Porosity Distribution Research Articles

Coupling μ-computed tomography and multi-scale modelling to assess the mechanical performance of material extrusion metal components

The porosity defects arising in objects produced by metal Material Extrusion (MEX) additive manufacturing affect the macroscopic mechanical behaviour. This paper presents a new approach integrating μ-computed tomography (μXCT) and multi-scale finite element analysis to evaluate the mechanical performance of components fabricated by metal MEX. The porosity information from μXCT is mapped into the finite element model, allowing to define the volume fraction of porosity to each finite mesh element. Then, the Mori-Tanaka homogenization technique is used to estimate the effective mechanical properties in each integration point, assuming a representative volume element composed by a metal matrix with a void. The reliability of the proposed approach was assessed using tensile specimens of stainless steel 316L produced by metal MEX. The numerical predictions were compared with experimental measurements, namely the strain field evolution measured by digital image correlation (DIC). The results highlight the detrimental influence of the porosity distribution, evaluated in the specimen using μXCT, on the strain distribution during the loading stage. The numerical predictions are in agreement with the experimental measurements, i.e. the difference is lower than 11%. Therefore, the proposed approach offers valuable insights for evaluating the mechanical performance of components produced by metal MEX, focusing on the detrimental effects of porosity defects.

Free Vibration of Axially Loaded Functionally Graded Porous Cracked Beams

This study employed a method of analysis to examine the free oscillation behavior of functionally graded (FG) porous-cracked beams under axial loads and varied boundary conditions. The cracked beam system was composed of interconnecting beam segments kept together by massless rotating springs. Based on the Timoshenko beam theory (TBT) or Euler–Bernoulli theories (EBT), each segment was sectionally flexible. Using a power-law function, mechanical features were expected to gradually change along with the height of the beam. Two different pore distributions, even and uneven, were also explored. Subsequently, Hamilton’s theory was used to derive the equations of kinematic motion for FG-cracked porous beams, and the transfer matrix (TMM) approach was used to get the determinantal equation. A parametric analysis was performed to evaluate how cracks, porosity distribution, slenderness ratio, volume fraction index, boundary conditions, and axial load affect the dynamic characteristics of FG beams. The results revealed that the suggested analytical approach provided several findings that were similar to the existing analytical outcomes in the literature. Moreover, the computer analysis demonstrated that porosity, especially when there were cracks, significantly affected the eigenfrequencies of FG beams. Hence, this study opened the door for possible applications in a variety of engineering settings by offering some crucial insights into the complex dynamics of FG porous-cracked beams.

Effect of porosity distribution on flexural and free vibrational behaviors of laminated composite shell using a novel sinusoidal HSDT

Effect of porosity distribution on flexural and free vibrational behaviors of laminated composite shell using a novel sinusoidal HSDT

Free vibration analysis of hybrid CNT/GPL-reinforced Porous composite plates under fluid-loading

The present study aims to explore free vibration analysis of hybrid reinforced porous composite plates subjected to fluid loading. The hybrid composite comprises a porous core layer covered by two reinforced porous face sheets. Graphene Platelets (GPLs) and Carbon Nanotubes (CNTs) are considered as reinforcement materials. The linear three-dimensional piezo-elasticity theory is employed to model the structural part of the system, while the classical Rayleigh integral is used to obtain the fluid interaction part. The accuracy and reliability of the proposed model are validated by comparing the calculated natural frequencies of the plate in vacuum and water-loaded conditions with those reported in the literature. For the first time, several parametric studies are performed to investigate the effects of dimension ratios, porosity distributions, reinforcement dispersion pattern, porosity coefficient, and weight fraction of nanofiller on the natural frequency of hybrid reinforced porous composites. The results indicate that adjusting the porosity and weight fraction of the face sheets can enhance stiffness without changing the mass, emphasizing the importance of hybrid composites for achieving optimal stiffness while maintaining a constant mass. Furthermore, the influence of core layer porosity distributions on the composite behavior differs from that of porosity distributions in the face layers. Additionally, the effectiveness of the reinforcement pattern depends on the type of porosity distribution in the face layers.

