Effects Of Material Properties Research Articles

Multiscale modelling and characterisation of fused filament fabricated neat and graphene nanoplatelet reinforced G-polymers

AbstractIn this study, the fused filament fabrication of novel biodegradable G-polymer is investigated, including also filaments reinforced by graphene nanoplatelets. A combined framework of computational multiscale modelling and experimental studies is applied to characterise and model the mechanical behaviour of composite and nanocomposite materials, fabricated using a 3D-printer by depositing G-polymer filaments in +45$$^\circ$$ ∘ and $$-45^\circ$$ - 45 ∘ angles. The investigation is performed on both hot-extruded single filaments and 3D-printed specimens. Experimental results of hot-extruded single filaments are utilized on the microscale to extract the macroscale constitutive models. At the microscale level, representative volume elements with different percentages of penetration are analyzed to compute the effective orthotropic elastic material properties. A comprehensive comparison study is conducted using different micromechanical models, multiscale simulation outputs, and the mechanical properties resulting from experiments. The accuracy of the results obtained from the homogenization technique is validated against realistic finite element microstructural models and experimental measurements. The results demonstrate that computational homogenization, when coupled with accurate property characterisation, serves as a reliable tool for predicting the elastic response of 3D-printed parts. Furthermore, the proposed framework reduces the need for extensive experimental replication and lowers manufacturing costs.

Material Homogenization of Human Femur Bone Material Using a New Weighted Approach

Abstract The design of efficient and safe biocompatible artificial implants for bone replacement and reconstructions requires a thorough understanding of natural bone material. A new homogenization approach is therefore used to predict effective material properties of the human femur bone. The bone structure is idealized as a functionally graded composite made of different quantities of a collagen protein matrix reinforced by hydroxyapatite mineral acting as the filler. Two distinct composite models were investigated, one where the mineral reinforcements were assumed to be randomly dispersed inclusions in a matrix of collagen, and a second model wherein the minerals were assumed to be unidirectional fibers. Predicted results for longitudinal and transverse elastic modulus from the models compare very well with range of values from published experimental data. It is also compared to those predicted using classical homogenization models. These material properties are then used to obtain the structural response of a bone plate section under transverse load.

Isogeometric free vibration of functionally graded porous magneto-electro-elastic plate reinforced with graphene platelets resting on an elastic foundation

This article investigates the free vibration behavior of functionally graded porous reinforced with graphene platelets magneto-electro-elastic (FGP-GPL-MEE) plates. The FGP-GPL-MEE plate is supported by the Winkler-Pasternak foundation and subjected to the initial external electric voltage and magnetic loads. The governing equations for FGP-GPL-MEE plates are derived from the combination of Hamilton's principle and the refined plate theory (RPT) with four variables. The FGP-GPL-MEE plate is formed by combining three porosity distributions of functionally graded materials and three patterns of graphene platelets dispersion distributed along the plate thickness. Using the modified Halpin-Tsai model, effective material properties of the FGP-GPL-MEE plate are estimated. Isogeometric approach (IGA) is used to discretize the plate geometry and extract mode shapes and natural frequencies. The effects of various parameters such as porosity distributions, porosity coefficient, GPLs distributions and magnetic and electric potentials on the natural frequencies of the FGP-GPL-MEE plate are performed. The results indicate that the GPLs reinforcement can be significantly enhanced the natural frequencies of the FGP-GPL-MEE plate. Moreover, the free vibration behavior is significantly influenced by porosity, as well as magnetic and electric fields. The results of this study provide valuable insights into the vibrational characteristics of FGP-GPL-MEE plates.

Engineered moiré photonic and phononic superlattices.

