Functional Grading of a Transversely Isotropic Hyperelastic Model with Applications in Modeling Tricuspid and Mitral Valve Transition Regions.

Surgical simulators and injury-prediction human models require a combination of representative tissue geometry and accurate tissue material properties to predict realistic tool-tissue interaction forces and injury mechanisms, respectively. While biological tissues have been individually characterized, the transition regions between tissues have received limited research attention, potentially resulting in inaccuracies within simulations. In this work, an approach to characterize the transition regions in transversely isotropic (TI) soft tissues using functionally graded material (FGM) modeling is presented. The effect of nonlinearities and multi-regime nature of the TI model on the functional grading process is discussed. The proposed approach has been implemented to characterize the transition regions in the leaflet (LL), chordae tendinae (CT) and the papillary muscle (PM) of porcine tricuspid valve (TV) and mitral valve (MV). The FGM model is informed using high resolution morphological measurements of the collagen fiber orientation and tissue composition in the transition regions, and deformation characteristics predicted by the FGM model are numerically validated to experimental data using X-ray diffraction imaging. The results indicate feasibility of using the FGM approach in modeling soft-tissue transitions and has implications in improving physical representation of tissue deformation throughout the body using a scalable version of the proposed approach.

Accurate and Efficient Thermal Stress Analyses of Functionally Graded Solids Using Incompatible Graded Finite Elements.

Functionally graded materials have found a wide usage in high temperature applications. The smooth transition from one material to another, in graded materials, may reduce thermal stresses, residual stresses and stress concentration factors as well as utilize properties of both materials. To perform accurate and efficient finite element analysis for heat transfer and transient thermal stress analyses in two-dimensional functionally graded materials, incompatible graded finite elements are developed and verified. User-defined subroutines in ABAQUS are developed to address the gradation of material properties within an element. An emphasis is made on an incompatible graded finite element (QM6) which is accurate and efficient compared to linear four-node (Q4) and quadratic eight-node (Q8) elements. With the help of posteriori error estimation, a critical comparison is made among three types of solid elements. Modified 6-node (QM6) incompatible graded elements provide better accuracy than Q4 elements and take less computational time than Q8 elements, thereby showing QM6 as an optimal element for engineering analysis.

Solid lubricant behavior of MoS2 and WSe2-based nanocomposite coatings.

Tribological coatings made of MoS2 and WSe2 phases and their corresponding combinations with tungsten carbide (WC) were prepared by non-reactive magnetron sputtering of individual targets of similar composition. A comparative tribological analysis of these multiphase coatings was done in both ambient air (30-40% relative humidity, RH) and dry nitrogen (RH<7%) environments using the same tribometer and testing conditions. A nanostructural study using advanced transmission electron microscopy of the initial coatings and examination of the counterfaces after the friction test using different analytical tools helped to elucidate what governs the tribological behavior for each type of environment. This allowed conclusions to be made about the influence of the coating microstructure and composition on the tribological response. The best performance obtained with a WSex film (specific wear rate of 2 × 10-8 mm3 N-1m-1 and a friction coefficient of 0.03-0.05) was compared with that of the well-established MoS2 lubricant material.

Stiffness and stability of bamboo stem- A optimal design perspective.

During the evolution process, a bamboo stem achieves a significant height (up to 20 m) to fulfil its phototropic requirements. While on land, the stem is mostly subjected to bending load which makes it liable to fail by uprooting. However, this failure is prohibited by smart structure of bamboo stem which includes graded arrangement of fibre bundles in the cross-section and a tapered cantilever form of the stem. This paper attempts to understand the optimal design of bamboo stem through the relationship between the stellar arrangement of stiff fibre bundles in the cross-section and the tapered form. In this work, a comparison between two types of stellar arrangement, namely uniform and graded, is presented in view of non-linear bending analysis through elastica theory and fracture-induced delamination, both numerically. It is observed from the results that a bamboo stem prefers to evolve with graded stellar arrangement which provides gradation of stiffness and toughness over the cross-section; the trend in toughness being opposite to that of stiffness. Moreover, interplay of stellar arrangement and gradation of stiffness-toughness thereof is found to be the governing mechanism for ensuring its mechanical integrity and stability in view of an optimal design perspective. The smart structure of bamboo is recommended for bio-mimicking.

