Lamb Waves Propagation Characteristics in Functionally Graded Sandwich Plates.

Functionally graded materials (FGM) have received extensive attention in recent years due to their excellent mechanical properties. In this research, the theoretical process of calculating the propagation characteristics of Lamb waves in FGM sandwich plates is deduced by combining the FGM volume fraction curve and Legendre polynomial series expansion method. In this proposed method, the FGM plate does not have to be sliced into multiple layers. Numerical results are given in detail, and the Lamb wave dispersion curves are extracted. For comparison, the Lamb wave dispersion curve of the sliced layer model for the FGM sandwich plate is obtained by the global matrix method. Meanwhile, the FGM sandwich plate was subjected to finite element simulation, also based on the layered-plate model. The acoustic characteristics detection experiment was performed by simulation through a defocusing measurement. Thus, the Lamb wave dispersion curves were obtained by V(f, z) analysis. Finally, the influence of the change in the gradient function on the Lamb wave dispersion curves will be discussed.

On the Computational Study of a Fully Wetted Longitudinal Porous Heat Exchanger Using a Machine Learning Approach.

The present study concerns the modeling of the thermal behavior of a porous longitudinal fin under fully wetted conditions with linear, quadratic, and exponential thermal conductivities surrounded by environments that are convective, conductive, and radiative. Porous fins are widely used in various engineering and everyday life applications. The Darcy model was used to formulate the governing non-linear singular differential equation for the heat transfer phenomenon in the fin. The universal approximation power of multilayer perceptron artificial neural networks (ANN) was applied to establish a model of approximate solutions for the singular non-linear boundary value problem. The optimization strategy of a sports-inspired meta-heuristic paradigm, the Tiki-Taka algorithm (TTA) with sequential quadratic programming (SQP), was utilized to determine the thermal performance and the effective use of fins for diverse values of physical parameters, such as parameter for the moist porous medium, dimensionless ambient temperature, radiation coefficient, power index, in-homogeneity index, convection coefficient, and dimensionless temperature. The results of the designed ANN-TTA-SQP algorithm were validated by comparison with state-of-the-art techniques, including the whale optimization algorithm (WOA), cuckoo search algorithm (CSA), grey wolf optimization (GWO) algorithm, particle swarm optimization (PSO) algorithm, and machine learning algorithms. The percentage of absolute errors and the mean square error in the solutions of the proposed technique were found to lie between 10-4 to 10-5 and 10-8 to 10-10, respectively. A comprehensive study of graphs, statistics of the solutions, and errors demonstrated that the proposed scheme's results were accurate, stable, and reliable. It was concluded that the pace at which heat is transferred from the surface of the fin to the surrounding environment increases in proportion to the degree to which the wet porosity parameter is increased. At the same time, inverse behavior was observed for increase in the power index. The results obtained may support the structural design of thermally effective cooling methods for various electronic consumer devices.

A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells.

This article explores a three-dimensional solid isogeometric analysis (3D-IGA) approach based on a nonlocal elasticity theory to investigate size effects on natural frequency and critical buckling load for multi-directional functionally graded (FG) nanoshells. The multi-directional FG material uses a power law rule with three power exponent indexes concerning three parametric coordinates. Nanoshell's geometries include the square plate, cylindrical and spherical panels with the side length considered in a nanoscale with various thickness ratios. Because 3D-IGA utilizes an approximation of NURBS basic functions to integrate from geometry modeling to discretized domain, it does not require any hypotheses for deformations distribution and stress component through the plate's thickness. Therefore, the results from the 3D solution are obtained accurately with any thickness ratio of the shells. The numerical solutions are verified by those published in several pieces of literature to determine the current approach's accuracy and reliability. After a convergence solution is examined, a quartic NURBS basic function can yield ultra-converged and high-accurate results with a low computational cost. The findings show the size effect parameters which significantly impact the frequencies and the critical buckling factors of the multi-directional FG nanoshells. Generally, increases in the size effect parameters will cause declines in the frequencies and the critical buckling factors of the nanoshells.