Recent discoveries of Mott insulating and unconventional superconducting states in twisted bilayer graphene with moiré superlattices have not only reshaped the landscape of 'twistronics' but also sparked the rapidly growing fields of moiré photonic and phononic structures. These innovative moiré structures have opened new routes of exploration for classical wave physics, leading to intriguing phenomena and robust control of electromagnetic and mechanical waves. Drawing inspiration from the success of twisted bilayer graphene, this Perspective describes an overarching framework of the emerging moiré photonic and phononic structures that promise novel classical wave devices. We begin with the fundamentals of moiré superlattices, before highlighting recent studies that exploit twist angle and interlayer coupling as new ingredients with which to engineer and tailor the band structures and effective material properties of photonic and phononic structures. Finally, we discuss the future directions and prospects of this emerging area in materials science and wave physics.

Semi-analytical framework for modelling of surface heating and its impact on nonlinear stability of nanotube reinforced doubly curved porous fiber composite panels

In elevated temperatures, the stiffness of the panel deteriorates and can lead to loss of stability of structures. Hence, the stability analysis of thin-walled structures is a critical investigation in the thermal environment. Finding such criticality, the present semi-analytical study investigated the nonlinear stability behaviour of porous doubly curved thin-walled panels subject to surface heating like dome heating and localised heating. To improve the stiffness of the panel, the matrix is reinforced with carbon nanotubes (CNTs). Improper mixing of such nanoparticles can lead to agglomeration or bundling effect, which may reduce the structure's stiffness. Still, its investigation in surface heating can be an essential aspect that is found to be untouched by researchers for porous shell panels. The effective material properties of the three-phase composite panel are determined using the Eshelby-Mori-Tanaka (E-M-T) approach and the Chamis homogenisation technique. Using the variational principle, governing equations are derived and further simplified to non-linear algebraic equations using the Galerkin technique. Gibson and Ashby foam model is used to model cell structure. It is observed that a complete agglomerated state results in higher post-buckling strength, a continuous deformation path due to biaxial compression and curved geometry, and porosity of cellular structure distribution and cell walls are the important parameters to study the stability of panel in a thermal environment are the major conclusions drawn from the current study. Current investigation can be an important contribution towards modelling aircraft structure in supersonic airflow and furnace walls of thermal power plants subjected to localised heating.

Dynamic homogenization of inhomogeneous elastic media based on energy equivalence

This paper presents a new method of dynamic homogenization of periodic elastic media under harmonic antiplane deformation based on energy equivalence. The dynamic homogenization is based on two main steps, (1) determining the dispersion relation and the detailed local response in a representative volume element (RVE) by analyzing the propagation of Bloch waves and (2) using energy equivalence between the periodic and effective media to determine the effective properties. The method is first applied to a one-dimensional periodic medium, from which the analytical solutions of the effective material properties are obtained. The results are compared with that from the original periodic medium and an excellent agreement is observed. The dynamic homogenization method is then applied to general two-dimensional periodic media to determine the effective properties and to predict wave fields under typical loading conditions. Illustrative examples are presented and compared with the results from the multiple scattering model. The method has also been applied to multiscale modeling of complicated inhomogeneous media containing multiple groups of periodic inhomogeneities. By treating each group as a homogeneous material with effective properties determined by the current homogenization method, the wave field is obtained using the boundary element method. The resulting wave fields from the current method show an excellent agreement with that from the multiple scattering model with matching local response details.

Free vibration analysis of functionally graded composite plates reinforced with linearly and nonlinearly distributed carbon nanotubes in hygrothermal environments

This article presents a novel investigation of the free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates under hygrothermal environments. It explores both uniform and non-uniform (functionally graded) distributions of CNTs across the plate thickness for the first time. The effective material properties of the CNTRC, considering temperature and moisture dependence, are determined using the extended rule of mixture. First-order shear deformation theory (FSDT) is employed to derive the governing equations incorporating hygro-elastic and thermo-elastic relations. These equations are solved using the finite element method. A validation study verifies the accuracy of the employed approaches. Subsequently, a comprehensive parametric study investigates the influence of plate geometry (length-to-width and width-to-thickness ratios), CNTs volume fraction, boundary conditions, linear and non-linear CNTs distributions, and hygrothermal environments on the free vibration behavior of polymeric nanocomposite plates reinforced with CNTs fillers is conducted. The results reveal that the increase in temperature and moisture leads to a decrease in the effective stiffness of the FG-CNTRC plates.

