Equivalent Material Properties Research Articles

A two‐stage pseudo‐inverse approximation method for the identification of viscoelastic structure

This study aims to develop a two‐stage pseudo‐inverse approximation method for the identification of material properties of viscoelastic structures, which is described by the Boltzmann model and is probed by a cantilever probe. First, a first stage pseudo‐inverse method was used to determine the equivalent M, C, and K matrices of a probe from the measured input and output data of a vibration test for the probe only. The equivalent material properties (c, k) of a viscoelastic structure were estimated by a second stage pseudo‐inverse method using a reduced equation of motion for the combined system of probe and test viscoelastic structure. Since the signal processing of noises which connect to the measured data is the key point to influence the final identification results, a digital filter applied to the measured signals under different levels of noise interference is thus discussed in this paper. The numerical simulations and experimental results demonstrate that the identification method based on the two‐stage pseudo‐inverse approximation is feasible.

A wire-woven cellular metal: Part-II, Evaluation by experiments and numerical simulations

Wire-woven bulk Kagome (WBK) is a new truss-type cellular metal fabricated by systematic assembly of helical wires in six directions. In Part-I of this work, analytic solutions for equivalent material properties, such as yield stress and elastic modulus of WBK under compression and shear were derived. The load capacities of a WBK-cored sandwich panel under bending were predicted for various failure modes, and optimal designs of the WBK-cored sandwich panel were determined. In this work, the overall performance of a WBK-cored sandwich panel under shear and bending loads were evaluated in more detail by experiment and finite element (FE) simulation. Using comparisons with our experimental and numerical results, we show that the simple analytic solutions obtained in Part-I gave effective and accurate solutions. Hence, the model optimally designed on the basis of the analytic solutions gave the expected results. Furthermore, the WBK-cored sandwich panel showed excellent performance in terms of load capacity, energy absorption, and deformation stability after the maximum load point.

Identification of Equivalent Material Properties for 3-D Numerical Modeling of Induction Heating of Ferromagnetic Workpieces

This paper presents a methodology to study nonlinear electromagnetic phenomena inside ferromagnetic pieces where eddy currents are driven by an external supply source in the medium frequency range. The proposed methodology takes, as reference, a nonlinear time-harmonic solution of the iron part and then identifies, by means of an optimization procedure, the magnetic permeability values of an equivalent layered linear material which would give the same value of Joule losses of the nonlinear case. This approach has been applied to a test configuration obtaining good results.

균질화 기법을 이용한 딤플 튜브형 인터쿨러의 유한요소해석 및 검증

Three-dimensional finite-element methods(FEM) have been used to analyze the thermal stress of an exhaust gas recirculation(EGR) cooler due to thermal and pressure load. Since efficiency and capability of the heat exchanger are mainly dependent on net heat transferring area of the EGR cooler system, the tube inside the system has a numerous dimples on the surface. Thus for finite element analysis, firstly the dimple-typed tube is modeled as a plain element without the dimple, and then the equivalent thermal conductivities and elastic modulus are calculated. This work describes the numerical homogenization procedure of the dimple-typed tube and verifies the equivalent material properties by comparison of a single unit and the actual full model. Finally, the homogenization scheme presented in this study can be efficiently applied to finite element analyses for the thermal stress and deformation behavior of the EGR cooler system with the dimple-typed tube.

INVESTIGATION ON THE EQUIVALENT MATERIAL PROPERTY OF CARBON REINFORCED ALUMINUM LAMINATES

Fiber metal laminates as one of new hybrid materials with the bonded structure of thin metal sheets and fiber/epoxy layers have been developed for the last three decades. These kinds of materials can provide the characteristics of the excellent fatigue, impact and damage tolerance with a relatively low density. Because metal sheets and fiber/epoxy layers are bonded each other, the bonding between two materials is critical. In this study, the bonding strength is investigated experimentally with respect to surface roughness of metal sheets. The equivalent material properties of carbon reinforced aluminum laminates as the input data in the numerical simulation are also investigated and compared with the experimental result. The application of the equivalent material property to the numerical simulation can provide the high degree of efficiency in the build-up of the finite element model and the numerical simulation.

