Effects Of Material Properties Research Articles

Static analysis of shear-deformable aircraft wings using a multilayered functionally graded material model

This study presents a comprehensive investigation of the static analysis of a shear-deformable aircraft wing made of functionally graded materials (FGMs). A finite element-based multilayered FGM model is employed for this purpose. In order to ensure the safe structural design of the aircraft wing, it is crucial to analyze the transverse displacement of the wing under various loading conditions. The presented model employs a power-law distribution based on the rule of mixture to derive the effective material properties of the FGM wing. The analysis focuses on three standard FGM aircraft wing profiles, namely NACA 0009, NACA 2424, and NACA 4415, which are representative of commonly used geometries in aircraft design. Additionally, the study explores the effects of volume fraction index, loading conditions, boundary conditions, and aspect ratio on the static analysis of the shear-deformable FGM aircraft wing. These parameters play a significant role in shaping the static behavior of the wings and offer valuable insights into the design of FGM aircraft wings.

Numerical vibroacoustic analysis of multi-layered composite structure under hygrothermal loading using coupled FEM-IBEM micromechanical model

The vibroacoustic responses of multi-layer composite shallow shell panels subjected to harmonic mechanical excitation in hygrothermal environment is numerically investigated. A homogenized micromechanical finite element (FE) based on the higher-order mid-plane kinematics replicating quadratic function as well as the through the thickness stretching effect together with the indirect boundary element (IBE) scheme has been first time employed. The isoparametric Lagrangian element with zero-order Hermitian interpolation function (10 degrees of freedom per node) is used for structural model discretization to attain the hygro-thermo-elastic natural frequencies via Hamilton’s principle. The uniqueness of the model is the incorporation of the effective material properties under combined hygrothermal loading via a micromechanics approach. An IBE method is then implemented to attain structure-surrounding coupling and the Helmholtz wave equation is solved to compute the sound radiation responses. The effectiveness of the model is tested by converging it with the similar analytical/numerical results as well as the experimentally acquired data for vibrational as well as acoustic responses. The present scheme is further hold out for solving diverse numerical illustrations. The geometrical parameters, volume fraction of fiber, layup, and support conditions alongside the hygrothermal load is found to have significant influence on the hygro-thermo-acoustic characteristics. The functional inferences will assist in designing the imminent multi-layered structures that serve under the influence of severe hygrothermal loading during high-performance engineering applications.

Nonlinear vibration study of a rotor blade based on a novel non-polynomial function

This work investigates the nonlinear free vibration of a turbomachinery blade, which is idealized as a rotating, conical, twisted shell of varying thickness reinforced with graphene platelets. Using the von Karman type of nonlinearity, the dynamic equilibrium equation for the twisted panel is obtained and solved by finite element method. The impact of the centrifugal force caused by rotation is taken into account, but the effect of the Coriolis force is neglected. The functionally graded twisted tapering conical shell has two alternative ways in which graphene platelets (GPLs) are reinforced in the thickness direction. The rule of mixture and the modified Halpin-Tsai model are used to compute the effective material properties of the twisted shell. The strain displacement relation is based on a new non-polynomial shear deformation theory. The parametric analysis performed at the endshows that nonlinear frequency increases when twist angle, rotational speed, tapper ratio, and weight fraction of GPLs increase. It is also observed that mode shapes are severely impacted by twist angle and rotational speed.

Finite element analysis of natural frequencies of the FGM porous cooling plate with cutouts: A multilayered FGM approach