Nonlinear vibrations of variable speed rotating graphene platelets reinforced blades subjected to combined parametric and forced excitation

It is generally acknowledged that the disturbance of rotating speed will cause parametric resonance for blades, and the presence of rotor displacement also can make the blade vibrate transversely. However, the coupled resonance mechanism of blades under the combined action of rotating speed disturbance and rotor displacement is not yet clear. To answer this question, this article investigates the nonlinear coupled resonance behavior of rotating blades in two cases: typical tuned (the frequency ratio of parametric and forced excitations equals 2:1) and frequency ratio detuned. A nonlinear vibration equation for rotating blades is established based on Euler beam theory in conjunction with geometric nonlinearity. The mixing rule and modified Halpin-Tsai model are used to calculate the effective properties of GPLRMF materials. Subsequently, using the method of varying amplitudes (MVA), an approximate analytical solution of the coupled resonance response is derived, the Jacobian matrix is used to determine the stability of non-trivial solutions, and the accuracy of the analytical results is verified with the aid of numerical solutions. Finally, the steady-state response of typical tuned and detuned coupled resonance is analyzed, and the influence mechanism of factors such as excitation amplitude, excitation phase angle and other parameters on coupled resonance is studied in detail. The results indicate that the supercritical coupled resonance curve exhibits double resonance peaks and jumps. Meanwhile, the steady-state response of coupled resonance highly depends on the excitation phase angle.

Uncertainty quantification for locally resonant coated plates and shells

The effect of uncertainty in design parameters on the acoustic performance of coated plates and coated shells for maritime applications is presented. The locally resonant coatings are designed using a viscoelastic material with an impedance similar to water and embedded with layers of inclusions. Both voids and hard inclusions, which respectively exhibit monopole and dipole resonance scattering, are considered. Effective medium approximation theory is employed to characterise the layers of inclusions as homogenised layers with effective material and geometric properties. The coating is then modelled as a multilayered equivalent fluid composed of alternating layers of the homogeneous viscoelastic material and the homogenised layers of inclusions. The coating is bonded to a rigid backing plate and the acoustic response is calculated using the transfer matrix method. The coating is also externally applied to an elastic cylindrical shell. The acoustic response is calculated by expressing the shell displacements and acoustic pressures in the coating and exterior domain in terms of Fourier series expansions, and applying continuity equations at each interface between the shell surface, coating layers and the surrounding water. Efficient stochastic models based on the non-intrusive polynomial chaos expansion (PCE) method are developed by transforming the analytical models for the coated plates and shells into computationally efficient surrogate models using point collocation. Uncertainty in dominant design parameters associated with the geometry of the inclusions and material properties of the coating is examined. The influence of the design parameters for inclusions tuned to different resonance frequencies and for multiple layers of inclusions is also reported. Strong acoustic performance of coating designs occurs in a broad frequency range around local resonance of the inclusions. For all coating models, uncertainty in parameters which predominantly influence the local resonance of the inclusions were observed to yield the greatest variation in the acoustic responses of the coated plates and shells.

Thermal modeling of porous medium integrated in PCM and its application in passive thermal management of electric vehicle battery pack

