. The accuracy of numerical simulation was validated by comparing the simulation results with the experimental results. The flow field distribution in the concentric cylinder models with four slit aspect ratios was studied. The results of the wavy vortex flow indicated that the slit depth has a remarkable impact on the heat transfer process of the flow in the annulus. It can be found that the wall shear stress at the inner cylinder experiences a significant decrease with slit depth increasing. The wall shear stress at the inner cylinder of model h* = 0.75 was the largest among four models. Furthermore, jet-like flow and heat transfer enhancement became stronger as shear stress increased. The model with 0.75 slit aspect ratio had the largest heat transfer augmentation among four models.

Thermal and diffusion induced stresses in a structural battery under galvanostatic cycling

When charging or discharging a structural battery composite heat will be generated and the active electrode materials will expand or shrink, inducing internal stresses within the material. These stresses may cause mechanical and/or electrical failure. It is therefore crucial to be able to predict the stress state when evaluating the performance of the material. In this paper, a semi-analytical framework to predict the thermal and diffusion induced stresses in a structural battery under galvanostatic cycling is presented. The proposed model is a concentric cylinder (CC) model coupled with an axisymmetric diffusion model and a one-dimensional heat generation model. The present study shows that the heat generated during electrochemical cycling must be accounted for when evaluating the internal stress state in structural battery composites. Furthermore, the results show that the charge/discharge current, lamina dimensions and residual stresses have significant effect on the internal stress state and effective properties of the composite lamina.

Micromechanics-based predictions of effective properties of a 1-3 piezocomposite reinforced with hollow piezoelectric fibers

Presented is a development of models for predicting the effective properties of a piezocomposite reinforced with hollow piezoelectric fibers. The models are established based on micromechanics of representative volume element so-called modified concentric cylinders model. Predicted are five effective elastic constants, two effective piezoelectric coefficients, one effective dielectric permittivity, and two thermal expansion coefficients. Numerical results of a chosen material system are discussed. Comparisons with finite-element method show very good agreements. The predicted effective properties of the piezocomposite with hollow fibers provide the enhancement in several performance parameters up to three times as high as those with solid piezoelectric fibers.

Coefficients of thermal expansion of unidirectional fiber-reinforced composites using unit-cell model

Coefficients of thermal expansion of some uniaxially fiber-reinforced composites have been evaluated using three-phase unit-cell model. Results have been compared with the values predicted by two other models based on composite cylinders assembly (CCA), and also with some earlier reported experimental values. An extension of the two-phase unit-cell model has also been presented for the evaluation of thermal expansion coefficients of three-phase composites. The formulation has been used to evaluate the overall coefficients of thermal expansion of AS-graphite/epoxy system with a low modulus coating on the fibers. The results have been compared with the results obtained from the Sutcu's recursive concentric cylinders model for composites containing coated fibers. From the comparison of results of the unit-cell models (both, two-phase and three-phase) with the results obtained from some other models available in the literature, it is concluded that the overall thermal properties of fiber-reinforced composites evaluated by the unit-cell model can be used as effectively as by any other model.

A mixed-form solution to the macroscopic elastic properties of 2D triaxially braided composites based on a concentric cylinder model and the rule of mixture

Understanding the elastic properties of 2D triaxially braided composites (2DTBCs) is fundamental for further analysis and design of structural components made from 2DTBCs. Based on a concentric cylinder model (CCM) and the rule of mixture (RoM), we reformulated the global stiffness of 2DTBCs for the anisotropic carbon fiber reinforcement to replace the currently available formulations for the isotropic glass fiber reinforcement with a replacement scheme. First, the global stiffness calculated from CCM, Quek's model and Shokrieh's model was compared for clarification. It was found that Shokrieh's model had the relatively worse performance under the same conditions. Second, the performances of Shokrieh's model, CCM, Quek's model and CCM+RoM (Reuss-type and Voigt-type) were compared using available experiments under various braiding configurations and our experiments on the hybrid carbon/glass fiber reinforced 2DTBCs, which revealed that Quek's model and CCM+RoM (Reuss-type) could yield equivalently great results, and CCM+RoM (Reuss-type) performed even better in some cases.

