Mechanical Theory Research Articles

Investigation on fatigue damage of buton rock asphalt mixtures using semi-circular bending (SCB) and digital image correlation (DIC) techniques

The fatigue performance evaluation indices of Buton rock asphalt (BRA) modified asphalt mixture struggles to accurately characterize damage evolution process under repeated loads of the traffic. This study employs digital image correlation (DIC) technology to assess the fatigue behavior of BRA modified asphalt mixture, quantify the correlation between macroscopic response and local deformation, and verify the accuracy of evaluation indices. By capturing strain and displacement fields, the fatigue damage evolution of BRA modified asphalt is analyzed. Based on fracture mechanics theory, BRA’ s improvement of fatigue performance is quantified. Results show that vertical displacement captured by DIC can divide the three stages of fatigue cracking. The global horizontal strain(GExx)and cumulative horizontal strain(CExx) proposed in this study better characterize the nonlinear fatigue damage evolution compared to horizontal strain(Exx). Adding BRA delays crack initiation, reduces propagation rate, and enhances fatigue performance. Strain field evolution was quantitatively analyzed, and horizontal strain density(DE) and global horizontal strain density(GDE) were proposed as fatigue damage indicators. At the same load level, these indicators in BRA modified asphalt mixture, both pre- and post-aging, exceeded those of neat asphalt mixture. These findings provide a novel and accurate approach for evaluating the fatigue damage behavior of BRA modified asphalt mixture, laying the foundation for future performance-based designs.

Analysis of Force Distribution and Motion Characteristic of Hybrid-Driven Tensegrity Parallel Mechanism

Abstract Tensegrity parallel mechanisms is a novel spatial structure composed of cable-based and rigid-based chains, which is characterized by lightweight, multi-stability, high precision, good stiffness, and high load-bearing capacity. This paper focuses on the six-degree-of-freedom tensegrity parallel mechanism, analyzing its static equilibrium and presenting the force equilibrium equations. A model for cable tension distribution optimization is established, utilizing different P-norm objective functions to optimize the distribution of tension in cables and rigid links, discussing the reasons for unreasonable tensions in the system. Under given constraints on the motion pairs of the mechanism, the workspace of the mechanism is plotted, and factors influencing the size of the workspace are analyzed. Finally, the singularity of the mechanism is addressed based on the Jacobian matrix, demonstrating the feasibility of reaching the space volume by the mechanism. It has certain reference significance for the configuration theory and analysis methods of tensegrity parallel mechanisms and rigid-flexible coupling mechanisms, and provides a reference for the further promotion and application of mechanisms.

A thermodynamically‐based fractional model combined viscoelastic‐viscoplastic‐ductile damage with application to fiber‐reinforced polymer composites

AbstractA thermodynamically‐based fractional viscoelastic‐viscoplastic‐damage constitutive model combined with continuous damage mechanics (CDM) theory was established, in order to describe the rate‐dependent nonlinear behavior of fiber‐reinforced polymer composites (FRPCs). The fractional Helmholtz free energy consists of four contributions: viscoelastic (VE), viscoplastic (VP), hardening and damage, in which the VE and VP parts are constructed by fractional Zener and Scott‐Blair (SB) element forms respectively. The constitutive equation is obtained through Helmholtz free energy for the fractional Zener model, and plastic flow and hardening evolution law are all derived in the process. The ductile damage, coupled to both VE and VP free energy parts, is introduced through fractional damage energy release rates to model the degradation of material properties. The corresponding strain energy release rate and dissipation contributions are also derived. The fractional implicit time integration algorithms of proposed model are presented. The model is applied to validate tests of FRPCs under various loading conditions. The model validation and comparison are presented by simulating experimental data and existing models in the literature. And the corresponding evolution of dissipated energy is discussed to further valid the characterization ability of the model.Highlights A thermodynamical fractional constitutive model was developed for FRPCs. The Helmholtz free‐energy potential for fractional Zener model is adopted. The physical significance of fractional order parameters is explored. Fractional implicit integration algorithm of proposed model is implemented. The validation and comparison of the model are presented under various loads.