This study comprehensively investigates the natural frequency analysis of a shear-deformable functionally graded porous plate with cutouts, utilizing an FE-based multilayered FGM model. Analyzing natural frequencies is vital to prevent catastrophic failure in porous plates, particularly in cooling plates. Cutouts in cooling plates enhance heat dissipation, improve airflow or fluid contact, reduce weight, customize battery layouts, optimize structural integrity, simplify installation, and enable precise thermal management in critical areas. The present study employs an FE-based multilayered FGM model that considers three distinct porosity distributions (even, uneven, and sinusoidal) and incorporates a power law distribution based on a modified rule of mixture to derive the effective material properties of the FGM porous plate. Furthermore, this investigation comprehensively explores the influences of variables such as volume fraction index, thickness ratio, porosity distribution, and porosity index on the natural frequency analysis of shear-deformable FGM porous plates with cutouts, encompassing both conventional and unconventional boundary conditions. This extensive examination elucidates the collective impact of these variables on the vibrational behavior of FGM plates featuring cutouts. These parameters significantly impact the vibration behavior of the FGM plate with cutouts. The results affirm the efficacy of the presented model in analyzing intricate FGM structures.

Fast construction of cluster interaction matrix for data-driven cluster-based reduced-order model and prediction of elastoplastic stress-strain curves and yield surface

The data-driven cluster-based reduced-order model (CROM) methods[47–50] are very effective for predicting the nonlinear effective properties of heterogeneous materials. The Cluster Interaction Matrix (CIM) in these methods can be regarded as a clustered discrete Green's function and is the critical part of CROM methods, which more and more scholars have realized. However, the explicit expression of Green's function is available only for homogeneous material. The CIM for heterogeneous materials needs to be calculated through numerical approaches, which face the challenge of computational efficiency. Therefore, this paper proposes an efficient method to construct the CIM of heterogeneous materials. By deriving the Green's function in Fourier space under the governing equation of FCA, the CIM of homogeneous materials that can provide the self-equilibrium stress field is calculated efficiently. Then, to avoid the effects of stress averaging on clusters, we augment the proposed cluster-element interaction matrix with the self-equilibrium stress basis vector of heterogeneous material without introducing additional computational cost. Based on the augmented cluster-element interaction matrix, the self-equilibrium stress space is improved, and the CIM of highly heterogeneous materials is calculated using the minimum complementary energy principle. The proposed algorithm significantly improves the offline computational accuracy of FCA, enabling efficient prediction of nonlinear effective properties and yield surface under complex load paths. Numerical examples demonstrate the efficiency and accuracy of the proposed method. In addition, we provide the relationship between the CIMs of a homogeneous material of FCA and SCA. Based on the proposed algorithm in this paper, it can be helpful for other CROM methods.

Coupled five-parameter dynamics of Mindlin and third-order shear deformable FG graphene-platelets reinforced viscoelastic plates with geometric and material imperfections

The present work investigates the coupled five-parameter dynamics, in particular, the coupled five-parameter structural resonance frequency, of functionally graded (FG) graphene-platelets reinforced viscoelastic plates in the presence of geometric and material (porosity) imperfections, based on the Mindlin theory and the third-order shear deformation plate theory (TSDPT). Various imperfections are often found in structures as a result of the challenges in manufacturing and operations over time. Geometric imperfection is considered in the FG reinforced plate structure by modelling an initial curvature in the out-of-plane direction. Material imperfections, in the form of closed-cell voids, are formulated as uniform and non-uniform FG porosity distributions. Uniform and thickness-wise FG gradation effects of graphene-platelets are accounted for in the determination of the effective material properties using a two-dimensional Halpin-Tsai micromechanics model, in conjunction with the rule of mixtures. Viscoelasticity of the FG imperfect plate structure is modelled by employing the Kelvin-Voigt model to consider energy dissipation. Using the Mindlin plate theory and the TSDPT, five equations of motion, which are coupled through the five parameters u, v, w, ϕ1, and ϕ2, are derived using Hamilton's variational principle. An assumed mode method is then employed to obtain the real and the imaginary components of resonance frequencies. The combined influences of the different effects on the structural resonance are examined. The results obtained offer a comprehensive understanding of how the FG graphene-platelets, FG porosity, plate thickness, geometric imperfection, and the utilisation of two different shear deformation plate theories collectively influence the coupled five-parameter dynamics of the FG graphene-platelets reinforced viscoelastic plate structure with imperfections. It was found that the difference in frequency resulted from the use of the two plate theories is most dominant with the FG GX and/or FG PX graphene-platelets reinforced porous plates, and that geometric imperfection was found to alter a graphene-platelets reinforced plate's sensitivity towards material imperfection.