A computational framework for crack propagation in spatially heterogeneous materials.

This paper presents a mathematical formulation and numerical modelling framework for brittle crack propagation in heterogeneous elastic solids. Such materials are present in both natural and engineered scenarios. The formulation is developed in the framework of configurational mechanics and solved numerically using the finite-element method. We show the methodology previously established for homogeneous materials without the need for any further assumptions. The proposed model is based on the assumption of maximal dissipation of energy and uses the Griffith criterion; we show that this is sufficient to predict crack propagation in brittle heterogeneous materials, with spatially varying Young's modulus and fracture energy. Furthermore, we show that the crack path trajectory orientates itself such that it is always subject to Mode-I. The configurational forces and fracture energy release rate are both expressed exclusively in terms of nodal quantities, avoiding the need for post-processing and enabling a fully implicit formulation for modelling the evolving crack front and creation of new crack surfaces. The proposed formulation is verified and validated by comparing numerical results with both analytical solutions and experimental results. Both the predicted crack path and load-displacement response show very good agreement with experiments where the crack path was independent of material heterogeneity for those cases. Finally, the model is successfully used to consider the real and challenging scenario of fracture of an equine bone, with spatially varying material properties obtained from CT scanning. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.

Challenges on optimization of 3D-printed bone scaffolds.

Advances in biomaterials and the need for patient-specific bone scaffolds require modern manufacturing approaches in addition to a design strategy. Hybrid materials such as those with functionally graded properties are highly needed in tissue replacement and repair. However, their constituents, proportions, sizes, configurations and their connection to each other are a challenge to manufacturing. On the other hand, various bone defect sizes and sites require a cost-effective readily adaptive manufacturing technique to provide components (scaffolds) matching with the anatomical shape of the bone defect. Additive manufacturing or three-dimensional (3D) printing is capable of fabricating functional physical components with or without porosity by depositing the materials layer-by-layer using 3D computer models. Therefore, it facilitates the production of advanced bone scaffolds with the feasibility of making changes to the model. This review paper first discusses the development of a computer-aided-design (CAD) approach for the manufacture of bone scaffolds, from the anatomical data acquisition to the final model. It also provides information on the optimization of scaffold's internal architecture, advanced materials, and process parameters to achieve the best biomimetic performance. Furthermore, the review paper describes the advantages and limitations of 3D printing technologies applied to the production of bone tissue scaffolds.

Controlling and Optimizing Entropy Production in Transient Heat Transfer in Graded Materials.

This paper presents a numerical analysis of the transient heat transfer problem arising when a functionally graded material is subjected to a fixed temperature difference. Varying the gradation of the system, the thermal performance of the material is assessed both in time-dependent and steady-state conditions by means of temperature profiles and entropy production. One of the main contributions of this paper is the analysis of the system in the transient, from which it is found that the entropy production has a non-monotonic behaviour since maximum and minimum values of this physical quantity could be identified by varying the grading profile of the material. The latter allows to propose an optimization criterion for functionally graded materials which consists of the identification of spatial regions where temperature gradients are large and find thermal conductivity profiles that attenuate those gradients, thus reducing the thermal stresses present inside the material.

3D-Printing of Functionally Graded Porous Materials Using On-Demand Reconfigurable Microfluidics.

Tailoring the morphology of macroporous structures remains one of the biggest challenges in material synthesis. Herein, we present an innovative approach for the fabrication of custom macroporous materials in which pore size varies throughout the structure by up to an order of magnitude. We employed a valve-based flow-focusing junction (vFF) in which the size of the orifice can be adjusted in real-time (within tens of milliseconds) to generate foams with on-line controlled bubble size. We used the junction to fabricate layered and smoothly graded porous structures with pore size varying in the range of 80-800 µm. Additionally, we mounted the vFF on top of an extrusion printer and 3D-printed constructs characterized by a predefined 3D geometry and a controlled, spatially varying internal porous architecture, such as a model of a bone. The presented technology opens new possibilities in macroporous material synthesis with potential applications ranging from tissue engineering to aerospace industry and construction.