Strain energy density maximization principle for material design and the reflection in trans-scale continuum theory

Traditional efforts in the design of damage-tolerant structural materials were largely exercises in optimizing the combination of strength and ductility. However, the simultaneous consideration of these two conflicting mechanical indices, improving one inevitably sacrifices the other, makes the design extremely complex and difficult, due to the dilemma of choosing between them. Here, physically guided by the energy variational expression in trans-scale continuum mechanics theory, we propose a general mechanics principle for material design that involving only one index: towards strong and tough material the strain energy density limit (w) should be maximized, i.e., strain energy density maximization principle, referred to as wmax principle. It aims to guide the attainment of exceptional comprehensive mechanical properties, while circumventing the dual-index dilemma by employing a singular index w. Extensive experimental data analyses prove that (i) the maximum wmax always exists, at a critical dimension of characteristic microstructure dc,micro, and (ii) w can effectively index strength-ductility synergy and the wmax is conjugated with both high strength and high ductility, verifying the validity of wmax principle. The universality, practicality and downward compatibility are also examined. The dc,micro approaches twice the span of strain gradient region around internal boundary, suggesting that the microstructure state with wmax is the critical state with strongest strain gradient. Importantly, the w improvement as a function of the characteristic size of either microstructure or deformation field can be well captured by strain gradient theory, confirming the consistence between the wmax principle, experimental results and trans-scale continuum theories. This principle opens up a new design concept for advanced structural materials from the perspective of microstructure-w-mechanical properties relationship.

Step-by-step silicon carbide graphitisation process study in terms of time and temperature parameters

This work investigates the temperature and time as key parameters for graphene formation on the silicon carbide surface during the high thermal decomposition process. Measurements were performed using various experimental techniques under ultra-high vacuum conditions. The graphitisation process was divided into various stages, after which the surface chemical composition and atomic structures were analysed in detail. It has been shown that despite the known theory of graphitisation mechanism and initial condition for occurrence of this process, the application of different temperatures and heating times affect the quality and quantity of formed graphene layers. Applying a temperature too low or annealing the sample for a too short time led to an inefficient silicon sublimation process. On the other hand, too high temperature during flashing modifies the visibility of surface structures, which may be crucial for other investigations and potential applications of such systems.

Effective modeling of open quantum systems by low-rank discretization of structured environments.

The accurate description of the interaction of a quantum system with its environment is a challenging problem ubiquitous across all areas of physics and lies at the foundation of quantum mechanics theory. Here, we pioneer a new strategy to create discrete low-rank models of the system-environment interaction, by exploiting the frequency and time domain information encoded in the fluctuation-dissipation relation connecting the system-bath correlation function and the spectral density. We demonstrate the effectiveness of our methodology by combining it with tensor-network methodologies and simulating the quantum dynamics of complex excitonic systems in a highly structured bosonic environment. The new modeling framework sets the basis for a leap in the analysis of open quantum systems, providing controlled accuracy at significantly reduced computational costs, with benefits in all connected research areas.

Continuum Mechanics Applied to the Biomechanics of Motion.

Continuum Mechanics is the discipline that studies the motion and deformation of material bodies, and is at the basis of both Solid Mechanics and Fluid Mechanics. This works aims at highlighting how a basic education in modern Continuum Mechanics can be of fundamental importance not only in the Biomechanics of Tissue, but also in the Biomechanics of Movement. The latter is largely based on Rigid Body Mechanics, which can be considered as a simple particular case of the general theory of Continuum Mechanics. As an example, a straightforward methodology for the extraction of the angular velocity from motion analysis data is illustrated. The method is based on a quantity that is more primitive than the angular velocity: the spin tensor.

Investigation of Phosphazene Superbase Interactions with [PCl2N]3.