The effects of gradient index, aspect ratio, porosity, and boundary conditions on the buckling behavior of functionally graded porous beams: A k-out-of-n system reliability analysis

Functionally graded materials are a class of multifunctional materials that exhibit spatial variation in composition and microstructure. This deliberate variation is designed to effectively manage and manipulate changes in thermal, structural, or functional qualities within the material. The current study explores the system reliability of functionally graded porous beams (FGPB) subjected to buckling, focusing on the interplay of gradient index (0, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10), aspect ratio (5, 10, 15, 20, 25, 30 and 35), porosity index (0, 0.1 and 0.2) and boundary conditions (simply supported, clamped–clamped and clamped-free), with a particular emphasis on the k-out-of-n system reliability assessment, employing three distinct methods such as Evolutionary, GRG Non-linear, and Lagrangian. The results show the system's sensitivity to changes in distribution parameters, with the Lagrangian method being the most robust and stable. The 10-out-of-12 system reliability analysis demonstrates that aspect ratio and even porosity distribution are reliable, while uneven porosity is not. This study enhances structural reliability analysis in FGPBs, enhancing system reliability considerations and paving the way for further advancements in structural reliability analysis.

Linear finite element formulation for free vibration and buckling analyses of multi-directional FGP doubly curved shallow shells in thermal environment

ABSTRACT This paper presents the free vibration and buckling analyses of multi-directional functionally graded porous doubly curved shallow shells resting on Pasternak elastic foundations in a thermal environment. For the first time, a linear finite element formulation using the refined high-order shear deformation theory, combined with the Hermitian function, is developed to compute the vibration and buckling behaviour of doubly curved shallow shells. Mechanical properties of MFGP material change according to the length, width and thickness directions and the porosity distribution including even and uneven. The doubly curved shallow shell is operated in uniform, linear and non-linear temperature environments. The convergence and accuracy of the proposed method are verified by comparing numerical results with published works. In addition, a comprehensive numerical investigation was carried out to evaluate the influence of parameters on the natural frequency and critical buckling behaviour of MFGP doubly curved shallow shells.

Development of biochar molecular models with controlled porosity

Biochars are an exciting class of environmental materials with a wide range of applications, including carbon storage and sequestration, soil enhancement, and pollution remediation. However, the limited knowledge of their molecular structures and compositions and the lack of comprehensive understanding of the relationship between these structures and biochars’ diverse functionality, is hindering advancements in their development. In this work, we further advance the approach, first introduced by Wood et al. (2023), to constructing biochar molecular models; and now include control of microporosity (pores ≤ 2 nm size) within the developed models. We construct biochar models representative of woody biochars which are experimentally produced at 600–650 °C highest heating temperatures. Our models reproduce experimental H/C and O/C atomic ratios, percentage aromatic carbon, true density, cumulative porosity, and pore size distribution. The development of microporous biochar molecular models allows us to identify the importance of chemical structures involved in the assembly of biochar materials, and describe the relationship between these structures and obtained micropores. To facilitate other researchers integrating our approach into their work, we detail the steps taken, including the tests and reasons for each decision, in the construction of the biochar models. Furthermore, we share our developed molecular models in a format that can be easily integrated into other group’s work in the form of molecular dynamics simulations.

Laser–Ultrasonic Study of Local Porosity Distribution in Carbon Fiber Reinforced Plastic Stringer Panels

Laser–Ultrasonic Study of Local Porosity Distribution in Carbon Fiber Reinforced Plastic Stringer Panels

Prediction of Grain Porosity Based on WOA–BPNN and Grain Compression Experiment

The multi-field coupling of grain piles in grain silos is a focal point of research in the field of grain storage. The porosity of grain piles is a critical parameter that affects the heat and moisture transfer in grain piles. To investigate the distribution law of the bulk grain pile porosity in grain silos, machine learning algorithms were incorporated into the prediction model for grain porosity. Firstly, this study acquired the database by conducting compression experiments on grain specimens and collecting data from the literature. The back propagation neural network (BPNN) algorithm was optimized using three metaheuristic algorithms (genetic algorithm (GA), particle swarm optimization (PSO), and whale optimization algorithm (WOA)). Five machine learning models (GA–BPNN, PSO–BPNN, WOA–BPNN, BPNN, and random forest (RF)) were developed to predict the grain porosity using three input parameters (vertical pressure, grain type, and moisture content). The five models were assessed using four evaluation metrics: coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), to determine the best porosity prediction model. Finally, the generalization ability of the best prediction model was verified using the results of the grain cell box experiment on wheat piles. The results indicated that the WOA–BPNN model was the best prediction model with an R2 value of 0.9542, an RMSE value of 0.0079, an MAE value of 0.0044, and an MAPE value of 1.1467%. The WOA–BPNN model demonstrated strong generalization ability, confirming the feasibility of using this model to predict grain porosity. It also established an expression for the relationship between wheat porosity and the vertical pressure of the grain pile. This study presents a machine learning prediction method for determining the porosity of grain piles. The obtained porosity distribution law serves as a crucial basis for conducting comprehensive multi-field coupling analysis of grain piles and offers theoretical support for safe grain storage.