Functionally graded structures in the involucre of Job's tears.

Nature is filled with materials that are both strong and light, such as bones, teeth, bamboo, seashells, arthropod exoskeletons, and nut shells. The insights gained from analyzing the changing chemical compositions and structural characteristics, as well as the mechanical properties of these materials, have been applied in developing innovative, durable, and lightweight materials like those used for impact absorption. This research concentrates on the involucres of Job's tears (Coix lacryma-jobivar.lacryma-jobi), which are rich in silica, hard, and serve to encase the seeds. The chemical composition and structural characteristics of involucres were observed using scanning electron microscopy and energy-dispersive x-ray spectroscopy and optical microscopy with safranin staining. The hardness of the outer and inner surfaces of the involucre was measured using the micro-Vickers hardness test, and the Young's modulus of the involucre's cross-section was measured using nanoindentation. Additionally, the breaking behavior of involucres was measured through compression test and three-point bending tests. The results revealed a smooth transition in chemical composition, as well as in the orientation and dimensions of the tissues from the outer to the inner layers of involucres. Furthermore, it was estimated that the spatial gradient of the Young's modulus is due to the gradient of silica deposition. By distributing the hard, brittle silica in the outer layer and elastoplastic organic components in the middle and inner layers, the involucres effectively respond to compressive and tensile stresses that occur when loads are applied to the outside of the involucre. Furthermore, the involucres are reinforced in both meridional and equatorial directions by robust fibrovascular bundles, fibrous bundles, and the inner layer's sclerenchyma fibers. From these factors, it was found that involucres exhibit high toughness against loads from outside, making it less prone to cracking.

Biomechanical Evaluation of a Newly Developed Functional-Grade Composite Material for Pedicle Screws.

OBJECTIVE: Pedicle screw and rod systems are widely employed in spine surgeries and loosening due to insufficient mechanical stimulation on the bone is frequently encountered in pedicle screws. This mechanical stimulation problem also arises due to the high rigidity of the implant material. This study aimed to develop new pedicle screws with composite material to solve the pedicle screw loosening problem. METHODS: The vertebrae and vertebral disk were modeled in three dimension using computerized tomography images obtained from a patient. A commercially available pedicle screw was modeled using Fusion software, and all models were assembled in accordance with the surgical procedure. Pedicle screw models were also divided radially and longitudinally to resemble functionally graded materials, which are composite materials. The load was applied to the top of the T12 vertebra and the screw-vertebral system was fixed to the bottom of the L1 vertebra. RESULTS: The strain results on the vertebrae were examined according to the mechanostat theorem. According to the results, functionally graded material (FGM) pedicle screw decreased the strain on the vertebral bones, and the positive effects on the bone were determined when using the radially functionally graded screws. The maximum stress values were also examined to determine the strengths of all the models. CONCLUSION: In conclusion, FGM pedicle screw decreased the strain on the bone which is an important parameter for the loosening failure according to the study. The other important conclusion is that FGM pedicle screw can be the solution to the loosening of the screw but not in all vertebrae.

Machine Learning for Additive Manufacturing of Functionally Graded Materials.

Additive Manufacturing (AM) is a transformative manufacturing technology enabling direct fabrication of complex parts layer-by-layer from 3D modeling data. Among AM applications, the fabrication of Functionally Graded Materials (FGMs) has significant importance due to the potential to enhance component performance across several industries. FGMs are manufactured with a gradient composition transition between dissimilar materials, enabling the design of new materials with location-dependent mechanical and physical properties. This study presents a comprehensive review of published literature pertaining to the implementation of Machine Learning (ML) techniques in AM, with an emphasis on ML-based methods for optimizing FGMs fabrication processes. Through an extensive survey of the literature, this review article explores the role of ML in addressing the inherent challenges in FGMs fabrication and encompasses parameter optimization, defect detection, and real-time monitoring. The article also provides a discussion of future research directions and challenges in employing ML-based methods in the AM fabrication of FGMs.

