Multi-scale Analysis Method Research Articles

Multi-scale modeling and mechanical performance analysis of finger seals with plain woven C/C composite

The application of carbon fibers reinforced carbon matrix (C/C) composite can solve the local wear of metallic finger seals effectively. However, the performance of C/C composite finger seal is complex and variable, which further decreases the sealing performance and life. Therefore, a method of multi-scale modeling and mechanical performance analysis for plain woven C/C composite finger seals was conducted. The circumferential finger beams of C/C composite were modeled by multi-scale structural analysis and weaving simulation. The radial static and dynamic stiffness characteristics of finger beams were investigated. The results showed that the radial static stiffness of the finger beam with three layers was about 3 times that with single layer. The radial stiffness of circumferential finger beams presented a periodic distribution pattern with a period of 90°. The radial dynamic stiffness of C/C composite finger beams increased with the excitation displacement amplitude and rotor speed. But the magnitude and fluctuation degree of dynamic stiffness were greater than those of static stiffness. A large difference in radial stiffness will lead to local wear and hysteretic leakage. This study lays a foundation for the analysis and optimization of the hysteresis and wear characteristics of C/C composite finger seals.

Multidimensional multiscale complexity analysis of sediment dynamics in the Yanhe Watershed of the loess Plateau, China

The Yanhe Watershed, emblematic of the loess hilly-gully landscape and ecological fragility in China's Loess Plateau, has experienced significant soil erosion and extensive soil-water conservation measures. To elucidate sediment dynamics and identify influencing factors in this region from 1960 to 2020, a novel multidimensional multiscale complexity analysis (MMCA) method was developed, based on entropy and complexity perspectives. This method integrated the refined composite multiscale fuzzy entropy (RCMFE) with multidimensional complexity analysis, offering a nuanced evaluation of sediment complexity and its implications for water resource management and ecological restoration. The findings revealed two distinct stages of sediment complexity variations: 1971–1988 and 2000–present. During the first period, the operation of the Wangyao Reservoir predominantly influenced sediment dynamics, initially reducing sediment complexity through sediment interception but later increasing it during discharge phases, particularly at larger scales. After 2002, extensive vegetation restoration efforts significantly reduced sediment complexity but raised concerns about long-term ecosystem resilience. Over the past decade, urbanization and climate change have exacerbated sediment instability, especially over semi-annual scales. This study advocates for management strategies that prioritize ecosystem sustainability and address the challenges posed by climate change and urbanization, facilitating improved soil and water conservation efforts in the Yanhe Watershed and similar regions in the Loess Plateau.

Quantitative characterization of rubber three-body abrasion wear: multi-scale testing and analysis methods based on defect detection

Abrasive wear is one of the main causes of rapid deterioration of rubber serviceability. Therefore, it is necessary to obtain information on the degree of rubber abrasion and the wear mechanism. Due to the complex nature of abrasive surfaces, obtaining accurate information on rubber abrasion is often difficult and provides limited quantitative parameters. This study presents a method to quantify rubber abrasion through defect detection and analysis. Accurate and fast identification of typical abrasion defects is achieved, and in addition, macro- and microscopic characterization data are provided based on the distribution of defects to understand the degree of abrasion and the wear mechanism. Experimental validation demonstrated the fast and accurate characterization capability of the method, especially the advanced advantages at the microscopic level. The method achieves accurate and efficient characterization of rubber abrasion, which helps to advance the study of rubber tribological behavior and is important for guiding engineering applications and improving design.