Stretching-dominated deformation mechanism in a super square carbon nanotube network

Connecting straight carbon nanotube (CNT) arms with different CNT junctions, 2D CNT covalent networks can be theoretically constructed. The equivalent material properties of two kinds of 2D CNT network, the super square and super hexagon, are compared using molecular structure mechanics. Under uniaxial tensile loading in the principle direction, the super square could be regarded as a stretching-dominated network, while the super hexagon as a bending-dominated network. It is found that the super square has a higher stiffness than the super hexagon network. Similar to the super hexagon network, the aspect ratio of the CNT arm plays an important role in the properties of the super square network. Both the in-plane stiffness and Poisson’s ratio of the super square are proportional to the reciprocal of the tube aspect ratio.

On the Homogenization of Multilayered Interconnect for Interfacial Fracture Analysis

The interface crack problem for Cu/low- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> interconnect is considered using global-and-local finite element analysis. In the global analysis the thin film interconnect is represented by a homogenized layer with equivalent material properties. Local model around the interface crack tip is analyzed with displacement boundary condition extracted from the global modeling result to determine the fracture mechanics parameters. It is shown that, for the global-and-local modeling approach, interconnect homogenization using representative volume element (RVE) approach provides accurate prediction on the fracture mechanics parameters for an interface crack under either thermal or mechanical loads, while significant error occurs when the interconnect, even though having thickness less than 1/100 of the whole component thickness, is neglected in the global analysis. The problem of an interface crack between low- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> dielectric and etch-stop thin film in a flip-chip package under thermal excursion is also investigated as an application example of the global-and-local modeling approach.

Torsion of honeycomb FRP sandwich beams with a sinusoidal core configuration

A combined analytical, numerical and experimental investigation of honeycomb fiber-reinforced polymer (HFRP) sandwich beam samples subjected to torsion loads is conducted. The sandwich panel considered in this study has unique sinusoidal core geometry in the plane extending vertically between face laminates, and it has been used primarily as decking systems in highway bridges. Using a homogenization process and mechanics of materials approach, the equivalent core material properties for the honeycomb core geometry are found, and the material properties of face sheets are obtained by micro/macromechanics. Equivalent material properties of the core and face sheets are then used to evaluate effective torsional stiffness properties of HFRP panels. The torsional analysis includes the evaluation of core equivalent in-plane and out-of plane shear properties and panel apparent torsional stiffness properties. Finite element models using layered shell elements are used to correlate with the analytical and experimental results for HFRP beams samples in torsion. Two types of models are presented in the finite element simulation: an actual geometry model, where the core and face sheet geometry are defined by layer shell elements, and an equivalent plate model, for which the equivalent material properties of the core and face sheets are utilized. In order to verify the accuracy of the analytical and numerical predictions, several honeycomb sandwich beam samples with sinusoidal core waves oriented along the longitudinal or transverse or vertical directions and with different face sheet configurations are experimentally tested in torsion. The present analysis and characterization procedures can be used in design applications and optimization of honeycomb structures, and they can also be employed to verify or refine in-plane and out-of-plane shear equivalent material properties for the present and other honeycomb FRP panels.

Numerical derivation of averaged material properties of hollow concrete block masonry

The homogenization technique has been used to derive equivalent material properties of masonry units for many years. However, most previous research work has concentrated on the derivation of equivalent material properties of a solid brick masonry structure. Very few studies have been conducted to investigate the complex mechanical properties of a hollow concrete block masonry unit. In this paper, numerical simulations of laboratory tests are conducted to derive the equivalent material properties of a three-dimensional basic cell of hollow concrete block masonry. A double scalar damage model based on the concept of continuum damage mechanics is applied to modeling the failure of mortar joint and concrete. In the numerical model of the basic cell, the hollow concrete block and mortar with their nonlinear material properties are modeled in detail. By applying various displacement boundaries to the basic cell surfaces to simulate the displacement-controlled laboratory tests, the averaged stress and strain of the basic cell under different stress states are derived numerically. The homogenized or equivalent material properties of the hollow concrete masonry are determined from the averaged stress and strain relations of the basic cell. To check the validity of the derived equivalent material properties, the dynamic response and damage of a hollow concrete masonry panel subjected to airblast loading is modeled with the equivalent material properties or with the distinctive mortar and brick properties. The efficiency and accuracy of using the derived equivalent material properties in numerical modeling of hollow concrete brick masonry are demonstrated.