Dynamic response of sandwich beam with porous core excited by two harmonic loads travelling in opposite directions

This paper presents the time history response of a sandwich beam with a porous core subjected to two moving harmonic loads with opposite directions. In the modelling, the beam is combined of two isotropic face sheets and a porous core with symmetric porosity distribution. The quasi-3D shear deformation beam theory in conjunction with Hamilton's variational principle is utilized to set up the governing equations of motion. The Navier solution is used to obtain the displacement field. The accuracy of the study is validated by comparing with existing results in the literature for specific cases. Effects of the velocity and excitation frequency of the moving loads on the deflection-time history are investigated and discussed. Numerical results reveal that in the case of the double-moving harmonic loads in the antiphase, the resonance phenomenon cannot occur when the excitation frequency approaches the natural frequency of the beam.

Static Response of Functionally Graded Porous Circular Plates via Finite Element Method

The main purpose of this paper is to investigate the axisymmetric bending response of functionally graded porous (FGP) circular plates. The material properties are changed continuously in the thickness direction of the plate. Three distinct porosity distributions uniform, symmetric and monolithic are employed. The effect of porosity on the axisymmetric bending analysis of circular plates is examined parametrically. In this study, clamped and roller supports which commonly serve to achieve ideal boundary conditions in numerous engineering applications are used. The finite element method is employed for numerical analysis. The principal of the potential energy is used to obtain the governing equations. To generate the model of the FGP circular plates, an eight-node quadratic quadrilateral element with two degrees of freedom on each node is utilized. The results of this study are confirmed by the existing published literature. A good agreement between the results of the presented model and the previous literature has been observed. The results of the present study show that plate deflection increases with the increase of the porosity coefficient and the ratio of radius to thickness of circular plates. By increasing the porosity coefficient, the displacement values of the plates made of uniform porosity distribution is effected more than those of other porosity distributions.

Nonlinear Free Vibration Analysis of Functionally Graded Porous Conical Shells Reinforced with Graphene Nanoplatelets

The nonlinear vibration analysis of functionally graded reinforced with graphene platelet (FG-GRC) porous truncated conical shells surrounded by the Winkler-Pasternak elastic foundation is presented in this paper. An improved model for evaluating the material properties of porous composites is proposed. Three types of porous distribution and three patterns of graphene nanoplatelets (GPLs) dispersion are estimated. Coupled with the effect of the Winkler-Pasternak elastic foundation, the nonlinear governing equations are developed by using the Hamilton principle. The Galerkin integrated technique is employed to obtain the linear and nonlinear frequencies of the shells. After the present method is validated, the effects of the pores, GPLs, the Winkler-Pasternak foundation, and the semi-vertex are investigated in detail. The results show that the linear frequency can be raised by increasing the values of the mass volume of the GPL and foundation parameters. In contrast, the ratio of nonlinear to linear frequency declines as the mass volume of the GPLs and foundation parameters rises. Furthermore, it is found that the minimum ratio of nonlinear to linear frequency can be obtained as the semi-vertex angle is about 55º, and the effect of porosity distribution on the linear and linear frequencies might be neglected.