In this study, the reaction between phosphazene superbases and a chlorophosphazene trimer ([PCl2N]3) has been investigated. In this room temperature reaction, the phosphazene superbase (Me2N)3PN(Me2N)2P═NEt, commonly known as P2Et, was shown to behave as a nucleophile, displacing one of the chlorides from [PCl2N]3 and producing the tadpole-like structure 1. The reaction described herein is one of the few instances of a phosphazene superbase behaving as a nucleophile rather than a Brønsted base. Once formed, this structure contains contrasting reactivity, containing a weakly basic phosphazene head while maintaining a highly basic phosphazene tail of the tadpole. The mechanism of the reaction was explored by investigating the potential energy surface through density functional theory calculations at the B3LYP/6-311+G(d,p) level of quantum mechanical theory. It was determined that the reaction of P2Et with [PCl2N]3 followed a stepwise process beginning with the substitution of P2Et onto [PCl2N]3 with the concurrent loss of chloride. Subsequently, the chloride attacks the ethyl group of the P2Et moiety, and ethyl chloride is released, producing 1. Compound 1 was further characterized via 31P NMR spectroscopy, mass spectrometry, and X-ray crystallography.

Prediction of rotational bending fatigue life of bearing steel based on damage mechanics

Based on the theory of continuous damage mechanics, this paper proposes a fatigue damage evolution model and numerical calculation method considering the influence of vacuum chemical heat treatment process, and studies the rotational bending fatigue damage analysis and life prediction method of M50NiL bearing steel. Firstly, the constitutive model, fatigue damage evolution equation and material parameter calibration method in the theoretical model are given. Secondly, based on the ABAQUS platform, the damage mechanics-finite element numerical calculation method of fatigue damage analysis considering the influence of hardened layer is realized by writing the UMAT subroutine; then, the rotational bending fatigue test of M50NiL bearing steel treated by vacuum chemical heat treatment of quenching and tempering, carburizing and carbonitriding is carried out, and the influence of heat treatment process on fatigue performance is analyzed; finally, based on the proposed fatigue damage model and numerical calculation method, the rotational bending fatigue life of M50NiL bearing steel is predicted, and the results are compared with the experimental results to verify the correctness of the proposed method.

Eye microcirculation in glaucoma. Part 1. Diagnostic methods

Glaucoma is a socially significant disease, which is a wide group of polyetiological diseases. In the etiology of primary glaucoma, in addition to the mechanical theory, a vascular mechanism is also distinguished, and therefore, the search and development of the most informative and accurate method for studying ocular blood flow continues. Existing methods are divided into invasive and non-invasive. Invasive methods include angiography with intravenous fluorescein and indocyanine. Non-invasive methods include ultrasound Doppler mapping and pulsed Doppler modes, optical coherence tomography with angiography and laser speckle flowography. The review presents data on modern methods for ocular hemodynamics in glaucoma and ocular hypertension with technologies for studying retrobulbar blood flow and intraocular hemocirculation.

Method of understanding for investigation of crack propagation trajectory and fracture aspects in dental cracks on view of fracture mechanics theories.

Current research introduces understanding of dental-cracks mechanistic with fundamental fracture behavior in natural-teeth and orthodontics including mode I crack under both tension and compression, mode II crack under both clockwise-shear and anticlockwise-shear and mixed-mode cracks under both compression-shear and tension-shear. It depends on experimental models of transparent-Plexiglas including pre-cracks of different orientations angle (b) based on fundamental theoretical fracture analysis with comparison. Problem-concept, cracking aspects of fracture-initiation, propagation-direction, fracture-increment length, critical external-load and fracture path are predicted experimentally and theoretically using directional fracture approach and directional strain-energy density theory. Tests are carried out for (36) samples for compression and tension in LEFM. Friction-resistance between crack-surfaces is considered with derivation of equations and charts. Negative stress-intensity factor (-KI) is developed for solving complicated problems of cracks under occlusal compression loads. The occlusal loads are compression and shear producing lateral tensile mixed mode cracks. The critical propagation angle (qc), critical propagation load (sc) and critical propagation envelope of stress intensity factors (KI-KII) are developed with respect to crack orientation angle (b) with comparisons. They are necessary to predict the fracture propagation early before teeth-failure. It helps for prevention and control of dental-cracks, correct-restoration, prosthodontics, orthodontics, and development of new dental-materials and technologies.