The integration of a composite of porous medium with phase change material (PCM) offers significant advantages in thermal management systems, enhancing heat transfer efficiency and addressing various thermal regulation challenges. This approach utilizes the PCM's latent heat absorption and the enhanced thermal conductivity provided by the porous medium, resulting in optimized system performance. Its applicability spans across electronics cooling and building insulation systems. However, predicting the thermal behavior of this composite material is challenging, necessitating computational tools to anticipate its response under different conditions and evaluate its influence on cooling strategies. The objective of this study is to create a computational tool specifically tailored to evaluate constitutive parameters of this composite material, thereby providing a comprehensive description of its thermal behavior. To achieve this goal, the multiscale homogenization principle is employed to assess the composite's effective thermophysical material properties using the representative volume element approach. The repeating unit cell of the aluminum lattice is incorporated into the PCM to define a representative volume element. The finite element method (FEM) is utilized to solve the three-dimensional homogenization problem, yielding an orthotropic effective thermal conductivity due to the inherent symmetry of the repeating material cell. Moreover, the study leverages the apparent heat capacity method to effectively manage the phase transitions within the PCM domain, utilizing smooth and temperature-dependent functions to accurately describe the thermophysical properties of the PCM. Integrating the composite into battery pack thermal management, this study thoroughly examines thermal dynamics by comparing outcomes with and without PCM integration. The transient thermal problem is accurately tackled using the FEM, employing the evaluated effective constitutive parameters of the homogenized composite to minimize computational effort. The results indicate a notable decline in the highest temperatures of the battery pack, leading to a reduction of about 14 °C at the specific moment when the phase change material fully transitions into its liquid form. The obtained results emphasize the effectiveness and practical feasibility of the proposed thermal management strategy. The modeling approach presented provides a robust tool with significant efficiency in reducing computational time for analyzing the thermal behavior of large models, as the utilization of the homogenization technique notably decreases the computational time.

Effective properties of masonry structures and macro-model analysis with experimental verification

Masonry structures are the most prevalent type of buildings worldwide, and a significant portion are situated in seismic-prone areas. Thus, detailed information regarding their seismic strength and vulnerability is needed. The complexity of studying masonry structures lies in defining accurate and efficient models for representing masonry walls. In this context, there is a need for simplified methods that allow the modeling of masonry walls within a 3D structure. This work presents a methodology to define effective masonry properties from numerical analyses on representative volumes, using a damage model informed by experimental tests on units and mortar. These effective material properties serve as input parameters to model masonry walls within a macro-model approach, aiming to accurately capture the in-plane behavior and damage mechanisms with limited computational cost. The methodology is verified with experimental results and applied to real case studies in Cuenca, Ecuador.

Bending-based solution methodology using eigenvalue-eigenvector approach for analysis of foldable reinforced Golf Clubs cylindrical shell

This paper is organized to present eigenvalue-eigenvector based solution method for elastic bending analysis of foldable Golf Clubs cylindrical shell reinforced with graphene origami. The axisymmetric kinematic and constitutive relations are extended using the models with shear deformability and three-dimensional relations. The effective material properties are inserted into integration constants and constitutive relations in terms of angle and content of folded structure as well as thermal load. The virtual work principle is extended in order to derive governing equations and the eigenvalue-eigenvector method is applied for analytical solution. The results are presented along the longitudinal and radial coordinates with changes of angle and content of folded structure as well as thermal load. The results of this analysis may be used for optimized design and manufacturing of the golf clubs and other sport equipment.

The role of machine learning for insight into the material behavior of lattices: A surrogate model based on data from finite element simulation

In recent years, lattice structures have gained extensive attention due to their unique properties and great potential in various fields. Their effective material properties can be obtained by several means, e.g., numerical homogenization methods, finite element (FE) simulations, and experiments. Numerical homogenization methods involve certain assumptions, and thus, their applications are limited to those lattice structures satisfying all assumptions. On the contrary, although the FE simulations and experiments can be performed for all lattice structures, they are more time-consuming and tedious than the numerical homogenization methods, especially for lattice structures with complex geometry. In this study, a surrogate model is presented to address all the drawbacks mentioned above. More precisely, the effective elastic modulus of two-dimensional lattice structures with triangular unit cells is predicted by a surrogate model trained with the random forest algorithm. The dataset is generated from FE simulations. Several geometric details along with the elastic modulus of the parent material are selected as input features. These input features are varied to cover a wide range of lattice structures encountered in engineering applications. The correlation between input features is investigated to test their independence. Furthermore, the contribution of each input feature to the prediction of the surrogate models is also thoroughly examined. The accuracy of the proposed surrogate model is evaluated through comparisons with FE simulations, numerical homogenization methods, and experiments for untrained datasets.