Exploring Advanced Functionalities of Carbon Fiber-Graded PEEK Composites as Bone Fixation Plates Using Finite Element Analysis.

This study aims to address the challenges associated with conventional metallic bone fixation plates in biomechanical applications, such as stainless steel and titanium alloys, including stress shielding, allergic reactions, corrosion resistance, and interference with medical imaging. The use of materials with a low elastic modulus is regarded as an effective approach to overcome these problems. In this study, the impact of different types of chopped carbon fiber-reinforced polyether ether ketone (CCF/PEEK) functionally graded material (FGM) bone plates on stress shielding under static and instantaneous dynamic loading was explored using finite element analysis (FEA). The FGM bone plate models were established using ABAQUS and the user's subroutine USDFLD and VUSDFLD, and each model was established with an equivalent overall elastic modulus and distinctive distributions. The results revealed that all FGM bone plates exhibited lower stress shielding effects compared to metal bone plates. Particularly, the FGM plate with an elastic modulus gradually increased from the centre to both sides and provided maximum stress stimulation and the most uniform stress distribution within the fractured area. These findings offer crucial insights for designing implantable medical devices that possess enhanced mechanical adaptability.

The effects of different grading approaches in additively manufactured dental implants on peri-implant bone stress: A finite element analysis.

Additive manufacturing enables local grading of the stiffness of dental implants through targeted adjustment of the manufacturing parameters to meet patient specific requirements. The extent to which such a manufacturing approach affects the interaction between the implant body and the surrounding bone, and what grading is optimal, is currently insufficiently investigated. This study investigates the effect of different Young's modulus grading approaches on stresses in the peri-implant bone via finite element analysis. The implant geometry was kept constant and in the case of the implant a node-dependent elastic modulus was assigned. In this way, a vertical, a radial and three torus based grading approaches were created and examined. A load was then applied directly to the occlusal surface of the implant crown. It was found that a local grading utilizing a torus shape was most favourable in terms of an effective stress peak reduction. The best torus shape tested achieved a 22 % reduction of maximum principal stress and 6 % reduction of minimum principal stress compared to the uniform material. In clinical settings, this may provide benefits in situations of overload. Based on the results, a graded stiffness in dental implants appears to be of interest for developing advanced, patient-specific implant solutions.

Evaluating the effect of functionally graded materials on bone remodeling around dental implants.

OBJECTIVES: This study evaluates the potential for osseointegration and remodeling of customized dental implants made from Titanium-Hydroxyapatite Functionally Graded Material (Ti-HAP FGM) with optimized geometry, using the finite element method (FEM). METHODS: The study utilized CT scan images to model and assemble various geometrical designs of dental implants in a mandibular slice. The mechanical properties of Ti-HAP FGMs were computed by varying volume fractions (VF) of hydroxyapatite (0-20%), and a bone remodeling algorithm was used to evaluate the biomechanical characteristics of the ultimate bone configuration in the peri-implant tissue. RESULTS: The findings of the FEA reveal that osseointegration improves with changes in the density and mechanical properties of the bone surrounding Ti-HAP implants, which are influenced by the varying VF of hydroxyapatite in the FGM. SIGNIFICANCE: Increasing the hydroxyapatite fraction improves osseointegration, and appropriate length and diameter selection of Ti-HAP dental implants contribute to their stability and longevity.

Study on Optimization Strategy for the Composition Transition Gradient in SS 316L/Inconel 625 Functionally Graded Materials.