Prediction of rotational bending fatigue life of bearing steel based on damage mechanics

Based on the theory of continuous damage mechanics, this paper proposes a fatigue damage evolution model and numerical calculation method considering the influence of vacuum chemical heat treatment process, and studies the rotational bending fatigue damage analysis and life prediction method of M50NiL bearing steel. Firstly, the constitutive model, fatigue damage evolution equation and material parameter calibration method in the theoretical model are given. Secondly, based on the ABAQUS platform, the damage mechanics-finite element numerical calculation method of fatigue damage analysis considering the influence of hardened layer is realized by writing the UMAT subroutine; then, the rotational bending fatigue test of M50NiL bearing steel treated by vacuum chemical heat treatment of quenching and tempering, carburizing and carbonitriding is carried out, and the influence of heat treatment process on fatigue performance is analyzed; finally, based on the proposed fatigue damage model and numerical calculation method, the rotational bending fatigue life of M50NiL bearing steel is predicted, and the results are compared with the experimental results to verify the correctness of the proposed method.

Efficient photocatalytic degradation of microplastics by constructing a novel Z-scheme Fe-doped BiO2−x/BiOI heterojunction with full-spectrum response: Mechanistic insights and theory calculations

Recently, microplastics (MPs) have garnered significant attention as a challenging emerging pollutant to address. Here, a full-spectrum light-driven Fe-doping BiO2−x/BiOI (FBI) Z-scheme heterojunction was constructed for efficiently degrading MPs in waters. Compared with BiO2−x, Fe doping BiO2−x, and BiOI, the optimal photocatalyst (40-FBI) can cause deep cracks in the polyethylene terephthalate (PET) within 10 h under the irradiation of full-spectrum light. Meanwhile, FT-IR characterization revealed that the absorption peak intensities of the C-O group, CO group, -CH stretching vibration, and -OH group on the MPs surface gradually increased with degradation time. A series of experiments and theory calculations revealed that the introduction of Fe creates impurity levels, accelerating the separation of photo-generated carriers and reducing the work function of BiO2−x, thereby enhancing the transport of photo-generated carriers between Z-scheme heterojunctions. This study offers a valuable idea for designing an efficient photocatalyst by simultaneously introducing ion doping and constructing heterojunctions for enhancing MPs degradation.

A New model of gas-water two-phase seepage based on Newton's law of motion

The pore throat size, structure distribution, and lithology of porous media in gas reservoirs are varied, and the gas-water two-phase seepage law is complex, making it difficult to describe the seepage model. Newton's law of motion is a basic law of motion in classical mechanics, and its application in gas-water two-phase seepage modeling is an innovative practice of classical mechanics in seepage mechanics systems. Based on Newton's three laws of motion, a gas-water two-phase seepage model was established from the force analysis of fluid, and the relationship between velocity and pressure difference, pipe radius, water film thickness, viscosity, etc. was derived under the condition that the model reached a stable state, i.e., force balance. The relationship is referred to as the steady-state model. Subsequently. the equivalent permeability representation model was derived based on the steady-state model to calculate the permeability of rock samples with different channel distribution characteristics. The results were consistent with the measured values, and there is a good correspondence between channel distribution characteristics and permeability. The relative permeability calculation method was established based on the steady-state model and capillary pressure curve. The obtained relative permeability curve aligned with the two-phase seepage law and coincides with the relative permeability curve obtained by Poiseuille's law. Finally, a new productivity equation was derived based on the steady-state model, and the Inflow Performance Relationship (IPR) curve calculated by the gas well example was consistent with the traditional equation. The research results were based on the force analysis of fluid in porous media and fundamentally explored the law of fluid flow. The derived seepage model can be used to calculate reservoir permeability, the gas-water relative permeability curve, and gas well productivity analysis and to effectively guide gas reservoir development. The study was a successful application of the basic theory of mechanics in gas-water two-phase seepage in gas reservoirs.