A parametrical finite element analysis for functionally graded material overlay restoration.

The main cause of failure in bonded ceramic restorations is material fracture due to excessive stress concentration at the base of the prosthesis. The design of restorative functionally graded materials (FGM) could represent a major advance in dissipating mechanical stresses during occlusal contacts. The aim of this paper is to carry out a complete factorial design of finite element analyses to optimize a multilayer FGM introduced at the bottom of an overlay prosthesis. The number and thickness of layers vary within a spectrum compatible with ceramic shaping processes whereas Young's moduli variations are set in the range of dental tissues. For a 1.5-mm thick prosthesis, the optimal FGM configuration appears to be a 5 layers of 0.2 mm thickness with a linear distribution of Young's modulus from 30 to 70 GPa. This configuration was implemented in a 3D model of a restored tooth with realistic geometry to validate the proof-of-concept.

A numerical investigation for the development of functionally graded Ti/HA tibial implant for total ankle replacement: Influence of material gradation law and volume fraction index.

Stress shielding is one of the major concerns for total ankle replacement implants nowadays, because it is responsible for implant-induced bone resorption. The bone resorption contributes to the aseptic loosening and failure of ankle implants in later stages. To reduce the stress shielding, improvements can be made in the implant material by decreasing the elastic mismatch between the implant and the tibia bone. This study proposes a new functionally graded material (FGM) based tibial implant for minimizing the problem of stress shielding. Three-dimensional finite element (FE) models of the intact tibia and the implanted tibiae were created to study the influence of material gradation law and volume fraction index on stress shielding and implant-bone micromotion. Different implant materials were considered that is, cobalt-chromium, titanium (Ti), and FGM with Ti at the bottom and hydroxyapatite (HA) at the top. The FE models of FGM implants were generated by using different volume fractions and the rule of mixtures. The rule of mixtures was used to calculate the FGM properties based on the local volume fraction. The volume fraction was defined by using exponential, power, and sigmoid laws. For the power and sigmoid law varying volume fraction indices (0.1, 0.2, 0.5, 1, 2, and 5) were considered. The geometry resembling STAR® ankle system tibial implant was considered for the present study. The results indicate that FGMs lower stress shielding but also marginally increase implant-bone micromotion; however, the values were within the acceptable limit for bone ingrowth. It is observed that the material gradation law and volume fraction index influence the performance of FGM tibial implants. The tibial implant composed of FGM using power law with a volume fraction index of 0.1 was the preferred option because it showed the least stress shielding.

Functionally graded thick-walled tubes analysis by numerical methods.

Functionally graded materials are increasingly used in the practice of engineering design, as is the case with thick-walled tubes. The use of these constructive elements requires a calculation, which should be as accurate, as accessible and as fast as possible. The present work responds to these requirements. For the calculation of tubes with thick walls made of functionally graded materials, two new ways were used, based on the concepts of multilayer (material) wall and equivalent material. The multi-layered wall concept considers the tube wall made of several layers, as in the case of the well-known multilayer plates, and the equivalent material concept considers the thick-walled tube made of homogeneous and isotropic material, but with fictitious properties, equivalent in behavior to the functionally graded material. The influence of Poisson's ratio is illustrated by some comparative results. The development of the calculus, the validation of the models and the analysis of the results are based on the numerical calculus using the finite element method. The models used, the transverse plane model, the axial-symmetric plane model and the 3D longitudinal model, are made in several variants regarding the fineness of the mesh. The paper also analyzes the influence of the Poisson ratio variation, compared to adopting a constant value. The results of the study, the models and concepts used are useful to specialists and designers of structures of this type, they have a high degree of generality and present openings for the use of other calculation methods.

Printable functionally graded tibial implant for TAR: FE study comparing implant materials, FGM properties, and implant designs.

