Multiscale Behavior Research Articles

Dynamics of Sandy Shorelines and Their Response to Wave Climate Change in the East of Hainan Island, China

Beach erosion and shoreline dynamics are strongly affected by alterations in nearshore wave intensity and energy, especially in the context of global climate change. However, existing works do not thoroughly study the evolution of the sandy coasts of eastern Hainan Island, China, nor their responses to wave climate change driven by climate variability. This study focuses on the open sandy coast and assesses shoreline evolutionary dynamics in response to wave climate variability over a 30-year period from 1994 to 2023, using an open-source software toolkit that semi-automatically identify the shorelines (CoastSat v2.4) and reanalysis wave datasets (ERA5). The shorelines of the study area were extracted from CoastSat, and then tidal correction and outlier correction were performed for clearer shorelines. Combining the shoreline changes and wave conditions derived from ERA5, the dynamics of the shorelines and their response to wave climate change were further studied. The findings reveal that the average long-term shoreline change rate along the eastern coast of Hainan Island is 0.03 m/year, with 44.8% of transects experiencing erosion and 55.2% showing long-term accretion. And distinct evolutionary patterns emerge across different sections. Interannual variability is marked by alternating erosion and siltation cycles, while most sections of the coast experiences clear seasonal fluctuations, with accretion typically occurring during summer and erosion occurring in winter. El Niño–Southern Oscillation (ENSO) cycles drive changes in parameters including significant wave height, mean wave period, wave energy flux, and mean wave direction, leading to long-term changes in wave climate. The multi-scale behavior of the sandy shoreline responds distinctly to the ongoing changes in wave climate triggered by ENSO viability, with El Niño events typically resulting in accretion and La Niña periods causing erosion. Notably, mean wave direction is the metric most closely linked to changes in the shoreline among all the others. In conclusion, the interplay of escalating anthropogenic activities, natural processes, and climate change contributes to the long-term evolution of sandy shorelines. We believe this study can offer a scientific reference for erosion prevention and management strategies of sandy beaches, based on the analysis presented above.

MPFEM investigation on densification and mechanical structures during ferrous powder compaction

Metal powder compaction is a crucial process in powder metallurgy, significantly affecting the final properties of compacts. However, the quantitative characteristics of multi-scale mechanical structures and the microscopic densification behavior, taking into account the influence of friction conditions, remain unclear. This study utilises a two-dimensional multi-particle finite element method to analyse the ferrous powder compaction. The evolution of powder densification, powder deformation and multi-scale mechanical behaviour under different friction coefficient conditions are analyzed quantitatively and qualitatively. Results reveal that powder densification occurs in distinct stages, with lower friction coefficients promoting greater powder densification, as observed from relative density and coordination number. Additionally, as the axial strain increases, plastic strain gradually rises whilst roundness decreases. Higher friction coefficients are associated with higher equivalent plastic strain but lower powder roundness. The Von Mises stress exhibits different stages of increase with the increment of axial strain. Powders with lower friction coefficients exhibit lower levels of Von Mises stress. As axial strain increases, the number, length, strength and direction coefficient of force chains undergo different evolution processes. Force chains exhibit longer length, fewer numbers, lower strength and lower direction coefficients at lower friction coefficients.

Navier-Stokes: Singularities and Bifurcations

This article presents substantial advances in the analysis of the Navier-Stokes equations for both compressible and incompressible fluids, focusing on the formation of singularities, hypercomplex bifurcations, and regularity in Sobolev and Besov spaces. Through new theorems, we extend the theory of singularities in fluid dynamics and introduce quaternionic bifurcations, representing an innovative extension of classical bifurcation theory. Moreover, we delve into the investigation of the regularity of compressible fluids, exploring the conditions under which solutions remain smooth or develop singularities. These contributions are fundamental to the understanding of global regularity issues, directly linked to the renowned Millennium Prize problem, which seeks definitive answers on the existence and smoothness of solutions to the Navier-Stokes equations. Additionally, we discuss how these theoretical advancements offer new approaches to unresolved problems related to the formation of singularities in turbulent flows and the multiscale behavior of solutions, which are crucial for a comprehensive understanding of fluid dynamics. This work not only broadens the scope of traditional mathematical analysis of the Navier-Stokes equations but also establishes a robust theoretical framework for the investigation of bifurcations and regularity in advanced functional spaces, fostering a deeper understanding of global regularity phenomena and the complex dynamics governing fluid systems.