A hierarchical model for concurrent material and topology optimisation of three-dimensional structures

This paper presents an extension of the hierarchical model for topology optimisation to three-dimensional structures. The problem addressed covers the simultaneous characterisation of the optimal topology of the structure and the optimal design of the cellular material used in its construction. In this study, hierarchical suggests that the optimisation model works at two interconnected levels, the global and local levels identified, respectively, with the structure and its material. The class of cellular materials, defining the material microstructure, is restricted to single scale cellular materials, with the cell geometry locally optimised for the given objective function and constraints. The model uses the asymptotic homogenisation model to obtain the equivalent material properties for the specific local microstructures designed using a SIMP based approach. The necessary optimality conditions for the hierarchical optimal design problem are discussed and approximated numerically by a proper finite element discretisation of the global and local analysis and design problems. Examples to explore and demonstrate the model developed are presented.

Impact analysis of fiber reinforced polymer honeycomb composite sandwich beams

Large scale fiber reinforced polymer (FRP) composite structures have been used in highway bridge and building construction. Recent applications have demonstrated that FRP honeycomb sandwich panels can be effectively and economically applied for both new construction and rehabilitation and replacement of existing structures. This paper is concerned with impact analysis of an as-manufactured FRP honeycomb sandwich system with sinusoidal core geometry in the plane and extending vertically between face laminates. The analyses of the honeycomb structure and components including: (1) constituent materials and ply properties, (2) face laminates and core wall engineering properties, and (3) equivalent core material properties, are first introduced, and these properties for the face laminates and equivalent core are later used in dynamic analysis of sandwich beams. A higher-order impact sandwich beam theory by the authors [Yang MJ, Qiao P. Higher-order impact modeling of sandwich beams with flexible core. Int J Solids Struct 2005;42(20):5460–90] is adopted to carry out the free vibration and impact analyses of the FRP honeycomb sandwich system, from which the full elastic field (e.g., deformation and stress) under impact is predicted. The higher order vibration analysis of the FRP sandwich beams is conducted, and its accuracy is validated with the finite element Eigenvalue analysis using ABAQUS; while the predicted impact responses (e.g., contact force and central deflection) are compared with the finite element simulations by LS-DYNA. A parametric study with respect to projectile mass and velocity is performed, and the similar prediction trends with the linear solution are observed. Furthermore, the predicted stress fields are compared with the available strength data to predict the impact damage in the FRP sandwich system. The present impact analysis demonstrates the accuracy and capability of the higher order impact sandwich beam theory, and it can be used effectively in analysis, design applications and optimization of efficient FRP honeycomb composite sandwich structures for impact protection and mitigation.

Homogenization technique of discrete atoms into smeared continuum

A homogenization technique was developed and presented to replace a discrete atomic domain by an equivalent continuum domain that could be discretized into finite elements. Equivalent material properties of the smeared continuum domain were computed from the atomic model. Using the developed technique, a computationally efficient analysis could be performed for a large size of domain by proper mixture of a discrete atomic region and a smeared continuum region. In addition, this technique provided a means for multi-scale analysis. Examples for static and dynamic analyses were provided to demonstrate the technique.

Free vibration analysis of perforated plate submerged in fluid

An analytical method to estimate the coupled frequencies of the circular plate submerged in fluid is developed using the finite Fourier-Bessel series expansion and Rayleigh-Ritz method. To verify the validity of the analytical method developed, finite element method is used and the frequency comparisons between them are found to be in good agreement. For the perforated plate submerged in fluid, it is almost impossible to develop a finite element model due to the necessity of the fine meshing of the plate and the fluid at the same time. This necessitates the use of solid plate with equivalent material properties. Unfortunately the effective elastic constants suggested by the ASME code are found to be not valid for the modal analysis. Therefore in this study the equivalent material properties of perforated plate are suggested by performing several finite element analyses with respect to the ligament efficiencies.

