Material Length Research Articles

Revealing failure loads of cyclically loaded H-steel columns from a thermodynamic perspective

Steel failure is always defined by phenomena such as yielding and buckling. A steel structure may fail under complex conditions such as cyclic or biaxial loading, but determining its critical stress is complex. A set of cyclic loading tests of H-steel columns with material Q345B and length 1500mm is selected as a case study, and thermodynamic-based failure analysis theories and methods are applied to reveal their failure loads. This work first transforms amplitude strain data under cyclic loading into state variables and divides them into six parts. The network-free renormalization method (based on the relativity of state variables/subparameters) can be used to characterize the stressing state evolution of H-steel columns. Further, the phase transition loads can be detected by applying clustering analysis criteria because of their attractor effect. On the other hand, Wilson's phase transition theory defines phase transition loads as the fixed points of renormalization, which can be verified by comparing the before and after renormalization (part and overall) results. Lastly, the economy index (EI) is defined as the ratio of the biaxial moment triangle area S2 to the steel column volume at the elastoplastic branch (EPB) point to verify the safety and economy of the EPB-based seismic performance design for H-steel columns. EPB-based designs increase the EI of Class IV and III H-steel columns by 258.8% and 365.8%, respectively. Thus, this work provides a new reference for thermodynamic-based failure and seismic performance analysis of H-steel columns.

Closed-Form Solution for Scale-Dependent Frequencies of Shear Deformable Cellular Microplates Coated by Piezoelectric Polymeric Skins Consisting of FG Distributed CNTs

In this work, a rectangular cellular microplate is taken into consideration which is embedded between two functionally graded carbon nanotube-reinforced composite layers that have the piezoelectric ability. Different patterns for the carbon nanotube dispersion are considered. Moreover, an external electrical voltage is applied to them. The displacements are described based on a higher-order shear deformation theory which is called hyperbolic theory and the size influence is captured via the modified couple stress formulations. The governing motion equations are then derived using the variational technique and Hamilton’s principle. Then, for simply supported edge conditions, a closed-form solution is provided. Next, it turns to validate the results in simpler states, and after that, the effect of the most prominent parameters on the results is investigated. It is observed that by increasing the external applied voltage to the face sheets, the frequencies are reduced. Also, the natural frequencies have a tendency to decrease as the dimensionless material length scale parameter increases. This study’s outcomes may help design and manufacture micro-/nano-electro systems, sensors and actuators, small-scale devices, and other engineering structures.

Vibration characteristics of piezoelectric pipe conveying fluid subjected to fluid-structure-electrical interaction

This paper mainly investigates the vibration characteristics of piezoelectric pipe conveying fluid subjected to fluid-structure-electrical interaction. Based on the Hamilton’s principle, the dynamic equations of the cantilever piezoelectric pipe subjected to the weight and fluid-structure-electrical interaction are established and solved by using the Galerkin method. Ultimately, complex frequency and critical flow velocity are obtained. The main discussion focused on the influence of electromechanical coupling, resistive load, and dimensionless capacitance on the critical flow velocity under different lengths of piezoelectric materials. It also examined the dynamic trajectories of the real and imaginary parts of the complex frequency under various mass ratios and resistive loads. Furthermore, it explored the impact of parameters representing voltage on the stability of the system. The results indicate various stability evolutions under different lengths of piezoelectric materials, flow velocities, and parameters representing voltage. The stability of the system pipe is influenced by factors such as the length of the piezoelectric material and resistive load.

A Higher-Order Theory for Nonlinear Dynamic of an FG Porous Piezoelectric Microtube Exposed to a Periodic Load

This paper investigates the nonlinear dynamic deflection, natural frequency, and wave propagation in functionally graded (FG) porous piezoelectric microscale tubes under periodic load, hygrothermal conditions, and an external electric field. The piezoelectric material used to make the smart microtubes has pores that may be smoothly changed or uniformly distributed over the tube wall. Here, three types of porosity distribution are taken into consideration. The nonlinear motion equations are constructed using a novel shear deformation beam theory and the modified couple stress theory (MCST). The nonlinear motion equations are solved using the fourth-order Runge–Kutta technique and the Galerkin approach. The effects of various geometric parameters, porosity distribution type, porosity factor, periodic load amplitude and frequency, material length scale parameter, moisture, and temperature on the nonlinear dynamic deflection, natural frequency, and wave frequency of FG porous piezoelectric microtubes are explored through a number of parametric investigations.