Nonlinear vibrations of auxetic honeycomb thin plates based on the modified Gibson functions

Auxetic honeycombs possess many excellent properties, making them ideal cores for sandwich structures that can absorb energy effectively. This paper investigates the nonlinear vibrations of auxetic honeycomb composite plates, focusing on the primary resonance, super-/sub-harmonic resonances of the composite plates. Two pure panels sandwich an auxetic honeycomb core to form the honeycomb composite plate. The proposed modified Gibson function enables the derivation of effective material properties. By considering geometric nonlinearity, the nonlinear motion equations are derived through the implementation of the Hamilton principle, and then nonlinear ordinary differential equations are given by introducing stress functions and the Galerkin method. The nonlinear response curves are then determined by the multiple scale method. The impact of important parameters on the nonlinear vibration of auxetic honeycomb composite plates is evaluated in this study.

A representative volume element model to evaluate the effective properties of flexoelectric nanocomposite

In this paper, a computational homogenization approach is developed to investigate the effective material properties of flexoelectric nanocomposites. The analysis incorporates the isogeometric analysis (IGA) to solve an electromechanically coupled system using a 3D representative volume element (RVE) model with periodic boundary conditions. In particular, a micromechanical analysis is carried out to represent the microstructure of a heterogeneous domain composed of an elastic matrix and cylindrical flexoelectric fibers. The numerical simulations indicated that while the effective tensor of piezoelectricity is isotropic, the flexoelectricity tensor is transversely anisotropic concerning the geometry of the composite’s phases. Furthermore, the flexoelectricity coefficients, μ¯3113 and μ¯3333, which couple the polarization to the strain gradients with respect to the longitudinal axis, improved remarkably with increasing the inclusion’s volume fraction. The presented computational methodology and the findings of this study is expected to contribute valuably towards the design of flexoelectric nanostructures and devices.

Design of acoustic coatings with symmetric and asymmetric resonant inclusions

An acoustic coating for underwater applications, designed using periodically distributed cavities and hard spherical particles embedded in a soft matrix, is herein modelled as monopolar and dipolar scatterers positioned along the centre of a sound hard duct. Modified equations of motion for the scatterers account for resonance phenomena as well as multiple scattering of waves by a lattice. Combinations of monopolar and dipolar scatterers in the direction of the incident sound field are considered. The acoustic performance of the various coating designs composed of symmetric and asymmetric resonant inclusions are compared. The influence of asymmetry in coating designs, arising from variation in scatterer size and material distribution, on effective material properties and Willing coupling are reported.

Generalized Kelvin-Voigt viscoelastic modeling and numerical study of Free-Damped vibrations in MR elastomer reinforced with graphene platelets

This study focuses on the modeling and numerical analysis of a novel composite plate, which consists of a laminated magnetorheological elastomer (MRE) reinforced with graphene platelets (GPLs). The investigation begins with the determination of the mechanical properties of the MRE, utilizing a modified generalized Kelvin-Voigt viscoelastic model. Through nonlinear regression analysis and the nonlinear least squares technique, the dependencies of the storage and loss modulus of the magnetorheological (MR) matrix are evaluated, considering factors such as the magnetic field, iron particles, and excitation frequency. The proposed model is validated by comparing the obtained results with existing experimental data from the literature, employing root mean square error and correlation coefficients as metrics of consistency. Next, the homogenization process is applied to the composite media, which involves integrating the MR elastomer matrix and GPL reinforcements using the Halpin-Tsai micromechanical approach. This procedure enables the extraction of effective material properties governing the behavior of the composite structure. The theoretical framework, encompassing third-order plate theory, linear elasticity, and viscoelasticity, is then employed to derive the dynamic equations of the composite plate, employing Hamilton's principle as a guiding principle. To solve the dynamic problem and obtain the complex frequencies characterizing the system, the generalized differential quadrature (GDQ) method is implemented. This numerical technique offers a robust and accurate solution approach, providing comprehensive insights into the vibrational behavior of the composite plate. The study conducts a thorough investigation, exploring the performance achieved by incorporating GPL reinforcements within the MRE matrix. Specifically, the effects of different volume fractions of iron particles and varying magnetic fields are comprehensively examined and analyzed. Through this comprehensive exploration, a profound understanding of the behavior of the composite plate and its response to external stimuli is attained. The findings highlight the potential advantages of integrating GPL reinforcements and offer valuable insights for optimizing the design and performance of such composite structures in practical applications. The research contributes to the advancement of knowledge in the field of composite materials and opens up new possibilities for innovative and high-performance structural designs.