Multi-mode high resolution TFM imaging of microdefects based on laser ultrasonic full matrix capture

The identification and visualization of submillimeter microdefects have long been a critical focus within the realm of ultrasonic testing. The utilization of high-frequency signals is imperative due to the small acoustic interaction structure. An additional benefit of using lasers is their non-contact nature and ability to utilize multiple imaging modes, effectively reducing false or missed detections and enhancing credibility. This study proposes an advanced optimization algorithm for imaging and quantitative evaluation of submillimeter microdefects using laser ultrasonic full matrix capture (FMC) and total focusing method (TFM). The analysis of acoustic directionality under laser excitation and detection provides a foundation for mode selection. In preprocessing, the multi-scale principal component analysis (MSPCA) method is introduced to suppress coherent noise and blind spots. Moreover, phase coherence methods are implemented to further reduce mode artifacts, background noise, and residual surface acoustic wave (SAW). Additionally, multi-mode imaging and mode fusion are achieved using reflected longitudinal waves, reflected shear waves, converted longitudinal waves, and converted shear waves. Experiments were carried out on two different types of microdefects, namely side drilled holes (SDHs) and blind holes (BHs), resulting in high resolution TFM imaging with a minimum BH size of 0.3 mm. The outcomes demonstrate the efficacy of MSPCA in suppressing coherent noise, with further enhancement in imaging quality after phase coherence weighting. In addition, the −6 dB threshold of multi-mode images also provided the size information. This research is poised to contribute to the resolution of quality assessment challenges in powder metallurgy, welding, and additive manufacturing processes.

A multiscale Gaussian expansion method for low-frequency multimodal damping analysis of variable stiffness acoustic black hole beams

To address the issues of slow convergence and poor accuracy in existing dynamics methods caused by non-uniform variable cross-sections and layered material stiffness variations in variable stiffness acoustic black hole structure (VSABH). A multiscale Gaussian expansion method (MSGEM) is proposed in this paper. The structural dimensions are taken into account, and the structural parameters of multiple shape functions are adaptively selected based on stiffness and cross-sectional variation parameters. This results in the formation of shape function groups of various scales, which in turn creates the matrix of multi-scale Gaussian function groups. The feature information of the displacement field is realized to be extracted from multiple scales, and the fitting error of MSGEM to the displacement field of VSABH beam is within 2.02%. The missing solution of eigenfrequency of Gaussian expansion method is avoided, and the modal vibration patterns are basically matched, which verifies the validity of MSGEM. Meanwhile, the advantages of low-frequency multimodal vibration reduction of VSABH beams are highlighted from several aspects, and the trend of the adjustment of the vibration reduction characteristics of VSABH beams by different parameters is clarified, which provides valuable design guidance for ABH metamaterials oriented to low-frequency vibration reduction.

Dynamic Progressive Failure Analysis of 3D Five-directional Braided Composites under Transverse Compression Based on Macro-scale Heterogeneous Model

At present, there are few systematic researches on macro-scale heterogeneous modeling and numerical simulation of dynamic mechanical properties of 3-D braided composites. In this paper, the parametric virtual simulation model of 3D five-directional braided composites is realized in the way of “point-line-solid” based on the integrated design idea of process-structure-performance. And the impact compression numerical simulation of the material is carried out by using multi-scale analysis method. The effects of strain rate and braiding angle on transverse impact compression properties and fracture characteristics of composites is studies and verified by comparing the test results with the numerical simulation results systematically. The dynamic failure mechanism of the matrix and fiber bundles during the impact compression process is revealed. The results show that the macro-scale heterogeneous simulation model of 3D five-directional braided composites established is effective, and the numerical simulation results agree well with the test results. The matrix fracture and shear failure of fiber bundles are presented simultaneously under transverse impact compression. The failure of fiber bundles and matrix mainly concentrates on two main fracture shear planes. And the included angle between the fracture shear planes and the vertical direction is consistent with the corresponding internal braiding angle of specimens.