Tip‐Enhanced Raman Spectroscopy Coherence Length of 2D Materials: An Application to Graphene

Herein, a protocol is presented for determining the tip‐enhanced Raman spectroscopy (TERS) coherence length (Lc) of the two main Raman bands of graphene. This method involves performing approach curve experiments and plotting the normalized areas of the G and 2D bands as a function of tip–sample distance. The resultant data are fitted using a specific TERS formula to extract Lc. The results indicate different coherence lengths for the G and 2D bands in graphene as and nm. While this protocol is specifically done for graphene, the underlying theoretical framework, based on mode symmetry, can be extended to other 2D materials, such as transition metal dichalcogenides. This demonstrates the versatility and potential of TERS in exploring the coherence properties of various 2D materials.

Engineering the structure-directed functional properties of brominated organic additives for high-performance Li-CO2 batteries

In recent years, functional brominated organic additives in electrolytes have been widely studied during the CO2ER (CO2 evolution reaction) and CO2RR (CO2 reduction reaction) processes for Li-CO2 batteries. Due to their different structures, the functions of these additives are always unpredictable, multiple and limited. There seems to be a lot of materials to choose from for an additive, but there is no well-established and effective methodology to guide the selection. Herein, we introduced B3BPE, E4BCT and BPB into electrolytes for Li-CO2 batteries and focused on the structure-directed engineering of additives, including the position of halide substituent groups, the chain length of organic materials, their chain-break product as well as their corresponding difference in electrochemical properties, as additives for comparison. As a result, B3BPE has the longest chain length and strongest polarity. Experiments coupled with density functional theory simulations indicate that this structure exhibits the stronger interaction with Li2CO3, which benefits the CO2ER process, the charging voltage can be maintained at 3.90 V for 120 cycles even with a Super P cathode. In this work, we provided an electrolyte-selection engineering for brominated organic compounds, further inspiring in-depth understanding for bromide additives in future high-performance Li-CO2 batteries.

Axisymmetric Hertzian contact problem accounting for surface tension and strain gradient elasticity

In this paper, we investigate the axisymmetric Hertzian contact problem at micro-/nanoscale. The deformation of material bulk is described by a simplified theory of strain gradient elasticity, and the influence of surface tension is integrated based on the surface elasticity theory. Using the Mindlin's potential function method and double Fourier integral transform, the normal surface displacement induced by a concentrated force is derived in a closed form. Following this, the contact between a rigid sphere and an elastic half-space is formulated in terms of singular integral equation, which is numerically solved by applying the Gauss-Chebyshev method. The results indicate that the distribution of contact pressure is distinctly different from that in classical elasticity theory. The indented substrate tends to perform stiffer due to the effects of surface tension and strain gradient elasticity. When the contact radius is comparable with the material length parameter, the indentation force (depth) can be ten (three) times of that given by classical Hertz theory.

Study on impact resistance performance of MSWIFA-based low-carbon fiber-reinforced concrete