Tibial implants with functionally graded material (FGM) for total ankle replacement (TAR) can provide stiffness similar to the host tibia bone. The FGM implants with low stiffness reduce stress shielding but may increase implant-bone micromotion. A trade-off between stress shielding and implant-bone micromotion is required if FGMs are to substitute traditionally used Ti and CoCr metal implants. The FGM properties such as material gradation law and volume fraction index may influence the performance of FGM implants. Along with the FGM properties, the design of FGM implants may also have a role to play. The objective of this study was to examine FGM tibial implants for TAR, by comparing implant materials, FGM properties, and implant designs. For this purpose, finite element analysis (FEA) was conducted on 3D FE models of the intact and the implanted tibia bone. The tibial implants were composed of CoCr and Ti, besides them, the FGM of Ti and HA was developed. The FGM implants were modelled using exponential, power, and sigmoid laws. Additionally, for power and sigmoid laws, different volume fraction indices were taken. The effect of implant design was observed by using keel type and stem type TAR fixation designs. The results indicated that FGM implants are better than traditional metal implants. The power law is most suitable for developing FGM implants because it reduces stress shielding. For both power law and sigmoid law, low values of the volume fraction index are preferrable. Therefore, FGM implant developed using power law with 0.1 vol fraction index is ideal with the lowest stress shielding and marginally increased implant-bone micromotion. FGM implants are more useful for keel type fixation design than stem type design. To conclude, with FGMs the major complication of stress shielding can be solved and the longevity and durability of TAR implants can be enhanced.

Functionally graded bi-material interface for Porcelain Veneered Zirconia dental crowns: A study using viscoelastic finite element analysis.

OBJECTIVES: During the manufacturing of Porcelain Veneered Zirconia (PVZ) dental crowns, the veneer-core system undergoes high-temperature firing cycles and gets fused together which is then, under a controlled setting, cooled down to room temperature. During this cooling process, the mismatch in thermal properties between zirconia and porcelain leads to the development of transient and residual thermal stresses within the crown. These thermal stresses are inherent to the PVZ dental crown systems and render the crown structure weak, acting as a precursor to veneer chipping, fracture, and delamination. In this study, the introduction of an intermediate functionally graded material (FGM) layer at the bi-material interface is investigated as a potentially viable alternative for providing a smoother transition of properties between zirconia and porcelain in a PVZ crown system. METHODS: Anatomically correct 3D crown models were developed for this study, with and without the FGM layer modeled at the bi-material interface. A viscoelastic finite element model was developed and validated for an anatomically correct bilayer PVZ crown system which was then used for predicting residual and transient stresses in the bilayer PVZ crown. Subsequently, the viscoelastic finite element model was further extended for the analysis of graded sublayers within the FGM layer, and this extended model was used for predicting the residual and transient stresses in the functionally graded PVZ crown, with an FGM layer at the bi-material interface. RESULTS: The study showed that the introduction of an FGM layer at the bi-material interface has the potential to reduce the effects from transient and residual stresses within the PVZ crown system relative to a bilayer PVZ crown structure. Furthermore, the study revealed that the FGM layer causes stress redistribution to alleviate the stress concentration at the interfacial surface between porcelain and zirconia which can potentially enhance the durability of the PVZ crowns towards interfacial debonding or fracture. SIGNIFICANCE: Thus, the use of an FGM layer at the bi-material interface shows a good prospect for enhancing the longevity of the PVZ dental crown restorations by alleviating the abrupt thermal property difference and relaxing thermal stresses.

Finite element analysis of a generalized rotating FGM vessel subjected to thermo-mechanical loadings: Effect of Poisson ratio and inhomogeneity parameters.

Cylinders and thick walled cylindrical shells are commonly utilized in several industries to transport and store fluids under certain pressure and temperature conditions. In the present paper, a numerical solution is developed in order to investigate displacement, temperature and stress fields in a rotating pressure vessel made of generalized functionally graded material (FGM) subjected to different thermo-mechanical boundary conditions. The aim is to investigate the effect of Poisson ratio, internal pressure and temperature and inhomogeneity parameters on the stress and deformation distributions of the rotating pressure vessel. The material is considered isotropic nonhomogeneous and linearly elastic with its properties varying along the radial direction. Additionally, certain conditions, such as exterior or interior problems where r → ∞ or r → 0, respectively, are impossible to resolve using the variation of attributes as a power-law distribution. An approach to the spatial Young modulus distribution that is more broad has been suggested in the literature which can be applied to such physical challenges. The rotation of the pressure vessel is considered in the analysis, and the temperature distribution is assumed to be non-uniform. Since an analytical solution to the differential equation is not accessible, the conventional Galerkin discretization approach of the Finite Element Method (FEM) is applied, nowadays is considered one of the main numerical tools for solving Boundary Value Problems (BVP). It is addressed how stress, strain, and displacement are affected by the inhomogeneity parameter, rotation speed, pressure, temperature, and Poisson ratio. The examination of the various findings indicates that changes in the temperature profile, rotation, and inhomogeneity parameter on the thermoelastic field have a substantial impact on the stress and strain in the FGM cylinder. The findings indicate that the Poisson ratio and inhomogeneity parameters have a significant impact on the stress and deformation distributions. According to the results, the above-mentioned parameters can be adapted to control the thermoelastic filed in a FGM cylinder. The present research offers significant perspectives on the development and enhancement of rotating FGM pressure vessels intended for high-temperature applications.