Influence of nonlocal elasticity tensor and flexoelectricity in a rod: An asymptotic homogenization approach

This paper presents a methodology based on the asymptotic homogenization method (AHM) to model flexoelectric composites with nonlocal elasticity. The nonlocal elasticity tensor accounts for the long-range interactions between the strain gradient and the electric field, which affect the effective flexoelectric coefficients and the composite’s overall response. The local problems, the general expression of the higher-order contributions in the asymptotic expansion, and the homogenized formulation of the equilibrium problem for a one-dimensional flexoelectric composite material are derived, and details of the AHM are given. Closed formulas for the effective flexoelectric coefficients with higher-order contributions of the asymptotic expansions are found, which is a novel contribution to the field. Finally, numerical examples are reported and discussed. Herein, the influence of different material constituents on the effective properties of various one-dimensional periodic composite materials is studied. The solutions to the homogenized problem for different material configurations are given.

Thermo-mechanical analysis of functionally graded nickel/titanium alloys under different process parameters of directed energy deposition

The build-up of residual stress and porosity plays an important role in the mechanical properties of as-built parts during directed energy deposition (DED). However, the thermo-mechanical behavior of functionally graded nickel/titanium alloys (FGNTAs) in the DED process remains unclear. In this study, a computationally efficient thermo-mechanical coupled model of DED-printed FGNTAs with different porosities is developed. The temperature-dependent effective material properties of FGNTAs are first determined based on the rule of mixture. Subsequently, the temperature, residual stress, and deformation fields within as-built FGNTAs are predicted using the differential quadrature method. The predicted results show excellent agreement with the predictions and experimental data in the literature. Furthermore, the effect of key parameters on the thermo-mechanical responses of DED-printed FGNTAs is investigated, including energy density, porosity distributions, part dimensions, temperature settings, and structural modes. The results show that the residual stress and vertical deflection increase with the higher energy input, length-to-width ratio, and evener porosity distributions, while decreasing with larger porosity, preheating as well environment temperatures, external loads, and power index. These results can provide a useful guideline for the design and manufacturing of high-quality FGNTAs during DED.

Mechanics and Computational Homogenization of Effective Material Properties of Functionally Graded (Composite) Material Plate FGM

Mechanics and Computational Homogenization of Effective Material Properties of Functionally Graded (Composite) Material Plate FGM

High‐speed fatigue testing of high‐performance concretes and parallel frequency sweep characterization