The accumulation of carbide slag (CS), red mud (RM), and municipal solid waste incineration fly ash (MSWIFA) has led to significant environmental pollution issues, necessitating urgent resource utilization. Building upon the previously developed CS-MSWIFA synergistic activation RM-slag cementitious system, this study aims to further incorporate iron tailings sand and polypropylene fibers to prepare fiber-reinforced concrete. The systematic investigation focuses on the influence of cementitious material types, aggregate types, fiber shapes, lengths, and dosages on the impact resistance of concrete. Furthermore, an impact damage evolution equation and life prediction model were developed based on the two-parameter Weibull distribution. Results indicate that the type of cementitious material and aggregate has minimal influence on the impact resistance of concrete, while the addition of fibers significantly enhances its impact resistance, shifting the failure mode from brittle to ductile. Mesh polypropylene fibers with a length of 12 mm and a volume dosage of 1.0 % demonstrate excellent impact resistance, with initial and final crack numbers reaching 78 and 105, respectively. This represents an increase of 136.4 % and 200.0 % compared to the control concrete without fibers. The findings of this study offer new avenues for the resource utilization of solid waste and provide theoretical foundations and technical support for the potential application of solid waste based fiber-reinforced concrete in structural engineering.

Prevalence of Malocclusion among School aged Children and Adolescents in Kabul, Afghanistan

One of the major public health concerns is the prevalence of malocclusion among school-aged children. Malaligned teeth and incorrect jaw posture are referred to as malocclusion, and they can cause a number of functional and cosmetic problems. The aim of this study was to investigate the prevalence of malocclusion in school-aged children and adolescents in Kabul, Afghanistan. This descriptive cross-sectional study was conducted at the Faculty of Dentistry, Kabul University of Medical Sciences “Abu Ali Ibn Sina” (KUMS). The data were collected from High schools in Kabul, Afghanistan during 2019 and 2020. A sample of 479 children and adolescents, 236 females (49.3%) and 243 males (50.7%) 8-18 years old (mean age 14.16±2.8) were randomly selected from four high schools of different districts of Kabul city. We used the angle classification for sagittal plane malocclusion; open bite and deep bite for vertical plane malocclusions; cross bites for transverse plane malocclusion; midline diastema, spacing and crowding show the tooth material and arch length discrepancies. This study demonstrated that only 41 (8.6%) of subjects had normal occlusion while 92.4% of subjects had different types of malocclusions. Class I malocclusion was found in 275 subjects ( (57.4%, class II Division 1 in 63 subjects (13.1%), Class II Division 2 in 64 subjects (13.4%), Class III malocclusion in 36 subjects (7.5%), moreover, crowding in 183 (38.2%), spacing in 79 (16.5%), midline diastema in 54 (11.3%), crossbite in 77 subjects (16.1%), open bite in 23 subjects (4.8%) and deep overbite in 44 subjects (9.2%) were found. According to Angle’s classification of malocclusion class I malocclusion was the most prevalent malocclusion and class III was the least prevalent malocclusion in school-aged children and adolescents in Kabul city.

Volatile-char interactions during biomass pyrolysis: Effects of functionalized graphitized carbon nanotubes on volatile distribution of cellulose and its model compounds

Volatile-char interactions are prevalent in biomass pyrolysis processes. To gain deeper insights into their impact on biomass pyrolysis volatile distribution, interactions between volatile compounds and char during flash pyrolysis of glucose, cellobiose, and cellulose were investigated using a pyrolysis–gas chromatography/mass spectrometry detection technique, by modifying both the chain lengths of the raw materials and the functional groups of graphitized multi-walled carbon nanotubes (CNTs). The results reveal that volatile-char interactions markedly influence the distribution of the final pyrolysis products derived from glucose-based compounds. In the presence of any type of CNTs, dehydrated saccharides in the primary products, particularly levoglucosan (LG), exhibit the highest sensitivity to the interactions. Consequently, primary products such as LG and 5-hydroxymethylfurfural (HMF) undergo secondary pyrolysis, yielding compounds such as levoglucosenone (LGO) and 5-methyl-2-furancarboxaldehyde (FCM). Additionally, CNTs without functional groups are advantageous for the production of expensive LGO (The relative abundance reached 9.65%), whereas the relative abundance of FCM increases significantly with hydroxyl-, carboxyl-, and amino-modified carbon nanotubes. Particularly, the relative abundance of FCM is highest in the presence of amino-modified carbon nanotubes, regardless of whether the feedstock is glucose, cellobiose, or cellulose, with values of 25.14%, 23.32%, and 4.23%, respectively. Furthermore, consistent changes in product distribution trends among different glucose-based compounds under identical CNT conditions suggest that glycosidic bonds have minimal impact on volatile-char interactions.