Effect of Convective Cooling on the Temperature in a Friction System with Functionally Graded Strip.

An exact solution of the boundary-value problem of heat conduction was obtained with consideration of heat generation due to friction and convective cooling for the strip/semi-space system. Analytical solutions to this problem are known for the case with both friction elements made of homogeneous materials or a composite layer with a micro-periodic structure. However, in this study, the strip is made of a two-component functionally gradient material (FGM). In addition, the exact, asymptotic solutions were also determined at small and large values of the Fourier number. By means of Duhamel's theorem, it was shown that the developed solution for a constant friction power allows to obtain appropriate solutions with a changing time profile of this value during heating. Numerical analysis in dimensionless form was carried out for the FGM (ZrO2-Ti-6Al-4V) strip in combination with the cast iron semi-space. The influence of the convective cooling intensity (Biot number) on the temperature field in the considered friction system was investigated. The developed mathematical model allows for a quick estimation of the maximum temperature of systems, in which one of the elements (FGM strip) is heated on the friction surface and cooled by convection on the free surface.

The Mutual Influence of Thermal Contact Conductivity and Convective Cooling on the Temperature Field in a Tribosystem with a Functionally Graded Strip.

An analytical model to find the temperature field that has been developed for friction systems consists of a strip and semi-space. The strip is made of a two-component functionally graded material (FGM) with an exponentially changing coefficient of thermal conductivity. In contrast, the material of the semi-space is homogeneous. An appropriate boundary-value problem of heat conduction with constant specific friction power was formulated and solved using the Laplace integral transform method. The model takes into consideration the imperfect thermal friction contact between the strip and the semi-space, and also the convective cooling on the exposed surface of the strip. The appropriate asymptotic solutions to this problem for low and high values of Fourier number were obtained. It is shown how the determined exact solution can be generalized using Duhamel's formula for the case of a linearly reduction in time-specific friction power (a braking process with constant deceleration). Numerical analysis for selected materials of the friction pair was carried out in terms of examining the mutual impact on the temperature of the two Biot numbers, characterizing the intensity of the thermal contact conductivity and convective heat exchange on the exposed surface of the strip. The obtained results can be used to predict the temperature of friction systems containing elements made of FGM. In particular, such systems include modern disc braking systems.

Finite element analysis of FGM dental crowns using phase-field approach.

Functionally graded materials (FGMs) - categorized in advanced composite materials - are specially designed to reduce the stresses and failure due to material mismatches. Advances in manufacturing techniques have brought FGMs into use in a variety of applications. However, the numerical analysis is still challenging due to the difficulties in simulations of non-homogeneous material domains of complex parts. Presenting a numerical procedure that both facilitates the implementation of material non-homogeneity in geometrically complex mediums, and increases the accuracy of the calculations using a phase-field approach, this study investigates the usage of FGMs in dental prostheses. For this purpose, a porcelain fused to metal (PFM) mandibular first molar FGM crown is simulated and analyzed under the maximum masticatory bite force, and eventually the results are compared to a PFM crown prepared conventionally.

Effect of Functionally Graded Material (FGM) Interlayer in Metal Additive Manufacturing of Inconel-Stainless Bimetallic Structure by Laser Melting Deposition (LMD) and Wire Arc Additive Manufacturing (WAAM).