AbstractCycling loading of brittle materials like ultra‐high‐performance concrete (UHPC), which is often used in marine and civil structures, results in unexpected failures. When a material is subjected to cyclic loading, its mechanical properties change due to the evolution of (micro‐)fractures often denoted as damage. To better understand the effective material's properties under such kind of fatigue load and to relate the material's properties to the specific time‐dependent loading characteristics, the mechanical response of the material shall be characterized at characteristic harmonic excitations.Therefore, cyclic loading experiments are conducted to determine how the evolution of microfractures, that is, fatigue, affects the material's effective mechanical properties and after how many cycles microfractures further evolve towards meso‐ and macrofractures leading finally to a critical number of cycles to material's failure. The problem with such cyclic fatigue tests is that they are potentially “expensive” to conduct as the number of loading cycles at failure can be extremely high. Moreover, it is not possible to observe and characterize further the evolution of (micro‐)fractures within the different damage phases of the cycling experiment. Further, it is challenging to characterize the material's small‐strain stiffness evolution.In this investigation, a combination of a (high‐amplitude) high‐frequency excitation and a high‐speed fatigue testing approach is used for the high cycle fatigue experiment along with a characterization approach of the material properties using a (low‐amplitude) dynamic mechanical analysis (DMA). The test setup applies harmonic excitations for high and low amplitudes using a high‐voltage piezoelectric actuators. Furthermore, the failure modes of the material will be examined.The excitation frequency f for the fatigue test is significantly higher than in classical low‐ and high‐cyclic fatigue approaches, that is, Hz, allowing to reduce the overall time of the experimental investigation time to failure. Further, the frequency‐dependent number of cycles to failure is studied. Similar to standard DMA, effective complex mechanical properties of the material in tangential space are obtained in frequencies between 0.01 and 1000 Hz; while the observed mechanical properties of these materials change with increasing frequency. In the case of materials' behavior, by increasing the frequency, Young's modulus increases and Poisson's ratio decreases. Experimental fatigue results will be presented for UHPC samples. Harmonic experimental data include (direct) strain measurements in axial and circumferential directions as well as forces in axial directions. In addition, the resulting complex Young's modulus and evolving damage‐like “history” of UHPC will be shown.

Multiscale modeling of woven composites by deep learning neural networks and its application in design optimization

Due to complex yarn geometries and multiscale nature, it is very challenging to predict mechanical properties and strength constants of woven composites in an accuracy and efficient way. In this paper, mechanics of structure genome (MSG) is employed to predict effective material properties and strength constants of woven composites. The microscale analysis is performed to compute the effective properties and strength constants of yarns based on a hexagonal packed microstructure. Then, the mesoscale analysis is performed to compute the effective material properties and strength constants of woven composites. The accuracy and efficiency of the MSG method are compared with the computational homogenization method. In addition, simulation data using the MSG model is generated to train deep learning neural networks (DNN) models. The trained models provide ultra-efficient surrogate models with high accuracy. The DNN models are further applied to a design optimization problem to tailor geometry parameters to enhance the mechanical performance of plain woven composites, and the optimization can be efficiently solved with gradients from the DNN models. The developed computational framework can be applied to general woven composites featuring complex microscale and mesoscale features.

Graph neural network for predicting the effective properties of polycrystalline materials: A comprehensive analysis

We develop a polycrystal graph neural network (PGNN) model for predicting the effective properties of polycrystalline materials, using the Li7La3Zr2O12 ceramic as an example. A large-scale dataset with >5000 different three-dimensional polycrystalline microstructures of finite-width grain boundary is generated by Voronoi tessellation and processing of the electron backscatter diffraction images. The effective ion conductivities and elastic stiffness coefficients of these microstructures are calculated by high-throughput physics-based simulations. The optimized PGNN model achieves a low error of <1.4% in predicting all three diagonal components of the effective Li-ion conductivity matrix, outperforming a linear regression model and two baseline convolutional neural network models. Sequential forward selection method is used to quantify the relative importance of selecting individual grain (boundary) features to improving the property prediction accuracy, through which both the critical and unwanted node (edge) feature can be determined. The extrapolation performance of the trained PGNN model is also investigated. The transfer learning performance is evaluated by using the PGNN model pretrained for predicting conductivities to predict the elastic properties of the same set of microstructures.:

On characterizing the viscoelastic electromechanical responses of functionally graded graphene-reinforced piezoelectric laminated composites: Temporal programming based on a semi-analytical higher-order framework