A practical multiscale analysis for nonlinear RC structures using a smart substructure replacement strategy

This paper presents a novel practical multiscale analysis (MSA) method for simulating local damages in large reinforced concrete (RC) structures during seismic events. Traditional techniques like the finite element (FE) method often struggle to balance computational costs with detailed simulation. The proposed method facilitates sequential local refinement from macroscopic to mesoscopic scales of RC structures, focusing strategically on critical areas prone to damage and cracking. Key features include: (1) 'Correction forces' enable integration and collaboration among models of different refinement levels, keeping models unchanged (i.e., without additions, deletions, or further refinement of elements), streamlining analysis and independent implementation across methods, scales, and platforms. (2) A smart replacement strategy ensures smooth transitions and prevents abrupt force changes between models at different refinement levels. (3) A ‘training process’ before performing the replacement and a semi-explicit method guarantee the accuracy and efficiency of the MSA method. (4) Parallel and distributed computing is seamlessly applied, significantly accelerating the analysis at each level. Implemented in the open-source software OpenSees, this method is illustrated through three examples that efficiently capture both the macroscopic mechanical responses and detailed local damage behaviors. This approach provides a valuable tool for the refined analysis of large-scale RC structures.

Electric–Mechanical coupling analysis of two-dimensional piezoelectric heterogeneous materials in flexible electric devices with extended multiscale isogeometric analysis

Piezoelectric heterogeneous materials are widely used in flexible electronic device design, enhancing sensitivity to external stimuli like pressure and acceleration. Despite their usefulness, analyzing these inherently periodic structures poses significant computational challenges. In response, this paper presents a multiscale isogeometric analysis approach tailored for simulating piezoelectric materials. We introduce an electric–mechanical coupling model using isogeometric analysis (IGA) for two-dimensional piezoelectric membrane structures, assuming the plane stress hypothesis. Our proposed algorithm enables precise calculation of both displacement and electric potential solutions, demonstrating superior convergence properties compared to traditional finite element methods. Furthermore, we extend this approach to multiscale isogeometric analysis for computing numerical solutions in porous structures and heterogeneous composite piezoelectric materials under tensile and bending conditions. Through rigorous numerical testing, we evaluate the proposed extended multiscale isogeometric analysis method, showcasing its efficacy in achieving a balance between computational efficiency and simulation accuracy. This IGA-based electro-mechanical coupling model and numerical algorithm pave the way for more streamlined and precise simulations of piezoelectric materials within the context of flexible electronic devices.

In-situ laser surface remelting of laser powder bed fused AlSi10Mg alloy at argon and nitrogen protective gases: Multiscale analysis

In the recent decades, laser powder bed fusion (LPBF) of aluminum alloy has been widely used in many fields. However, the poor surface quality, inevitable defects, and limited mechanical performance are obvious obstacles. In-situ laser surface remelting (LSR) is a promising method to give a second opportunity for the defect elimination. In this work, the LSR protective gas (argon and nitrogen) on the surface roughness, porosity, and microstructure of LPBF-fabricated AlSi10Mg alloy are experimentally compared. The nitrogen shows significant superiority in the surface flatness and densification enhancement compared with argon gas. After LSR at nitrogen gas, the average grain size reduces by 8.7 % and the low-angle grain boundaries increases from 70.9 % to 99.7 %. Moreover, a two-dimension mesoscale FEM (Finite Element Method, FEM) model is established to investigate the movement of multi pores inside the molten pool. Attributed to the lower density and dynamic viscosity and larger thermal conductivity, the combination of multi pores is significantly drastic with obvious surface fluctuation during LSR at nitrogen gas. According to the density functional theory (DFT) calculation, the absolute adsorption energies of nitrogen on Al (100) and Al (110) surfaces are generally larger, revealing that the argon gas is easier to be adsorbed on the processing aluminum layer during LSR treatment. Furthermore, the vacancy defects in the aluminum layer play positive roles in the adsorption of gas. This work establishes the importance of the protective gas on the LSR treatment, and provides a multiscale analysis method for the pore evolution.

An efficient multiscale method for subwavelength transient analysis of acoustic metamaterials.