A size-dependent nonlinear isogeometric approach of bidirectional functionally graded porous plates

Recent progress in materials science and fabrication technologies, such as additive manufacturing (AM) or 3D printing, has facilitated the design and production of intricate multi-directional functionally graded (FG) materials which are playing a pivotal role in interdisciplinary engineering applications. Developing mathematical modeling for such nanostructures, however, remains challenging. The primary objective of this research, therefore, is to present a mathematical model for studying the static bending characteristics considering the geometric nonlinearity of bidirectional FG nanoplates with internal pores. The mathematical formulations are established by utilizing the first-order shear deformation theory and the von-Kármán assumption within the framework of an isogeometric approach based on NURBS basis functions. To account for the influence of both strain gradient and nonlocal elasticity, we adopt the nonlocal strain gradient theory including two independent material length scale parameters to predict the geometric nonlinearity performance of structures at small-scale levels. The mechanical properties of multi-directional FG material models are assumed to be continuously graded in two directions based on power law, while internal pores can be dispersed into two typical distribution patterns. Several numerical investigations are performed to evaluate the substantial impact of certain parameters on the nonlinear deflections of bidirectional FG nanoplates with pores under various conditions. Compared to existing studies, the key contribution is to present a robust numerical model aimed at elucidating both the stiffness-softening and stiffness-hardening mechanisms of multi-directional FG nanostructures under static bending conditions with geometric nonlinearity. These findings enhance our insights into nonlinear bending performance and contribute valuable design guidelines for future small-scale engineering structures. These innovative designs have become popular and are now crucial in state-of-the-art engineering applications, such as aerospace, nuclear systems, or thermal resistance devices.

Unraveling the impact of pore length on the conversion reaction of Fe3O4/carbon anodes in lithium-ion batteries

Despite numerous studies investigating Fe3O4/porous carbon anode materials for high-performance lithium-ion batteries (LIBs), the inherent limitations of the Fe3O4 conversion reaction, such as low reversibility and sluggish kinetics, continue to pose significant challenges. While modifying the porous structure of Fe3O4 anodes has demonstrated considerable promise in overcoming these limitations, the precise relationship between the porous structure and Fe3O4 conversion behavior still remains unclear. Here, we explore the impact of the pore length of the anode active material on the electrochemical performance of LIBs. Using two different composites of Fe3O4 and porous carbon with varying pore lengths as model materials, we conduct various in-depth electrochemical and ex-situ analyses. Our findings confirm that a shorter pore length facilitates higher Li+ ion diffusivity compared to longer pore length. Consequently, the conversion reaction of Fe3O4 to Fe and Li2O during lithiation process can be expedited, leading to a decrease in the resistance at the solid electrolyte interphase. As a result, we demonstrate that shortening the pore length of the porous anode composite materials can enhance the initial Coulombic efficiency (CE), reversible capacity, and rate capability of LIBs.

Size-Dependent Finite Element Analysis of Functionally Graded Flexoelectric Shell Structures Based on Consistent Couple Stress Theory

The functionally graded (FG) flexoelectric material is a potential material to determine the structural morphing of aircrafts. This work proposes the penalty 20-node element based on the consistent couple stress theory for analyzing the FG flexoelectric plate and shell structures with complex geometric shapes and loading conditions. Several numerical examples are examined and prove that the new element can predict the size-dependent behaviors of FG flexoelectric plate and shell structures effectively, showing good convergence and robustness. Moreover, the numerical results reveal that FG flexoelectric material exhibits better bending performance and higher flexoelectric effect compared to homogeneous materials. Moreover, the increase in the material length scale parameter leads to a gradual increase in the natural frequencies of the out-of-plane modes of FG flexoelectric plate/shell, while the natural frequencies of the in-plane modes change minimally, resulting in the occurrence of mode-switching phenomena.