The electromechanical responses of single and multi-layered piezoelectric functionally graded graphene-reinforced composite (FG-GRC) plates are studied based on an accurate higher-order shear deformation theory (HSDT) involving quasi-3D sinusoidal plate theory and linear piezoelectricity. These FG-GRC plates are composed of randomly oriented graphene nanoplatelets (GPLs) reinforcing fillers and the piezoelectric PVDF matrix considering two different distribution patterns such as linear- and uniform- distribution (LD and UD) of GPLs across the thickness. The modified Halpin-Tsai (HT) and Rule of mixture (ROM) models are utilized to determine the effective material properties of FG-GRCs. The analytical model of FG-GRCs is extended further to analyze the time-dependent linear viscoelastic electromechanical behavior of the system based on Biot model of viscoelasticity in the framework of inverse Fourier algorithm. The viscoelastic electromechanical responses include the static deformation and electric responses of simply supported FG-GRC plates which are investigated by considering transverse mechanical and external electrical loading, as well as other critical parameters like aspect ratio and weight fraction of GPLs. The numerical results reveal that the electromechanical response of FG-GRC plates can be enriched due to the addition of a small weight fraction of GPLs. The coupled multiphysics-based computational framework proposed here for predicting the viscoelastic electromechanical behavior of laminated composites can be exploited for stimulating and developing a wide range of micro-electro-mechanical systems (MEMS) and devices incorporating time-dependent programming features.

Process-induced distortion of triaxially braided composites considering different geometric parameters using simplified constitutive model with effective property

Herein we present a prediction method for the process-induced distortion (PID) of a 2-D triaxially braided composite (TBC) structure at the macroscopic level based on a simplified constitutive model and analytical model for the effective material properties (EMPs). This method can quickly predict the PID considering viscoelastic characteristics and different geometric parameters of the 2-D TBC. The PID trend with curing time of an L-shaped TBC flange was analyzed in detail using a finite element-based curing simulation. Furthermore, the effects of the geometric parameters on the EMPs and PID of the 2-D TBC were investigated. A primary finding is that the in-plane shear modulus of the 2-D TBC had a significant effect on the PID of the cured 2-D TBC structures. This prediction method can be utilized for designing composite structures and molds, thus contributing to the improvement of dimensional precision and capabilities of composite materials and structures.

Numerical study on damped nonlinear dynamics of cracked FG-GNPRC dielectric beam with active tuning

Functionally graded (FG) graphene nanoplatelets (GNPs) reinforced composite (FG-GNPRC) is widely used in various engineering fields due to its high-performance and multifunctional features. Cracks generated in complex environments have a significant impact on the structural behavior of FG-GNPRC structures. This paper studies the damped nonlinear dynamics of cracked FG-GNPRC dielectric beam subjected to mechanical excitation and electrical field. The effective material properties of the composites are determined by the effective medium theory (EMT). Based on Timoshenko beam theory and nonlinear von Kármán strain–displacement relationship, the governing equations which incorporate damping and dielectric properties are derived by using energy method. Stress intensity factor (SIF) of cracked FG-GNPRC beam at the crack tip is calculated via finite element method. Differential quadrature (DQ) and incremental harmonic balance (IHB) methods combined with arc-length algorithm are utilized to discretize and solve the nonlinear system. After validation of the model and solution, the effects of crack depth and location, damping, FG distribution and the attributes of GNP and the electric field on the dynamic response of the system are comprehensively investigated. The study indicates that when an electric field is applied, the amplitude ratio of cracked FG-GNPRC beam with profile V is the largest when the crack is close to the edge, whereas profile A exhibits the largest value when the crack is near the mid-span. In addition, the generated bending moment enables profiles A and V to transit into profile U at a certain voltage or GNP aspect ratio due to the existence of electrostatic stress.

Finite Element Analysis of Additively Manufactured Continuous Carbon Fiber-Reinforced Composites

AbstractThe objective of this study is to provide a numerical modeling approach for continuous carbon fiber (CCF)-reinforced fused filament fabricated composites. Although these materials have been extensively studied, an effective numerical modeling technique for their mechanical performance does not exist. To fill this technical gap, a numerical modeling approach based on finite element analysis is presented. The effective material properties of the Onyx matrix when voids are present are derived by the Kerner model. The material properties of CCF-reinforced composites are modeled by Hashin’s model. Both the flexural and tensile properties are simulated. The modeling approach is validated against various experimental results.