A comparison of two biomaterial carriers for osteogenic protein-1 (BMP-7) in an ovine critical defect model

Critical size defects in ovine tibiae, stabilised with intramedullary interlocking nails, were used to assess whether the addition of carboxymethylcellulose to the standard osteogenic protein-1 (OP-1/BMP-7) implant would affect the implant's efficacy for bone regeneration. The biomaterial carriers were a 'putty' carrier of carboxymethylcellulose and bovine-derived type-I collagen (OPP) or the standard with collagen alone (OPC). These two treatments were also compared to "ungrafted" negative controls. Efficacy of regeneration was determined using radiological, biomechanical and histological evaluations after four months of healing. The defects, filled with OPP and OPC, demonstrated radiodense material spanning the defect after one month of healing, with radiographic evidence of recorticalisation and remodelling by two months. The OPP and OPC treatment groups had equivalent structural and material properties that were significantly greater than those in the ungrafted controls. The structural properties of the OPP- and OPC-treated limbs were equivalent to those of the contralateral untreated limb (p > 0.05), yet material properties were inferior (p < 0.05). Histopathology revealed no residual inflammatory response to the biomaterial carriers or OP-1. The OPP- and OPC-treated animals had 60% to 85% lamellar bone within the defect, and less than 25% of the regenerate was composed of fibrous tissue. The defects in the untreated control animals contained less than 40% lamellar bone and more than 60% was fibrous tissue, creating full cortical thickness defects. In our studies carboxymethylcellulose did not adversely affect the capacity of the standard OP-1 implant for regenerating bone.

An Equivalent Medium Method for the Vacuum Assisted Resin Transfer Molding Process Simulation

Computer simulation has been an efficient and cost-effective tool for liquid composite molding, including resin transfer molding (RTM), vacuum assisted resin transfer molding (VARTM), and resin infusion, compared to trial and error. The control volume finite element method (CVFEM) has been the predominant method for simulation. When the CVFEM simulation is used for the VARTM process, because of the existence of two distinct flow media: fiber preform and high permeable media (HPM), 3-D models are required. Since the HPM is usually much thinner than the fiber preform, a large number of nodes and elements need to be used in simulation, which significantly increases the computation load and time. In addition, the time-consuming preprocessing process makes simulation not feasible for industry applications. This article presents an equivalent medium method (EMM) for fast and accurate VARTM process simulation. This method increases the thickness of the HPM or both the HPM and the fiber preform and applies the equivalent material properties. This is an improved method over previously presented equivalent permeability method (EPM) by correcting its two shortcomings: (1) The EPM does not account for the influence of the porosity of HPM, thus the resin flow through HPM is changed and (2) The EPM does not consider the change of through-thickness permeability after the equivalence. A new mesh generation algorithm is also discussed, which provides a faster and more convenient way for preprocessing. The approach presented in this article provides the fundamental for developing a universal computer simulation tool for both the RTM and VARTM processes. The effectiveness of this approach has been validated by comparing to the conventional CVFEM simulation and experiments.

Investigation of overlay errors due to the interaction of optical and extreme ultraviolet mask fabrication processes

Overlay tolerances are becoming increasingly severe as lithography technology drives the minimum integrated-circuit feature size below 65nm. Manufacturable solutions at the lower nodes are essentially unknown. The goal of this article is to investigate overlay errors at the 45-nm node, for a mix-and-match of optical and extreme ultraviolet (EUV) lithographies. In particular, image placement errors induced during mask fabrication are predicted for a specified test pattern, which includes the possibility of having individual layers on the device wafer patterned by either optical or EUV lithographic processes. Finite element (FE) models have been developed to simulate the response of both optical and EUV masks during fabrication and chucking. In order to track image placement errors of the actual features within the pattern area, submodeling techniques were developed for the FE simulations. In addition, equivalent material properties were determined for the individual patterns used for the different optical and EUV masks. The FE simulations clearly indicate that the most significant source of overlay error is the fabrication of the optical reticle, primarily due to differences in chucking of the mask during e-beam patterning and exposure. Modeling results are being used by the industry to establish guidelines for reticle chucking and fabrication standards.