A length-free phase field model for epoxy adhesive materials based on modified Drucker–Prager criterion

Characterizing the cracking behavior of epoxy adhesive material is of great importance for composite structures. Recently, the phase field model has emerged as the preferred method for predicting the crack propagation. This paper presents a length-free phase field model considering the characteristics of epoxy adhesive materials. The proposed model is formulated within a framework that decomposes the phase field fracture driving force, ensuring that it adequately considers the tension/compression asymmetry of the epoxy adhesive materials. The effects of hydrostatic pressure, deviational stress, and friction are incorporated into the model by employing a modified Drucker-Prager failure criterion. The failure criterion is included in the phase field model using the effective stress invariants. Furthermore, the internal length scale, previously considered to lack real physical meaning, is reformulated based on material strength. This model addresses the challenge of measuring the internal length of epoxy materials. It serves as a valuable reference for applying phase field models to epoxy materials. The accuracy of the model is validated through an L-shaped plate simulation, and an attempt using the model to predict the crack development in thick epoxy adhesive joints is undertaken. Several representative samples are simulated, including three double cantilever beams with different configurations. The numerical results demonstrate a good correlation with experimental data, highlighting the potential of the model in simulating the crack propagation in epoxy adhesive joints.

Size-dependent vibration analysis of porous 3D-FG microshells in complex thermal environments using a neural network enhanced finite element model

This work aims to investigate the vibration behavior of porous three-directional functionally graded (3D-FG) microshells in thermal environments, where both mechanical and thermal material properties vary along three spatial directions following a power-law distribution, based on the modified couple stress theory (MCST). An isoparametric thermal element is employed for uncoupled heat conduction analysis, followed by dynamic analysis using a penalty solid element with three translation degrees of freedom (DOFs) and three rotation DOFs per node. However, due to the strong nonlinearity of the temperature field in 3D-FG microshells, obtaining exact temperature values at integration points in dynamic analysis requires a pretty dense mesh of the solid element. To overcome this issue, a back propagation (BP) neural network is utilized to predict the temperature field for various gradient indexes, enhancing the efficiency and precision of temperature distribution calculation. Numerical results demonstrate the effectiveness of the neural network enhanced finite element model. Furthermore, the effects of the material length scale parameter (MLSP), temperature difference, and gradient indexes on the natural frequencies are investigated. It is shown that higher structural stiffness weakens the impact of temperature difference on the frequency.

Computer Simulation for Determination of Critical Buckling Temperatures of Sandwich Microplates with Cellular Core and CNT-RC Piezoelectric Patches via MSGT

This study introduces a computational simulation which leads to obtaining the critical buckling temperatures of a sandwich microplate which is modeled based on the modified strain gradient theory. This theory includes three material length scale parameters. The core of the microstructure is made from cellular materials which is treated with piezoelectric carbon nanotubes-reinforced composite patches. An advanced trigonometric hyperbolic shear deformation theory, eliminating the need for shear correction factors, is employed to analyze the microstructure. Thickness-dependent variations in structural characteristics are observed based on predefined functions. The equilibrium equations are derived using the virtual displacement principle. Fourier series functions provide an analytical way of solving these equations. The findings are verified by comparison with earlier research that was published and used fewer complex combinations. The study looks at how several important factors affect the structure’s reaction to thermal buckling.

Determining the Cohesive Length of Rock Materials by Roughness Analysis

In this research, the cohesive length of various rock types is measured using quantitative fractography alongside a recently developed multifractal analysis. This length is then utilized to gauge material cohesive stress through the theory of critical distances. Furthermore, the fracture process zone length of different rings sourced from identical rocks is assessed as a function of ring dimensions and experimental measurements of fracture toughness, in accordance with the energy criterion of the finite fracture mechanics theory. Subsequently, employing the stress criterion within coupled finite fracture mechanics, the failure stress corresponding to the fracture process zone is determined for various rings. Ultimately, through interpolation, the critical stress corresponding to the cohesive length, quantified via quantitative fractography, is approximated. Remarkably, the cohesive stress values derived from both methodologies exhibit perfect alignment, indicating the successful determination of cohesive length for the analyzed rock materials. The study also delves into the significant implications of these findings, including the quantification of intrinsic tensile strength in quasi-brittle materials and the understanding of tensile strength variations under diverse stress concentrations and loading conditions.