Bimetallic structures manufactured by direct deposition have a defect due to the sudden change in the microstructure and properties of dissimilar metals. The laser metal deposition (LMD)-wire arc additive manufacturing (WAAM) process can alleviate the defect between two different materials by depositing the functionally graded material (FGM) layer, such as a thin intermediate layer using LMD and can be used to fabricate bimetallic structures at high deposition rates with relatively low costs using WAAM. In this study, the LMD-WAAM process was performed, and the microstructure of the fabricated bimetallic structure of IN625-SUS304L was investigated. The microstructure of the FGM zone of the LMD-WAAM sample was mainly fine equiaxed dendrite morphologies. In contrast, coarse columnar dendrite morphologies constituted the WAAM zone. The composition of the major alloying elements of the LMD-WAAM sample gradually changed with the height of the deposited layer. The microhardness of the LMD-WAAM sample tended to increase with an increasing Inconel content. In the case of the LMD-WAAM sample, the fracture occurred near the interface between 25% IN625 and 0% IN625; in the WAAM sample, the final fracture occurred in SUS304L near the interface. The tensile strength of the LMD-WAAM samples was inversely proportional to the laser power. The results showed that the LMD-WAAM samples had 8% higher tensile strength than the samples fabricated using only WAAM.

Influence of Functionally Graded Protective Coating on the Temperature in a Braking System.

A mathematical model of heat generation due to friction in a disc-pad braking system was developed with consideration of a thermal barrier coating (TBC) on the friction surface of the disc. The coating was made of functionally graded material (FGM). The three-element geometrical scheme of the system consisted of two homogeneous half-spaces (pad and disc) and a functionally graded coating (FGC) deposited on the friction surface of the disc. It was assumed that the frictional heat generated on the coating-pad contact surface was absorbed to the insides of friction elements along the normal to this surface. Thermal contact of friction between the coating and the pad as well as the heat contact between the coating and the substrate were perfect. On the basis of such assumptions, the thermal friction problem was formulated, and its exact solution was obtained for constant and linearly descending specific friction power over time. For the first case, the asymptotic solutions for small and large values of time were also found. A numerical analysis was performed on an example of the system containing a metal ceramic (FMC-11) pad, sliding on the surface of a FGC (ZrO2-Ti-6Al-4V) applied on a cast iron (ChNMKh) disc. It was established that the application of a TBC made of FGM on the surface of a disc could effectively reduce the level of temperature achieved during braking.

Mechanical behavior of an FGM-type frozen soil wall: Theory and numerical analysis.

With a laminate model foundation, we have used the complex variable function method to calculate the boundary displacement and stress of a frozen soil wall in a horizontal connecting passage. Using an actual engineering case, the effects of the number of divided layers of a functionally graded material-type frozen soil wall, the position of the freezing pipe and the section shape of the connecting passage on the displacements and tangential stresses of the frozen soil wall are discussed. The results indicate that the frozen soil wall as a temporary support structure exhibits a good supporting effect. With the increase of layers, the material strength of the frozen soil wall weakens, and the displacements and tangential stresses of the inner boundary increase. When the midline of the freezing pipe moves toward the inner boundary, the tensile area in the frozen soil wall begins to shift, and the displacements and tangential stresses of the inner boundary decrease differently. Thedistributions of internal boundary displacements and tangential stresses are significantly affected by the section shape of the frozen soil wall, and the internal boundary displacements and tangential stresses of the frozen soil wall of the small section are more uniform than those of the frozen soil wall of the large section.

Parametric Analysis of Thick FGM Plates Based on 3D Thermo-Elasticity Theory: A Proper Generalized Decomposition Approach.

In the present work, the general and well-known model reduction technique, PGD (Proper Generalized Decomposition), is used for parametric analysis of thermo-elasticity of FGMs (Functionally Graded Materials). The FGMs have important applications in space technologies, especially when a part undergoes an extreme thermal environment. In the present work, material gradation is considered in one, two and three directions, and 3D heat transfer and theory of elasticity equations are solved to have an accurate temperature field and be able to consider all shear deformations. A parametric analysis of FGM materials is especially useful in material design and optimization. In the PGD technique, the field variables are separated to a set of univariate functions, and the high-dimensional governing equations reduce to a set of one-dimensional problems. Due to the curse of dimensionality, solving a high-dimensional parametric problem is considerably more computationally intensive than solving a set of one-dimensional problems. Therefore, the PGD makes it possible to handle high-dimensional problems efficiently. In the present work, some sample examples in 4D and 5D computational spaces are solved, and the results are presented.