Wire arc additive manufacturing (WAAM) technology enables the fabrication of functionally graded materials (FGMs) by adjusting the wire feed speed of different welding wires in a layer-by-layer manner. This study aimed to produce SS 316L/Inconel 625 FGMs with varying transition compositions using dual-wire arc additive manufacturing (D-WAAM). An optimization strategy for transition gradients was implemented to exclude component regions that are prone to defect formation (notably cracking), as well as to retain other component regions, thereby enhancing the overall mechanical properties of FGMs. The study revealed grain boundary cracking and demonstrated the lowest microhardness and tensile properties within a 20 wt.% Inconel 625 transition gradient zone, which negatively impacts the overall mechanical properties of FGMs. Then, as the content of Inconel 625 in the first transition region increased, cracks disappeared, microhardness increased and better tensile properties were obtained. The most optimal mechanical properties were enriched at 50 wt.% Inconel 625 content. In conclusion, the compositional gradient optimization strategy proves efficacious in eliminating component regions with poor mechanical properties and microdefects, ensuring excellent overall mechanical characteristics of FGMs.

Methodological approaches in graded dental ceramics.

BACKGROUND: Functionally graded materials (FGM) with indistinct boundaries potentially eliminate the damaging stresses occurring at the interfaces. FGM applications in dental ceramics have enhanced their fatigue resistance and interfacial toughness. OBJECTIVES: This scoping review aims to map graded designs in dental ceramics, distinguish their methodological approaches with their material characteristics and properties, and understand the factors affecting the outcomes of each of the graded approaches. METHODS: A systematic electronic search was performed with the databases MEDLINE (PubMed), Scopus, Cochrane Library, EBSCO, and Google Scholar along with a manual search. RESULTS: About 2675 articles were initially found from all the searches with no date restriction till July 2023. After rejecting duplicates and based on exclusion criteria, about 52 articles were included. SIGNIFICANCE: Methodological approaches in grading such as glass-infiltration and silica-infiltration have been investigated on pre-sintered zirconia. The type of infiltration and the method of infiltrate application significantly influenced the phase transformation of zirconia, its microstructure, surface hardness, fracture toughness, flexural strength, wear, and fatigue strength of graded dental zirconia. Interlayers were accommodated between metal-ceramic and veneer-core all-ceramic layers. Fractions of zirconia-porcelain and alumina-porcelain showed high bending strength and better stress distribution. The results of finite element analysis studies predicted that using 10-layered graded layers reduced the stresses at the crown-cement-dentin interface.

Fabrication of translucent graded dental crown using zirconia-yttrium multi-slurry tape casting 3D printer.

This paper aims to fabricate functionally graded dental crown using a multi-slurry tape casting additive manufacturing technology. The different luminescence of the dental crown was obtained with different composition of zirconia and yttria. Zirconia with tunable mechanical properties and translucency are obtained by adding 3, 3.5, 4, 4.5, and 5 mol% of yttrium oxide to zirconia powder. After obtaining the printable slurry with maximum solid loading, the green bodies are prepared using the in-house built high-speed multi-ceramic tape casting technology. They are later sintered with two-stage sintering method. After the successful fabrication, the mechanical properties and translucency of the specimens were evaluated with Vickers hardness, three-point bending and translucency parameter tests. Finally, an FGM tooth crown with five photocurable slurries is proposed to demonstrate the translucent gradient effect of sintered part. The solid loading of 80% zirconia and 20% resin delivered samples without any surface cracks. The shrinkage ratio analysis showed that the sintered sample dimension was reduced by 20%, 20%, and 23% along X, Y, and Z directions. The samples fabricated with 3% yttrium oxide to zirconia delivered excellent hardness (1687 HV) and flexural strength (650.6 MPa). However, the relative luminescence increased with increasing the yttrium oxide for 3-5 mol%. With the optimized process parameters, the proposed dental crown is fabricated and analyzed for their shrinkage ratio, mechanical, and translucency properties. The study proposes the potential of fabricating customized dental crown with gradient translucent appearance.

Application of Surface Stress-Driven Model for Higher Vibration Modes of Functionally Graded Nanobeams.