A reduced-order homogenization framework is proposed, providing a macro-scale-enriched continuum model for locally resonant acoustic metamaterials operating in the subwavelength regime, for both time and frequency domain analyses. The homogenized continuum has a non-standard constitutive model, capturing a metamaterial behaviour such as negative effective bulk modulus, negative effective density and Willis coupling. A suitable reduced space is constructed based on the unit cell response in a steady-state regime and the local resonance regime. A frequency domain numerical example demonstrates the efficiency and suitability of the proposed framework.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

An efficient multi-scale method for failure mechanism analysis of SiCf/Ti composites with experimental validation

This study focuses on developing and validating a high-precision concurrent multi-scale finite element model considering the progressive damage model (PDM) and the cohesive zone model (CZM) for predicting the damage evolution of SiCf/Ti composites. At the macro-scale, a constitutive model describing the anisotropic damage criterion of SiCf/Ti composites was implemented by means of a user-defined subroutine (VUMAT). Meanwhile, based on the submodelling, a representative volume element (RVE) model was developed to systematically analyze the failure modes of the SiC fibers, the matrix, and the interface, respectively. Specifically, the crack initiation and propagation in the stress concentration zones were further discussed. Simultaneously, experimental methods were employed to verify the feasibility of the current model. During the uniaxial compression, the brittle fracture of the SiC fibers and ductile fracture of the matrix are the predominant failure modes of SiCf/Ti composites, with fiber fracture being the dominant factor. The crack initiates at the fibers, propagates rapidly to the fiber-matrix interface, and then extends into the matrix. Moreover, the fracture locations are suscepticle to stress concentrations, leading to the crack initiation and propagation. The predicted results show that the local damage has a significant effect on the failure mechanism of SiCf/Ti composites and this multi-scale model provides a scientific reference for the design and optimization of composites.

Multi-Scale Higher-Order Dependencies (MSHOD): Higher-Order Interactions Mining and Key Nodes Identification for Global Liner Shipping Network

Liner shipping accounts for over 80% of the global transportation volume, making substantial contributions to world trade and economic development. To advance global economic integration further, it is essential to link the flows of global liner shipping routes with the complex system of international trade, thereby supporting liner shipping as an effective framework for analyzing international trade and geopolitical trends. Traditional methods based on first-order global liner shipping networks, operating at a single scale, lack sufficient descriptive power for multi-variable sequential interactions and data representation accuracy among nodes. This paper proposes an effective methodology termed “Multi-Scale Higher-Order Dependencies (MSHOD)” that adeptly reveals the complexity of higher-order interactions among multi-scale nodes within the global liner shipping network. The key step of this method is to construct high-order dependency networks through multi-scale attributes. Based on the critical role of high-order interactions, a method for key node identification has been proposed. Experiments demonstrate that, compared to other methods, MSHOD can more effectively identify multi-scale nodes with regional dependencies. These nodes and their generated higher-order interactions could have transformative impacts on the network’s flow and stability. Therefore, by integrating multi-scale analysis methods to mine high-order interactions and identify key nodes with regional dependencies, this approach provides robust insights for assessing policy implementation effects, preventing unforeseen incidents, and revealing regional dual-circulation economic models, thereby contributing to strategies for global, stable development.

Full-Dimensional Proportional-Derivative Control Technique for Turing Pattern and Bifurcation of Delayed Reaction-Diffusion Bidirectional Ring Neural Networks

Abstract In neural networks, the states of neural networks often exhibit significant spatio-temporal heterogeneity due to the diffusion effect of electrons and differences in the concentration of neurotransmitters. One of the macroscopic reflections of this time-spatial inhomogeneity is Turing pattern. However, most current research in reaction-diffusion neural networks has focused only on one-dimensional location information, and the remaining results considering two-dimensional location information are still limited to the case of two neurons. In this paper, we conduct the dynamic analysis and optimal control of a delayed reaction-diffusion neural network model with bidirectional loop structure. First, several mathematical descriptions are given for the proposed neural network model and the full-dimensional partial differential proportional-derivative (PD) controller is introduced. Second, by analyzing the characteristic equation, the conditions for Hopf bifurcation and Turing instability of the controlled network model are obtained. Furthermore, the amplitude equation of the controlled neural network is obtained based on the multiscale analysis method. Subsequently, we determine the key parameters affecting the formation of Turing pattern depending on the amplitude equation. Finally, multiple sets of computer simulations are carried out to support our theoretical results. It is found that the diffusion coefficients and time delays have significant effects on spatio-temporal dynamics of neural networks. Moreover, after reasonable parameter proportioning, the full-dimensional PD control method can alleviate the spatial heterogeneity caused by diffusion projects and time delays.