Traveling wave vibration and critical rotating speed of rotating porous metal conical shell with elastic boundary conditions

This article examines the traveling wave vibration modes of rotating porous metal conical shell (PMCS) by exploiting the differential quadrature method (DQM). A series of artificial springs are introduced to the system to simulate arbitrary elastic support boundary conditions. Making use of the generalization virtual displacements principle and the first-order shear deformation theory (FSDT) of laminate plate, the theoretical formula is derived, in which both the Coriolis force and the initial circumferential tension brought on by the rotation of the conical shell are included. The trigonometric function is used to indicate the circumferential mode shapes, while the DQM is adopted in generatrix direction to acquire the unified solution. By comparing the present research results and those of the previous researches, the reliability and convergence of the present formulation and numerical simulation are confirmed. Considering three different porosity distributions of the PMCS, the effects of porosity distribution, geometrics, spinning speed, boundary constraint types and the circumferential wave number on frequencies and mode shapes of traveling wave vibration of the PMCS are investigated in detail. Furthermore, the critical rotating speed (CRS) and resonance angular speed are discussed for the rotating PMCS.

Analysis of the shear stresses in a filling line of parenteral products: The role of sterilizing filters

This study investigates the impact of shear stress on protein-based parenteral drug products, particularly during the filling process, with a focus on the filtration unit. A 3D computational replica of a real sterilizing filter was developed using a stochastic geometry generation methodology, able to replicate realistic values of permeability, porosity, and pore size distribution. Computational Fluid Dynamics simulations were employed to analyze fluid dynamics within the filtration unit. The evolution of shear stress for massless tracers was examined to assess average shear stress in the sterilizing filtration unit. The results provide insights into shear stress dynamics and suggest potential scale-down strategies for industrial applications. The presented analysis is novel compared to most estimations of shear stress in sterilizing filtration units, which generally rely on mathematical calculations.

Active vibration control of rotating smart bidirectional FGPTC subjected to internal mechanical shock

This study considers the active vibration control of a sandwich truncated cone, whose intermediate layer is made of bidirectional functionally graded (FG) porous material bonded with integrated piezoelectric actuator and sensor layers on its outer and inner surfaces. The material properties of the bidirectional functionally graded porous truncated cone (FGPTC), with even and uneven porosity distributions along the length and thickness directions, are changed using a power law function. The governing motion equations utilize the two-dimensional (2D) axisymmetric theory of elasticity rather than simple shell theories. The solving of the governing motion equations is accomplished through the utilization of graded finite element and Newmark methods. The study investigates the impact of dimensions, parameters, and porosity types on transient response behavior, including the semi-vertex angle and the ratio of truncated cone length to outer radius. Furthermore, the effects of power index, porosity volume fractions, rotational velocities, and boundary conditions are examined. Active vibration control (AVC) of the piezoelectric FGPTC is achieved by employing a closed-loop control algorithm based on velocity feedback. Several numerical simulations are conducted to evaluate the effectiveness of the proposed active vibration control system in reducing structural vibrations. The results demonstrate significant reductions in vibration amplitudes and improved structural stability achieved through the active control approach.

Development and characterization of ceramic-polymeric hybrid scaffolds for bone regeneration: incorporating of bioactive glass BG-58S into PDLLA matrix

In recent years, there has been a notable surge of interest in hybrid materials within the biomedical field, particularly for applications in bone repair and regeneration. Ceramic-polymeric hybrid scaffolds have shown promising outcomes. This study aimed to synthesize bioactive glass (BG-58S) for integration into a bioresorbable polymeric matrix based on PDLLA, aiming to create a bioactive scaffold featuring stable pH levels. The synthesis involved a thermally induced phase separation process followed by lyophilization to ensure an appropriate porous structure. BG-58S characterization revealed vitreous, bioactive, and mesoporous structural properties. The scaffolds were analyzed for morphology, interconnectivity, chemical groups, porosity and pore size distribution, zeta potential, pH, in vitro degradation, as well as cell viability tests, total protein content and mineralization nodule production. The PDLLA scaffold displayed a homogeneous morphology with interconnected macropores, while the hybrid scaffold exhibited a heterogeneous morphology with smaller diameter pores due to BG-58S filling. The hybrid scaffold also demonstrated a pH buffering effect on the polymer surface. In addition to structural characteristics, degradation tests indicated that by incorporating BG-58S modified the acidic degradation of the polymer, allowing for increased total protein production and the formation of mineralization nodules, indicating a positive influence on cell culture.