This paper employs a surface stress-driven nonlocal theory to investigate the synergistic impact of long-range interaction and surface energy on higher vibration modes of Bernoulli-Euler nanobeams made of functionally graded material. It takes into account surface effects such as the surface modulus of elasticity, residual surface stresses, surface density, and rotary inertia. The governing equation is derived through the application of Hamilton's principle. The novelty of this work lies in its pioneering approach to studying higher-order vibrations, carefully considering the combination of long-range interactions and surface energy in nanobeams of functionally graded materials through a well-posed mathematical model of nonlocal elasticity. This study conducts a parametric investigation, examining the effects of the nonlocal parameter and the material gradient index for four static schemes: Cantilever, Simply-Supported, Clamped-Pinned and Clamped-Clamped nanobeams. The outcomes are presented and discussed, highlighting the normalized nonlocal natural frequencies for the second through fifth modes of vibration in each case under study. In particular, this study illustrates the central role of surface effects in the dynamic response of nanobeams, emphasizing the importance of considering them. Furthermore, the parametric analysis reveals that the dynamic response is influenced by the combined effects of the nonlocal parameter, the material gradient index, the shapes of the cross-sections considered, as well as the static scheme analyzed.

Use of Functionally Graded Material to Decrease Maximum Temperature of a Coating-Substrate System.

A mathematical model for determining the temperature distribution in the system consisting of a coating deposited on the surface of substrate was proposed. The foundation material is homogeneous, while the coating is made of a functionally gradient material (FGM) with thermal conductivity increasing exponentially along the thickness. Heating processes of the outer surface of the coating were considered with a constant and linearly decreasing in time intensity of the heat flux. Such thermal loads are common in thermal problems of friction, particularly regarding frictional heating during braking. An exact (in quadrature) solution of the corresponding boundary-value problems of parabolic heat conduction was obtained. Asymptotic solutions to these problems were also found for small and large values of the Fourier number. Calculations were performed for a coating made of two-component FGM ZrO2-Ti-6Al-4V, applied on a cast iron substrate. In order to explain the effect of FGM on temperature, corresponding analysis was carried out for the coating made of a homogeneous (ZrO2) material.

Temperature during Repetitive Short-Term Operation of a Brake with Functionally Graded Friction Element.

The object of study is the temperature of a braking system, operating in repetitive short-term (RST) mode. One element of the considered friction pair is made of a functionally gradient material (FGM), and the other of a homogeneous material. To determine the temperature on the friction surfaces of both elements, the previously obtained, exact solution of the boundary value problem of heat conduction was adopted, with account of the heat generation due to the friction. A calculation scheme was proposed that takes into consideration thermal sensitivity of materials and variations of the friction coefficient under the influence of temperature. Calculations were performed for two-component FGM (ZrO2-Ti-6Al-4V) in combination with gray cast iron (ChNMKh). It was found that for selected friction pair materials, consideration of their thermal sensitivity reduces the time of braking and the value of temperature achieved on the friction surfaces. At the same time, the whole process was characterized by a good stability of braking with a slight decrease in efficiency in each subsequent cycle.

Design and Modification of a Material Extrusion 3D Printer to Manufacture Functional Gradient PEEK Components.

In recent years, the creative use of polymers has been expanded as the range of achievable material properties and options for manufacturing and post-processing continually grows. The main goal of this research was to design and develop a fully-functioning material extrusion additive manufacturing device with the capability to produce functionally graded high-temperature thermoplastic PEEK (polyether ether ketone) materials through the manipulation of microstructure during manufacturing. Five different strategies to control the chamber temperature and crystallinity were investigated, and concepts of thermal control were introduced to govern the crystallisation and cooling mechanics during the extrusion process. The interaction of individually deposited beads of material during the printing process was investigated using scanning electron microscopy to observe and quantify the porosity levels and interlayer bonding strength, which affect the quality of the final part. Functional testing of the printed parts was carried out to identify crystallinity, boundary layer adhesion, and mechanical behaviour. Furnace cooling and annealing were found to be the most effective methods, resulting in the highest crystallinity of the part. Finally, a functionally graded material cylindrical part was printed successfully, incorporating both low and high crystalline regions.