Multiscale Progressive Failure Analysis for Composite Stringers Subjected to Compressive Load.

The fiber-reinforced composite stringer is commonly used in large civil aircraft wing structures. Under compression loads, it exhibits complex failure modes, with matrix cracking being one of the most common. The quantitative analysis of matrix failure is important and difficult. To address this issue, a multiscale method combining the generalized method of cells (GMC) and macroscopic FEM models is employed to quantitatively predict matrix damage and failure. The extent of matrix damage in the composite structure is represented by the number of failed matrix subcells within the repeating unit cells. The 3D Tsai-Hill failure criterion is established for the matrix phase, and the maximum stress failure criterion is applied to the fiber subcell. Upon meeting the criterion, the stiffnesses of the failed subcells are immediately reduced to a nominal value. In the current study, the ultimate loads, failure modes and load-displacement curves of composite stringers subjected to compressive load are obtained by the experiment approach and the proposed multiscale model. The experimental and simulation results show good agreement, and the multiscale analysis method successfully predicts the extent of matrix damage in the composite stringer under compressive load. The number of failed matrix subcells quantitatively evaluates the damage extent within a 2 × 2 GMC model. The findings reveal that matrix subcell failures primarily occur in the 45° and -45° plies of the middle part of the stringer composite.

A Review of Research Progress on the Impact of Urban Street Environments on Physical Activity: A Comparison between China and Developed Countries

Creating healthy street environments to encourage physical activity is an effective strategy against non-communicable diseases exacerbated by rapid urbanization globally. Developing countries face more significant health challenges than developed ones. However, existing research predominantly focuses on the perspective of developed countries. To address the health challenges in developing nations, studies should not only draw on the findings from developed countries but also clearly define unique research processes and pathways. Consequently, this study conducts a comparative analysis between China, representing developing countries, and developed nations, using databases like China National Knowledge Infrastructure (CNKI) and Web of Science (WOS) and tools such as Citespace, Bicomb, and Statistical Package for the Social Sciences (SPSS) to explore research hotspots, developmental trajectories, thematic categories, and trends. The findings reveal a shift in developed countries from macro-material to micro-environmental elements under multidisciplinary scrutiny, while future topics may include street space evaluations and psychological healing. In China, research has been dominated by different disciplines at various stages, starting with medical attention to chronic disease prevention, which then shifted to traffic engineering’s focus on constructing green travel environments, and finally expanded to disciplines like landscape architecture examining the impact of street environment elements on pedestrian behavioural perceptions. Future themes will focus on promoting elderly health and urban health transport systems. Generally, research in developed countries exhibits a “bottom-up” approach, with practical issues at a “post-evaluation” stage, primarily based on the “socio-ecological model” and emphasizing multidisciplinary collaboration. Chinese research shows a “top-down” characteristic, driven by national policies and at a “pre-planning” stage, integrating theories such as Maslow’s hierarchy of needs and attention restoration theory, with relatively loose disciplinary cooperation. Overall, research is shifting from macro to human-centric scales and is progressively utilizing multi-source and multi-scale big data analysis methods. Based on this, future research and development recommendations are proposed for developing countries, with China as a representative example.

Hopf Bifurcation and Turing Instability of a Delayed Diffusive Zooplankton–Phytoplankton Model with Hunting Cooperation

In this paper, a diffusive zooplankton–phytoplankton model with time delay and hunting cooperation is established. First, the existence of all positive equilibria and their local stability are proved when the system does not include time delay and diffusion. Then, the existence of Hopf bifurcation at the positive equilibrium is proved by taking time delay as the bifurcation parameter, and the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are investigated by using the center manifold theorem and the normal form theory in partial differential equations. Next, according to the theory of Turing bifurcation, the conditions for the occurrence of Turing bifurcation are obtained by taking the intraspecific competition rate of the prey as the bifurcation parameter. Furthermore, the corresponding amplitude equations are discussed by using the standard multi-scale analysis method. Finally, some numerical simulations are given to verify the theoretical results.