The Strength and Minimum Wall Thickness of Wellhead Equipment for Ultrahigh-Pressure Oil and Gas Wells

Summary As oil and gas wells are drilled to greater depths, wellhead pressure is expected to exceed the 20 ksi (138 MPa) limit specified by API SPEC 6A and other industrial standards, necessitating the development of 25 ksi (172.4 MPa) equipment. This paper focuses on the strength design and analysis of ultrahigh-pressure wellhead equipment, reviewing various wall-thickness calculation formulas and design criteria based on basic mechanical theory. It traces the flange wall thickness calculations in API SPEC 6A, discusses issues with 25-ksi equipment, and analyzes safety factors, methods, and allowable stresses in different standards. The findings of the research indicate that for high-pressure equipment with a pressure of 25 ksi (172.4 MPa), the optimal ratio of outer diameter to inner diameter is 2, and the structure can meet the requisite strength requirements. The wall thickness design method for structures such as flanges in traditional American Petroleum Institute (API) specifications uses the maximum principal stress criterion for calculation, which is not applicable to high-pressure equipment. For high-strength steel with high yield ratio used in high-pressure equipment, yield strength and tensile strength should be combined in design and use, fully utilizing the material’s properties. It is recommended to use finite element analysis for high- and ultrahigh-pressure complex structures, following the latest design concepts such as elastic-plastic ASME standards. The research provides a theoretical basis for designing ultrahigh-pressure wellhead equipment.

Physics-Informed Neural Network (PINN) model for predicting subgrade settlement induced by shield tunnelling beneath an existing railway subgrade

For the shield tunnelling beneath an existing railway subgrade, factors such as disturbance during shield tunnel excavation can cause settlements of the existing subgrade above. Traditional prediction methods for subgrade settlement may not fully reflect the construction site conditions. Recently, machine learning has been widely applied due to its fast computation speed and accurate results. However, data-driven machine learning is considered a “black-box” algorithm, lacking a mechanical theory framework and having weak generalization capabilities. To address the limitations of machine learning and enhance the efficiency and accuracy of subgrade settlement prediction during shield tunnel construction, this paper proposes a prediction model based on a physics-informed neural network (PINN). Firstly, by integrating the non-uniform displacement mode function of the tunnel, the physical equations are constructed for the shield tunnel excavation process. Subsequently, the physical equations are coupled with the machine learning framework to develop a predictive model for shield tunnelling beneath an existing railway subgrade based on the PINN model. The performance of the proposed PINN model is evaluated through the application of two engineering cases and compared with traditional numerical simulations and data-driven machine learning. The results indicate that the proposed model can not only predict the settlement of the existing railway subgrade under scant and noisy monitoring data but also have accuracy in the inversion of tunnel displacement mode parameters. Finally, parametric analyses are conducted to reveal the influence of critical variables on the prediction performance of the PINN model.

Mathematical principles of mechanical movements

The article proves that kinematic and dynamic theories in classical mechanics by I. Newton, considered a mathematical model of body displacement, are based on the laws of arithmetic progression (or linear function), trigonometry and quadratic function (equation). It is shown that formulas, equations of motion and graphs of dependencies in these theories are mathematical mechanisms that implement the relationship between uniformly varying mechanical quantities and quantities that implement (modify) changes. It is shown that the transition of a uniform change of one value to an accelerated (progressive) change occurs according to the scheme of transition of a linear function into a quadratic equation. It is shown that the formula of an arithmetic progression (linear function) is created by moving from variables in a quadratic equation to a time variable, and from changing and changing parameters to the coordinate, velocity and acceleration of the progression. In order for the content of the article to correspond to the topic, priority was given to mathematical initiatives (prerequisites, originals) of all the problems under consideration.