Nonlocal strain gradient-based geometrically nonlinear vibration analysis of double curved shallow nanoshell containing functionally graded layers

It is a fact that while examining the mechanical behavior of nano/microscopic materials, size effects become apparent. This study aims at presenting a new approach to geometrically nonlinear vibration analysis of double curved shallow nanoshell on Kerr foundation containing functionally graded layers under the impacts of harmonic loading in the framework of nonlocal strain gradient theory and the classical shell theory. The three-parameter Kerr model is founded on the independence of the upper and lower elastic layers related to the shear layer. The motion equations of the double curved shallow nanoshell are deduced by introducing the Von Kármán strain-displacement relations. Governing equations are solved by displacement function method and Galerkin method to achieve the deflection differential equation, the fourth-order Runge-Kutta methods are implemented to solve the deflection differential equation of the dynamic system. In this study, the obtained outcomes are compared with other publications indicating that the theoretical results agree with the previously published ones. Afterward, the article investigates the effects of the material length scale parameter, the nonlocal parameter, the geometric parameters and the material properties on the geometrically nonlinear vibration analysis of the double curved shallow nanoshell containing functionally graded layers. This research paper can provide extensive references and valuable guidelines for the impact and application of double curved shallow nanoshell structures containing functionally graded layers.

Size-dependent nonlinear bending of microbeams based on a third-order shear deformation theory

In this paper, the size-dependent nonlinear bending of microbeams subjected to mechanical loading is studied using a finite element formulation. Based on the von Kármán nonlinear relationship and the third-order shear deformation theory, a size-dependent nonlinear beam element is derived by using the modified couple stress theory (MCST) to capture the microstructural size effect. The element with explicit expressions for the element vector of internal forces and tangent stiffness matrix is derived by employing the transverse shear rotation as a variable. Nonlinear bending of microbeams under different mechanical loading is predicted with the aid of Newton–Raphson iterative method. Numerical investigation shows that the derived element is efficient, and it is capable of giving accurate results by several elements. The obtained results reveal the importance of the micro-size effect on the nonlinear behavior of the microbeams, and the deflections are overestimated when the microstructural effect is ignored. The effects of the material length scale parameter, boundary conditions and loading type on the bending response of the microbeams are studied and highlighted.

Vibration of embedded restrained composite tube shafts with nonlocal and strain gradient effects

Torsional vibration response of a circular nanoshaft, which is restrained by the means of elastic springs at both ends, is a matter of great concern in the field of nano-/micromechanics. Hence, the complexities arising from the deformable boundary conditions present a formidable obstacle to the attainment of closed-form solutions. In this study, a general method is presented to calculate the torsional vibration frequencies of functionally graded porous tube nanoshafts under both deformable and rigid boundary conditions. Classical continuum theory, upgraded with nonlocal strain gradient elasticity theory, is employed to reformulate the partial differential equation of the nanoshaft. First, torsional vibration equation based on the nonlocal strain gradient theory is derived for functionally graded porous nanoshaft embedded in an elastic media via Hamilton’s principle. The ordinary differential equation is found by discretizing the partial differential equation with the separation of variables method. Then, Fourier sine series is used as the rotation function. The necessary Stokes' transformation is applied to establish the general eigenvalue problem including the different parameters. For the first time in the literature, a solution that can analyze the torsional vibration frequencies of functionally graded porous tube shafts embedded in an elastic media under general (elastic and rigid) boundary conditions on the basis of nonlocal strain gradient theory is presented in this study. The results obtained show that while the increase in the material length scale parameter, elastic media and spring stiffnesses increase the frequencies of nanoshafts, the increase in the nonlocal parameter and functionally grading index values decreases the frequencies of nanoshafts. The detailed effects of these parameters are discussed in the article.