Current status on manufacturing routes to produce metal matrix composites: State-of-the-art.

Owing to its excellent properties, Metal Matrix Composites (MMC) has gained popularity and finds application in aerospace, aircraft, shipbuilding, biomedical, biodegradable implant materials and many more. To serve the industrial needs, the manufactured MMC should have homogenous distribution along with minimum agglomeration of reinforcement particles, defect-free microstructure, superior mechanical, tribological and corrosive properties. The techniques implemented to manufacture MMC highly dominate the aforementioned characteristics. According to the physical state of the matrix, the techniques implemented for manufacturing MMC can be classified under two categories i.e. solid state processing and liquid state process. The present article attempts to review the current status of different manufacturing techniques covered under these two categories. The article elaborates on the working principles of state-of-the-art manufacturing techniques, the effect of dominating process parameters and the resulting characteristic of composites. Apart from this, the article does provide data regarding the range of dominating process parameters and resulting mechanical properties of different grades of manufactured MMC. Using this data along with the comparative study, various industries and academicians will be able to select the appropriate techniques for manufacturing MMC.

Numerical Modeling of Mechanical Behavior of Functionally Graded Polylactic Acid-Acrylonitrile Benzidine Styrene Produced via Fused Deposition Modeling: Experimental Observations.

Functionally graded materials (FGM) have attracted considerable attention in the field of composite materials and rekindled interest in research on composite materials due to their unique mechanical response achieved through material design and optimization. Compared to conventional composites, FGMs offer several advantages and exceptional properties, including improved deformation resistance, improved toughness, lightness properties, and excellent recoverability. This study focused on the production of functionally graded (FG) polymer materials by the additive manufacturing (AM) method. FG structures were produced by the fused deposition modeling (FDM) method using acrylonitrile benzidine styrene (ABS) and polylactic acid (PLA) materials, and tensile tests were performed according to ASTM D638. The effects of different layer thicknesses, volume ratios, and total thicknesses on mechanical behavior were investigated. The tensile standard of materials produced by additive manufacturing introduces geometric differences. Another motivation in this study is to reveal the differences between the results according to the ASTM standard. In addition, tensile tests were carried out by producing single-layer samples at certain volume ratios to create a numerical model with the finite element method to verify the experimental data. As a result of this study, it is presented that the FG structure produced with FDM improves mechanical behavior.

Analytical and numerical (FEA) solution for steady-state heat transfer in generic FGM cylinder coated with two layers of isotropic material under convective-radiative boundary conditions.

An investigation was carried out in order to develop an accurate analytical solution and a numerical (FEA) solution for steady-state heat transfer in a circular sandwich structure incorporated with convective-radiative boundary conditions. The dimensional governing equations and boundary conditions were developed in the form of a 4th order algebraic equation, and then the solution was obtained using Ferrari's method. By solving for the roots of the quartic equation, we were able to determine the dimensionless temperature fields of the FG sandwich composite. The findings obtained utilizing the exact analytical solution for the FG sandwich composite under thermal loads were satisfactorily validated against those data obtained using the Galerkin finite element approximation. The impact of geometric and thermo-physical characteristics, such as Biot number (Bii=1,2), Inner and outer surface thickness ratio (ri=1,2Ro), ambient temperature ratio (θd), radiation-conduction parameter (Nr), and thermal conductivity ratio (λ3λ1) on the efficiency of heat transfer, has also been studied. This study reveals the distinct effect of Biot number on the inner and outer layers of the composite cylinder. It shows that Bi1 has a negligent effect on temperature distribution; on the other hand, the outer surface (Bi2≤1) minimizes temperature variation. However, for design consideration, a thicker inner face sheet is not recommended in high thermal load, as Nr>4 has an insignificant impact on inner surface thickness on top surface temperature. Moreover, the outer surface temperature appears to be more sensitive to θd than the radiation-convection side. Furthermore, the given analytical solution is adequately verified against the proposed FEA method, having an error of less than 1.5%.