Effect of aluminum carbide interphase on the thermomechanical behavior of carbon nanotube/aluminum nanocomposites

The objective of this work is to investigate the coefficient of thermal expansion of carbon nanotube reinforced aluminum matrix nanocomposites in which aluminum carbide (Al4C3) interphase formed due to chemical interaction between the carbon nanotube and aluminum matrix is included. To this end, the micromechanical finite element method along with a representative volume element, which incorporates, carbon nanotube, interphase, and aluminum matrix is employed. The emphasis is mainly placed on the effect of Al4C3 interphase on the coefficient of thermal expansion of aluminum nanocomposites with random microstructures. The effects of interphase thickness, carbon nanotube diameter, and volume fraction on the thermomechanical response of aluminum nanocomposite are discussed. The results reveal that the effect of Al4C3 interphase on the coefficient of thermal expansion of the aluminum nanocomposites becomes more significant with (i) increasing the coefficient of thermal expansion volume fraction, (ii) decreasing the coefficient of thermal expansion diameter, and (iii) increasing the interphase thickness. It is clearly observed that the coefficient of thermal expansion varies nonlinearly with the carbon nanotube diameter; however, it decreases linearly as the carbon nanotube volume fraction increases. Furthermore, the axial and transverse coefficient of thermal expansions of aligned continuous and discontinuous carbon nanotube-reinforced aluminum nanocomposites with Al4C3 interphase are predicted. Also, the presented finite element method results are compared with the available experiment in the literature, rule of mixture, and concentric cylinder model results.

An analytical method for predicting the effective transverse thermal conductivity of nano coated fiber composites

A four-phase concentric cylinder model with interface effect is proposed. Based on the model and surface/interface theory, a generalized self-consistent method is developed for predicting the effective transverse thermal conductivity of nano coated fiber composites. An analytical solution is obtained for effective thermal conductivity by applying complex elastic theory. Comparisons with the finite element analysis (FEA) and other available theoretical methods show the efficiency and the accuracy of the present method. Numerical results show the dependence of the effective thermal conductivity of the nano composites when the size of fiber and coating are on the order of nanometer. The effects of the interface thermal constant and the coating thermal conductivity on the effective thermal conductivity are discussed. The present solutions are useful to the theoretical research and engineering applications of the nano coated fiber composites.

On the calculation of the macroscopic stiffness of 2D triaxially braided composites

The elastic property of 2D triaxially braided composites (2DTBC) is of interest. This work proposes to formulate the global stiffness of 2DTBC for anisotropic fibre reinforcement based on concentric cylinder model (CCM). The results of the global stiffness from CCM, Quek's model and Shokrieh's model are compared and the usage of each model is clarified. It is found that Shokrieh's model predicts less agreeable result with experiment due to the improper calculation of the local stiffness. The results of CCM and Quek's model are consistent and either one is recommended for use in practical situations.

STESS: Subway thermal environment simulation software

The ongoing city developments in China have resulted in the expansion of the city subway system as well. To provide design and operation guidance for the control system of the environment of subway stations and tunnels, Tsinghua University (Beijing, China) has undertaken a multiyear study of the environment and developed Subway Environment Simulation Software (STESS).The software can simulate the dynamic thermal environment in subways under different environmental control system. It is an effective auxiliary tool for design, operational decisions as well as economic analysis. Compared to Subway Environment Simulation (SES), STESS improves the airflow and underground unsteady heat transfer algorithm. Firstly, STESS adopts MMKP method instead of the four-step Runge-Kutta used in SES to solve unsteady flow to accelerate the convergence. Secondly, two-dimensional mode is used in STESS other than concentric cylinder model in the heat transfer algorithm to adapt to heterogeneous underground environment. And lastly, this software uses the Eigenvalue method to achieve the dynamic simulation of the heat transfer process. Tsinghua University also organized field tests in Beijing and Shanghai and verified the accuracy of STESS. This paper introduces the development history, technical features, program structure and main functions of STESS and presents the experimental validation performed on the software.

$$\varvec{N}$$-Layer concentric cylinder model (NCYL): an extended micromechanics-based multiscale model for nonlinear composites

A validated multi-scale computational mechanics framework for progressive failure modeling of composite structures is developed. Zhang and Waas (Acta Mech 225(4–5):1391–1417, 2014) proposed a micromechanics-based two-scale multiscale model which is able to predict the nonlinear response of a composite. Their proposed micromechanics analysis uses the analytical solutions derived from the concentric cylinder model along with the generalized self-consistent model to find the effective properties of the unidirectional fiber reinforced composites, which are dependent on constituent level fiber–matrix mechanical properties and fiber volume fraction. In this model, the composite material is represented by an inner fiber core and an outer matrix annulus. It should be noted that the 2-CYL fiber–matrix concentric cylinder micromechanics model can be extended to a concentric fiber and any number of \((N-1)\) matrix layers in general, keeping the volume fraction constant, hence called the N-cylinder model (NCYL), which can analytically calculate the strain and stress field within the fiber and matrix cylinders for a given applied remote composite strain field, acting on the outer boundary of the matrix cylinder. The spatial variation of strain and stress fields within the cylinder are the key determinants for progressive damage and failure analysis of composite structures and hence, they need to be predicted accurately. The advantage of the NCYL concentric cylinder model is that the matrix strain and stress fields can be found in a discrete manner for each layer and the evolution of damage can be localized at a particular layer of matrix. These results can be used at the sub-scale in a multi-scale analysis to calculate the effective nonlinear composite response at a global scale. This work is based on a full analytical solution, and hence, it delivers a distinct computational advantage in composite failure analysis. That is, high fidelity and computational efficiency are gained at the same time.