Two-scale asymptotic homogenization analysis of piezoelectric composite materials in generalized curvilinear coordinates

This paper presents a comprehensive study on applying the two-scale asymptotic homogenization method to derive the effective properties of piezoelectric composite materials characterized by generalized periodicity in curvilinear coordinates. The methodology involves formulating the homogenization problem in a general curvilinear framework suitable for materials with complex geometric configurations. By systematically deriving the homogenized equations and effective coefficients, the paper provides a robust theoretical foundation for understanding the macroscopic behavior of piezoelectric composites under various loading conditions. The model’s versatility is demonstrated through its application to specific curvilinear coordinate systems, including the helix coordinate system and cylindrical coordinates with wavy geometry. These examples highlight the potential of the proposed approach in analyzing and designing piezoelectric materials with intricate geometries. The state-of-the-art numerical homogenization methods have also validated the proposed homogenization method, ensuring its accuracy and robustness.

Stretchable-thickness model for dynamic responses of graphene origami reinforced badminton sport plate

In this article, we organize a stretchable-thickness model to present a frequency analysis for a composite plate applicable in badminton court which is reinforced with origami graphene. A higher order kinematic model is extended in this work including three bending, shear, and stretching functions, where the stretching functions is responsible for satisfying the out of plane shear strains and stresses at top/bottom surfaces of the badminton equipment. The sport or composites plate is manufactured from a copper matrix reinforced with graphene origami where the effective material properties are calculated based on micromechanical models as a function of volume fraction and folding degree of graphene origami, material properties of matrix and reinforcement and temperature. The numerical results are presented with changes of volume fraction, folding degree of reinforcement, and thermal loading along the thickness direction. The main novelty of this work is accounting thickness stretching deformation for the analysis of a graphene origami reinforced plate and investigating the responses of graphene origami as a new reinforcement. A verification investigation is presented for approve of the methodology, and solution procedure. An investigation on the order of deformation is presented for various thickness ratio of the badminton sport plate.

Micromechanical analysis for effective elastic moduli and thermal expansion coefficient of composite materials containing ellipsoidal fillers oriented randomly

In this study, we examine to derive the solutions of effective elastic moduli and thermal expansion coefficient for composite materials containing ellipsoidal fillers oriented randomly in the material using homogenization theories, which are the self-consistent method and the Mori–Tanaka method. This analysis is carried out by micromechanics combining Eshelby’s equivalent inclusion method for each theory. The solutions for effective elastic moduli and thermal expansion coefficient obtained on each theory are expressed by common coefficients composed of both the physical properties of the constituents of the composite material and geometrical factors depending upon the shape of the fillers. Moreover, these solutions enable us to calculate effective elastic moduli and thermal expansion coefficient for composite materials that contain randomly oriented fillers of various shapes and physical properties. By taking the limit of eliminating the existence of the matrix for these solutions, we can derive effective physical properties of polycrystalline materials. Using the obtained solutions, we investigate the effects of the shape of the fillers on the effective elastic moduli and thermal expansion coefficient. As a result, we confirm that these effective properties fall within the lower and upper bounds, and find that a characteristic result appears when the shape of the fillers is flake or oblate. Through comparisons between the analytical and experimental results, we confirm the practical usability of the solutions obtained in this analysis. Furthermore, we determine originally the shape factor for the filler and can show that this factor has the potential to provide guidelines for the optimal design of filler shape to improve the effective elastic properties of materials.