On the Prediction of Effective Material Properties of Cellular Hexagonal Honeycomb Core

Analytical expressions for the effective elastic properties of cellular hexagonal honeycomb core have been presented in this study. The elemental beam theory has been adopted for each component inside the ‘unit-cell’ to arrive at the different expressions for effective properties utilizing the strain energy concept. The length of the diagonal struts, vertical struts, and included angle, as well as the thickness of the struts have been kept as variable, so various forms of hexagonal honeycomb cellular structures can be investigated in this approach. Other conventional finite element approaches and numerical homogenization methods are rather time consuming to predict effective properties. Moreover, a change in basic cell configuration (i.e., depth) requires a complete new meshing and analysis. In comparison, the analytical approach presented here is simple and computes the effective properties in a fraction of the time that is required for FE analysis with a minimum change in the input file. The proper implementation of this method embedded in large quasi-static or impact dynamic simulations (where part of the structure could be modeled with detailed finite element mesh for cellular core that may initiate damage, and rest could be modeled with a single solid layer of equivalent material properties) would give high computational advantage, which is essential in large-scale aerospace modeling and simulation environment.

균질화기법에 기초한 유도전동기 권선 다발의 등가물성 유도

The electromagnetic noise generates when natural frequencies of a stator core with wingdings and frame coincide with or approach natural frequencies of the magnetic motive force. In order to suppress such noise, the estimation of natural frequencies of the motor is important at the design stage. However, the natural frequency analysis is not so easy because motor stator is in the laminated plate structure and windings are composed of wires, insulation sheets and vanishs. Thus the accurate prediction of the equivalent material properties of windings becomes an essential task. In this paper, we derive the equivalent material properties using homogenization methods.

A continuum mechanics-based non-orthogonal constitutive model for woven composite fabrics

Abstract A non-orthogonal constitutive model is developed to characterize the anisotropic material behavior of woven composite fabrics under large deformation. A convected coordinate system, whose in-plane axes are coincident with the weft and warp yarns of woven fabrics, are embedded in the shell elements. Contravariant stress components and covariant strain components in a constitutive relation are introduced into the convected coordinate system. The transformations between the contravariant/covariant components and the Cartesian components of the stress and strain tensors provide an approach for deriving the global non-orthogonal constitutive relations for woven composite fabrics. By taking advantage of the tensile–shear decoupling in the constitutive equation under the convected coordinate system, the material characterization of woven fabrics is simplified. As an essential part for these transformations, a fiber orientation model is developed, by using some fundamental continuum mechanics concepts, to trace the yarn reorientation of woven fabrics during deformation. The proposed material characterization approach is demonstrated on a balanced plain weave composite fabric. The equivalent material properties are obtained by matching with experimental data of tensile and bias extension tests on the woven composite fabric. Model validation is provided by comparing numerical results with experimental data of bias extension test and shear test. The development of this non-orthogonal model is critical to the ultimate goal, i.e. using numerical simulations to optimize the forming of woven composite fabric sheets.

Calculating the elastic moduli of steel-fiber reinforced concrete using a dedicated empirical formula

The equivalent inclusion method (EIM) is adopted to study the characteristics of the equivalent material properties of steel-fiber reinforced concrete as a function of the volume fraction and the length to diameter ratio of the fibers. It is found that the equivalent material moduli of concrete reinforce with randomly orientated and distributed fibers are insensitive to the length to diameter ratio of the steel fibers. A set of empirical formulae is then proposed for the purposes of engineering applications. The proposed empirical model can simplify the calculation of the equivalent material moduli. Verifications of the proposed empirical formulae with the EIM model and with experimental data are performed with two examples. The first is a compression test. The second is 4 point bending test. The empirical formulae, based on the equivalent inclusion method proposed in this study, represent an alternative means of quickly calculating the effective elastic modulus of steel-fiber reinforced concrete materials.