Damage and failure modelling of hybrid three-dimensional textile composites: a mesh objective multi-scale approach

This paper is concerned with predicting the progressive damage and failure of multi-layered hybrid textile composites subjected to uniaxial tensile loading, using a novel two-scale computational mechanics framework. These composites include three-dimensional woven textile composites (3DWTCs) with glass, carbon and Kevlar fibre tows. Progressive damage and failure of 3DWTCs at different length scales are captured in the present model by using a macroscale finite-element (FE) analysis at the representative unit cell (RUC) level, while a closed-form micromechanics analysis is implemented simultaneously at the subscale level using material properties of the constituents (fibre and matrix) as input. The N-layers concentric cylinder (NCYL) model (Zhang and Waas 2014 Acta Mech. 225, 1391-1417; Patel et al. submitted Acta Mech.) to compute local stress, srain and displacement fields in the fibre and matrix is used at the subscale. The 2-CYL fibre-matrix concentric cylinder model is extended to fibre and (N-1) matrix layers, keeping the volume fraction constant, and hence is called the NCYL model where the matrix damage can be captured locally within each discrete layer of the matrix volume. The influence of matrix microdamage at the subscale causes progressive degradation of fibre tow stiffness and matrix stiffness at the macroscale. The global RUC stiffness matrix remains positive definite, until the strain softening response resulting from different failure modes (such as fibre tow breakage, tow splitting in the transverse direction due to matrix cracking inside tow and surrounding matrix tensile failure outside of fibre tows) are initiated. At this stage, the macroscopic post-peak softening response is modelled using the mesh objective smeared crack approach (Rots et al. 1985 HERON 30, 1-48; Heinrich and Waas 2012 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, HI, 23-26 April 2012 AIAA 2012-1537). Manufacturing-induced geometric imperfections are included in the simulation, where the FE mesh of the unit cell is generated directly from micro-computed tomography (MCT) real data using a code Simpleware Results from multi-scale analysis for both an idealized perfect geometry and one that includes geometric imperfections are compared with experimental results (Pankow et al. 2012 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, HI, 23-26 April 2012 AIAA 2012-1572). This article is part of the themed issue 'Multiscale modelling of the structural integrity of composite materials'.

A Novel Field-Circuit FEM Modeling and Channel Gain Estimation for Galvanic Coupling Real IBC Measurements.

Existing research on human channel modeling of galvanic coupling intra-body communication (IBC) is primarily focused on the human body itself. Although galvanic coupling IBC is less disturbed by external influences during signal transmission, there are inevitable factors in real measurement scenarios such as the parasitic impedance of electrodes, impedance matching of the transceiver, etc. which might lead to deviations between the human model and the in vivo measurements. This paper proposes a field-circuit finite element method (FEM) model of galvanic coupling IBC in a real measurement environment to estimate the human channel gain. First an anisotropic concentric cylinder model of the electric field intra-body communication for human limbs was developed based on the galvanic method. Then the electric field model was combined with several impedance elements, which were equivalent in terms of parasitic impedance of the electrodes, input and output impedance of the transceiver, establishing a field-circuit FEM model. The results indicated that a circuit module equivalent to external factors can be added to the field-circuit model, which makes this model more complete, and the estimations based on the proposed field-circuit are in better agreement with the corresponding measurement results.

Steady-state energy release rate for fiber/matrix interface debond growth in unidirectional composites

Analytical closed form solution is derived for energy release rate due to steady-state debond growth along a broken fiber in unidirectional composite. The problem is represented by a three concentric cylinder model, where the broken and partially debonded fiber is embedded in resin and this unit is surrounded by homogenized effective composite. Parametric analysis shows that parameters in the very simple quadratic expression for energy release rate dependence on temperature change and mechanical strain are rather insensitive with respect to changes in constituent elastic properties and fiber content. The importance to have a large outer radius of the effective composite phase in the concentric cylinder model is demonstrated.