Vibrations of viscoelastic FG porous graphene-platelets reinforced doubly-curved shells via experimental characterisation of graphene platelets

This work explores the vibrations of viscoelastic functionally-graded (FG) porous graphene-platelets reinforced doubly-curved shallow shells via experimental characterisations of graphene platelets. In particular, the effects of ultrasonication time of graphene platelets, on the vibrations of graphene-platelets reinforced shells, are studied. This is of interest because graphene platelets are often ultrasonicated in solvents to achieve better dispersions during the fabrication of graphene-platelets/epoxy composite structures. In this study, geometric characteristics of the graphene platelets under different sonication times are quantitatively and qualitatively analysed through experimental characterisation techniques, including a laser diffraction particle size analyser, a scanning electron microscopy (SEM), and a scanning force microscopy (SFM). The geometric characteristics of graphene platelets are considered in the effective material properties using a micromechanics model of Halpin-Tsai. Different FG distributions of graphene platelets and closed-cell porosity are modelled. The Kelvin-Voigt viscoelastic model is used to consider the internal friction-induced energy dissipation for the polymeric composite shell. Hamilton’s variational principle and an assumed mode method are used to derive and solve the equations of motion, respectively, for the vibrations of the doubly-curved shells. The effects of graphene platelets sonication time, in combination with the effects of graphene platelets weight fraction, porosity coefficient, FG distributions, shell thickness ratio, and shell curvature radii, are scrutinised. The results show that increasing ultrasonication time reduces the shell’s out-of-plane dimensionless fundamental frequency as a result of the reduction in graphene platelets aspect ratio.

Thermo-foldable bending analysis of tunable shells using a higher-order modeling

This article investigates effect of a higher order kinematic modeling on the elasto-static bending results of a shell in double curved form. The graphene origami is introduced in this article as a novel nanofiller with some chemical process to arrive at a controllable material. A copper matrix is used as main constituent reinforced with folded graphene origami. The virtual work principle is used to derive governing equations of the thickness-stretchable shell. After derivation of the governing equations and to arrive at the solution, a class of formulas is used from valid sources for effective material properties of the shell. A verification test is presented before exploring the effect of all main affecting parameters of the graphene origami and ambient on the bending results. The results of this work may be used in the analysis of structures with controllable responses.

Multi-load effect on the deformation analysis of composite nano reinforced origami sandwich panel

Graphene origami in a copper matrix is used as a composition of core in a sandwich panel between two piezoelectric/piezomagnetic layers. More accurate modeling of the composite sandwich structure is performed using a higher-order model including thickness stretching term. Principle of virtual work is used in order to derive governing equations in terms of resultant components of force and moment as well as electromagnetic loads. The resultant components are derived in higher-order framework with accounting electric and magnetic potentials using the effective material properties of graphene origami in Halpin-Tsai and rule of mixture framework. The deformation/strain/stress components are analytically obtained in terms of thermal, mechanical, electrical, and magnetic loads as well as folding degree and content of graphene origami. Verification is performed for justification of the numerical results. A foldability dependent parametric analysis is presented to show controllability of stress, strain and deformations along the thickness direction.

Dynamic Analysis of Functionally Graded Sandwich Doubly Curved Nanoshells Using Variable Nonlocal Elasticity Theory

Sandwich nanoshells consisting of functionally graded materials (FGMs) offer promise in aerospace, energy and biomedical applications due to their tunable properties. However, a comprehensive understanding of the vibration behavior of such shells is lacking. This work develops an efficient analytical model to study free vibration of sandwich nanoshells with three FGM configurations: FGM face-sheets and metal core (Type A), FGM face-sheets and ceramic core (Type B), and FGM core and face-sheets (Type C). A doubly curved shell geometry representing spherical, hyperbolic–parabolic and cylindrical shells in addition to flat plates is considered. Effective material properties of nanolaminates are computed using a volume fraction-based model. First-order shear deformation theory and modified nonlocal elasticity theory with variable nonlocal parameters are employed to derive the governing equations. Hamilton’s principle is used to obtain the equations of motion. Navier’s solution technique analytically solves the equations for simply supported boundary conditions. Accuracy is validated through comparisons with literature results. Parametric studies analyze the influence of thickness ratio, material gradation, nonlocal parameter, and shell type on frequencies. Results show that Type A configuration yields the highest frequencies. Dimensionless frequency decreases with increasing nonlocal parameter and side-to-thickness ratio. The model provides design insights into vibration behavior of such nanosandwich structures with potential applications in nanodevices and energy harvesting.