Characterizing thermo-hydro-mechanical behavior of rock using a grain interface-based discrete element model (GIB-DEM)

Understanding the meso-structure evolution and macro-mechanical property changes in rocks under thermo-hydro-mechanical (THM) treatment is crucial for advancing and managing deep geological projects. However, due to complex discontinuity networks in rocks, achieving an accurate characterization that quantitatively correlates the micro-macro mechanical behaviors under THM conditions remains challenging. This study introduces a groundbreaking multi-scale analysis method called the grain interface-based discrete element model (GIB-DEM) to tackle this issue. By utilizing digital imaging processing (DIP) and meso-mechanical measurements, the GIB-DEM directly determines the meso-mechanical parameters of bonds, eliminating the need for complex calibration found in traditional methods. After validating the GIB-DEM through experimental and numerical Brazilian Splitting tests, we investigate the macro- mechanical behaviors of rock under different THM conditions. Our results indicate that the increase in the tensile strength at 75 °C is attributed to the tensile strength increase of quartz grain interfaces. The development of micro-cracks on the interfaces of feldspar and feldspar-quartz accounts for the decrease in tensile strength of rock under thermal and hydraulic treatment. Overall, this pioneering research provides valuable insights for optimizing Enhanced Geothermal System (EGS) projects and effectively managing Hot Dry Rock (HDR) resources.

PINN enhanced extended multiscale finite element method for fast mechanical analysis of heterogeneous materials

PINN enhanced extended multiscale finite element method for fast mechanical analysis of heterogeneous materials

On the Cauchy problem for acoustic waves in hereditary fluids: Decay properties and inviscid limits

This paper considers the viscous/inviscid Moore–Gibson–Thompson (MGT) equations with memory of type I in the whole space . For one thing, associating with a new condition on initial data, we derive the optimal estimates and the optimal leading term of the acoustic velocity potential for large time, where we analyze different contributions from viscous, thermally relaxing, as well as hereditary fluids on large time asymptotic behavior for the acoustic waves models. For another, by using the multiscale analysis and energy methods in the Fourier space, we demonstrate the inviscid limits (i.e., as the diffusivity of sound tends to zero), which match our Wentzel‐Kramers‐Brillouin (WKB) expansion of the solution. Finally, we give a further application of our results on large time behavior for the nonlinear Jordan‐MGT equation in viscous hereditary fluids.

Analysis of gas-cooled micro modular reactor (MMR) fuel

The gas-cooled micro modular reactor (MMR) is a novel concept with a compact fuel form consisting of thousands of tri-isotropic fuel (TRISO) particles dispersed in a silicon carbide matrix. The MMR fuel has a high volume packing fraction and is horizontally placed within graphite channels. This study demonstrates that the horizontal arrangement of MMR fuel within graphite channels resulted in a non-uniform gap between the fuel and graphite brick, leading to an "off-center" temperature distribution within the fuel, and resulting in differences in TRISO performance even within sub-zones positioned symmetrically in the radial direction. Given the complexity of the fuel structure and the challenges involved in simulation, a multi-scale and multi-physics coupled analysis method of MMR fuel was realized in this work by implementing physical models into the open-source finite element platform MOOSE. Thermal-mechanical analysis and failure analysis within sub-zones of the typical design MMR fuel during normal operation were conducted through simulation. The results indicate that higher-temperature sub-zones exhibit increased internal pressure within TRISO and show greater tensile stress in the Chemical Vapor Deposited Silicon Carbide (CVD-SiC) layer. Regarding fuel failure analysis, this work found limited impact from Pd penetration and kernel migration. Pressure-induced particle failure, closely associated with stress in CVD-SiC, emerges as the primary failure criterion. The probability of fuel failure is relatively low, and interfacial cohesive parameters have an impact on the SiC stress and the fuel failure probability at the highest level.