Static and dynamic behaviour of sandwich beams with porous core: Experiment and moving least squares mesh-free analysis

In this paper, the static and dynamic behaviour of sandwich beams with porous core are numerically analyzedand validated by experimental tests. The beam consists of a thick porous core with a uniform porosity distribution over its domain and two outer face layers. For the theoretical study, the virtual work principle is employed to derive the governing equation. A one-dimensional (1D) mesh-free approach, associated with the moving least squares Hermite interpolation, is developed to approximate the primary variable fields and discretize the governing equation. Additionally, a simple transformation method is applied to create Kronecker delta property of constructed shape functions, straightforwardly facilitating the imposition of the boundary condition, similar to the finite element method without additional techniques. The accuracy of the computational method is subsequently verified against previous literature. For the experimental tests, various mechanical responses, such as the natural frequency, static deflection, and deflection-time history of a cantilever porous sandwich beam consisting of cemboard faces and a concrete core with Expanded Polystyrene are measured and compared with the theoretical prediction. The outcomes of this study can be valuable for the design of sandwich beams with porous core.

Foaming and Physico-Mechanical Properties of Geopolymer Pastes Manufactured from Post-Metallurgical Recycled Slag.

This paper presents a research program aimed towards developing a method of producing lightweight, porous geopolymer composites for the construction industry based on industrial wastes. A direct method involving the addition of chemicals is currently most commonly used to produce the porous mineral structure of a geopolymer matrix. This relies on a reaction in a highly alkaline environment of the geopolymer to produce a gas (usually hydrogen or oxygen) that forms vesicles and creates a network of pores. This paper demonstrates the feasibility of producing a slag-based geopolymer paste foamed with aluminum powder, taking into account different parameters of fresh paste production: the mixing duration, its speed and the timing of foaming agent addition. The foaming process of the fresh paste in terms of the volumetric changes and temperature development of the fresh paste during the curing of the material are observed. After hardening, the physical properties (density and porosity) as well as the mechanical parameters (compressive strength and work of damage) are determined for the nine manufactured foamed pastes. Image analysis software was used to assess the porosity distribution of the material across the cross-section of the samples. The results enabled the design of the mixing procedure to be adopted during the manufacture of such composites.

Nonlinear Vibration of Saturated Porous Functionally Graded Plate in Thermal Environment

In this work we studied investigates the nonlinear vibrations of a rectangular saturated porous functionally graded (FG) plate on elastic foundations in thermal environment. The mechanical properties of the saturated porous material vary smoothly with the thickness in three different distributions of porosity including uniform, symmetrically irregular, and asymmetrically irregular. The basic equations are employed by the Reddy’s higher order shear deformation theory, incorporating the geometrically nonlinear von Kármán strain-displacement relationship, stress-strain relations based on the elastic theory for porous materials by Biot, and an analytical solution obtained through the Galerkin method and Airy’s stress function for the simply supported plate. The influence of the geometrical and material parameters, elastic foundations and temperature increment on the nonlinear vibrations of the saturated porous FG plate were specifically evaluated through numerical investigations. 
 
 

Nonlinear Optimized PID Vibration Control of Thermal-Dependent FG Composite Porous Plates Reinforced by Agglomerated CNTs

This research study aims to delve into the effects of carbon nanotubes (CNTs) agglomeration on the dynamic characteristics of smart functionally graded (FG) porous sandwich plates. The structure of the sandwich plate comprises a core layer that incorporates dispersed CNTs within a polymer matrix. In addition, two layers are equipped with piezoelectric sensors and actuators. The agglomeration of CNTs is mathematically modeled using the Eshelby–Mori–Tanaka approach, accounting for both complete and partial agglomeration states. Moreover, the study takes into account the thermal-dependent behavior of CNTs. Subsequently, an optimal nonlinear proportional-integral-derivative (PID) control scheme based on the Bat optimization algorithm is applied to mitigate vibrations within the composite structure. Unlike the fixed gains of the classical PID, the nonlinear version dynamically adjusts its parameters in real time, ensuring enhanced responsiveness and stability. Furthermore, a comprehensive numerical investigation is conducted to assess the impact of several parameters on the natural frequencies in the frequency domain. These parameters encompass porosity distributions, porosity coefficients, reinforcement patterns, weight fractions of nanofillers, temperature, and the agglomeration of CNTs. The vibration attenuation performance of both nonlinear and classical PID controllers is evaluated through numerical simulations. The findings indicate the robustness and rapid disturbance rejection of the proposed control scheme.