Анализ международных финансовых отношений через призму финансовых механизмов

The consistent isolation of Russia from the global monetary and financial system and its inherent financial mechanisms determines the need to study the possibility and feasibility of their use in the existing geopolitical conditions. The purpose of the study is to determine the nature of the relationship between the main international financial mechanisms and the consequences of external influence on them with the use of sanctions. A new approach was used, in which the analysis of processes in the modern global monetary and financial system was carried out through the prism of the main international financial mechanisms. This approach not only provides another perspective on their consideration, but also allows us to identify new aspects of their relationships and mutual influence. During the research, methods of comparative logical and contextual analysis, systematization, classification and generalization were used. Based on a synthesis of the theory of financial mechanisms and the concept of global liquidity, the relationship of key international financial mechanisms, as well as the role of international reserves, is shown. As a result of the study, it was concluded that it is impossible for Russia to use existing international financial mechanisms controlled by the United States under sanctions and the need to create new regional digital financial mechanisms with the participation of the EAEU countries and the BRICS states.

Application of vibrothermography to visualise hidden cracking process in concrete at the component scale

A thorough understanding of the cracking process in concrete structures, especially the initiation and expansion processes in the hidden stage, plays a decisive role in the maturity and completion of fracture mechanics theory. However, there exist few simple methods to detect the multi-crack development under the condition of unknown initiation area at the component scale and associated behaviours of the cracks during crack development. In this study, ultrasonic thermal excitation to visualise the multi-point hidden cracking process in concrete components was studied and hidden cracking detecting experiments were conducted. Multi-point initiation and expansion within the range of the components were achieved by destroying a suitably reinforced concrete beam using four-point bending tests with step-by-step cyclic loading. The cracking processes were monitored in real time via the auxiliary use of strain gauge groups and digital image correlation (DIC). The loading process was controlled based on the strain rules, and typical cracking stages were observed. The ultrasonic thermal excitation visualisation effect at typical cracking stages was studied via local monitoring using DIC. The results show that the ultrasonic thermal excitation visualisation method and the corresponding device proposed herein can be used to monitor hidden cracking processes in concrete at the component scale, while multi-point initiation and expansion of 0.01-mm-level crack groups can be detected in a simple and efficient manner.

Flexural toughness and stress-strain relationship of different types of steel fiber reinforced shotcrete in high geothermal environment

The shape of steel fiber plays a pivotal role in determining the mechanical properties of concrete. In this paper, the impacts of end-hooked, wavy and ultra-fine steel fibers (all with a doping amount of 1.0 %) on the compressive strength, flexural strength, flexural toughness, and strain-strain relationship of shotcrete under curing conditions of 20 ℃, 40 ℃, and 60 ℃ are studied. Furthermore, the flexural toughness of steel fiber shotcrete is evaluated using the energy absorption method, and a constitutive model for steel fiber shotcrete was established based on meso-damage mechanics theory. The results indicate that curing temperatures below 40 ℃ are conducive to enhancing the compressive strength, flexural strength, and flexural toughness of steel fiber shotcrete, while curing temperatures above 60 ℃ are unfavorable for the development of strength and toughness in steel fiber shotcrete. Regardless of the type of steel fiber, its incorporation can alleviate the negative impact of high-temperature curing on the strength and toughness of shotcrete. Under high-temperature curing conditions, the influence of end-hooked steel fibers on the strength of shotcrete is superior to that of corrugated and ultrafine steel fibers, while ultrafine steel fibers are beneficial for improving the flexural toughness of shotcrete. The slope, peak stress, and peak strain of the stress-strain curves of shotcrete cured at 40 ℃ and 60 ℃ with the addition of the three types of steel fibers are greater than those of concrete without steel fibers. Furthermore, the descending segment of the curve is wider and smoother, with a larger surrounding area, demonstrating good toughness, deformability, and ductility. The end-hooked steel fibers and ultrafine steel fibers exhibit superior performance in enhancing the toughness and ductility of shotcrete under high-temperature curing conditions compared to wavy steel fibers. Based on meso-damage theory, the impacts of curing temperature and steel fiber types on the constitutive model of shotcrete under axial compression were established, and the model parameters were discussed. The research results can provide theoretical support for the durability design of tunnel linings in high ground temperature environments.