Biomimetic multiscale structure with hierarchically entangled topologies of cellulose-based hydrogel sensors for human-computer interaction

The development of high-performance cellulose-based sensors with superior interfacial compatibility, flexibility, and strength has always been challenging. Drawing inspiration from the intricate multiscale hierarchy found in resilient natural materials, the incorporation of this structure into cellulose-based hydrogels using biomimetic strategies is anticipated to enhance their properties. Therefore, the cellulose/polyacrylamide (PAM) hybrid hydrogels are fabricated using the aqueous AlCl3/ZnCl2 system through an all-green one-pot method at room temperature, achieving efficient dissolution of cellulose at multiple scales and in-situ polymerization of polyacrylamide. The multiscale cellulose/PAM hydrogels achieve good interfacial compatibility, with the reinforcing mechanism being confirmed through a combination of experimental validation and atomic simulations. The findings underscore the key elements that drive the multiscale behavior of hydrogels, encompassing a range of factors such as multiple interfacial interactions, hierarchical molecular entanglements, and microskeleton reinforcement. The hydrogels exhibit satisfactory stretchability (412 %), compressive strength (1.2 MPa), conductivity (1.65 S m−1), and ultralong circulability (> 12,000 cycles), rendering them suitable for various scenarios of human-computer interaction. This work establishes a comprehensive interpretation of the strengthening mechanism in cellulose-based multiscale hierarchical structures, thereby providing novel insights for the advanced design strategies of other promising hierarchical materials.

Structural determinants of tendon multiscale mechanics and their sensitivity to mechanical stimulation during development in an embryonic chick model

There is an abrupt increase in the multiscale mechanical properties and load-bearing capabilities of tendon during development. While prior work has identified numerous changes that occur within the collagenous structure during this developmental period, the primary structural elements that give rise to this abrupt increase in mechanical functionality, and their mechanobiological sensitivity, remain unclear. To address this knowledge gap, we used a shear lag model along with ultrastructural imaging, biochemical/thermodynamic assays, and multiscale mechanical testing to investigate the dynamic structure-function relationships during late-stage embryonic chick development and to establish their sensitivity to mechanical stimulation. Mechanical testing and modeling suggested that the rapid increase in multiscale mechanics can be explained by increases in fibril length, intrafibrillar crosslinking, and fibril area fraction. To partially test this, we inhibited collagen crosslinking during development and observed a drastic reduction in multiscale mechanical behavior that was explained by a reduction in both fibril modulus and length. Using muscle paralysis to investigate mechanosensitivity, we observed a significantly impaired multiscale mechanical response despite minimal changes in fibril diameter and fibril area fraction. Additionally, the shear lag model found a trend toward lower fibril lengths with paralysis and experimental data found decreased crosslinking and fibril modulus values following flaccid paralysis. Together, these data suggest that both intrafibrillar crosslink formation and fibril elongation are critical to the formation of load-bearing capabilities in tenogenesis and are sensitive to mechanical loading. These findings provide critical insights into the biological and structural mechanisms that give rise to tensile load-bearing soft tissue. Statement of SignificanceDespite prior work investigating the structural and mechanical changes that occur during tendon development, there has not been a comprehensive analysis of how these simultaneous changes in structure and function are connected. In this study, we performed a comprehensive battery of mechanical and structural assessments of embryonic chick tendons and input these data into a shear lag model to estimate the individual importance of each structural change to the tendon mechanical properties. Additionally, we inhibited muscle activity in the embryos to evaluate the impact of mechanical stimulation on these evolving structure-function relationships during tendon development. These data provide insight into the primary structural elements that produce the tensile load-bearing capabilities of tendon, which will inform efforts to produce tissue engineered tendon replacements.

Multi-scale behaviour of sand-geosynthetic interactions considering particle size effects

The continuous evolution of digital imaging and sensing technologies helps in understanding the multi-scale interactions between soils and geosynthetic inclusions in a progressively better way. In this study, advanced techniques like X-ray micro-computed tomography (μCT) and profilometry are used to provide better understanding of the multi-scale interactions between sand and geosynthetic materials in direct shear interface tests. To cover the dilative and non-dilative interfaces and sands of different particle sizes, shear tests were carried out with a woven geotextile and a smooth geomembrane interfacing with three graded sands at different normal stresses. The shear response of different interfaces is analyzed in the light of 3D multi-scale morphology of particles and the roughness of tested geosynthetic surfaces to compare the peak and residual friction angles and shear zone thickness determined using Digital Image Correlation (DIC) technique. The average peak frictional efficiencies for sand-geotextile and sand-geomembrane interfaces are 0.84 and 0.52, respectively. The extent of the shear zone increased with the increase in particle size, with its average thickness ranging from 2.22 to 11.41 times the mean particle size. On a microscopic level, fine sands cause increased shear-induced changes on geomembrane surfaces because of their greater effective contact per unit area.

Accurate prediction of discontinuous crack paths in random porous media via a generative deep learning model

Pore structures provide extra freedoms for the design of porous media, leading to desirable properties, such as high catalytic rate, energy storage efficiency, and specific strength. This unfortunately makes the porous media susceptible to failure. Deep understanding of the failure mechanism in microstructures is a key to customizing high-performance crack-resistant porous media. However, solving the fracture problem of the porous materials is computationally intractable due to the highly complicated configurations of microstructures. To bridge the structural configurations and fracture responses of random porous media, a unique generative deep learning model is developed. A two-step strategy is proposed to deconstruct the fracture process, which sequentially corresponds to elastic deformation and crack propagation. The geometry of microstructure is translated into a scalar of elastic field as an intermediate variable, and then, the crack path is predicted. The neural network precisely characterizes the strong interactions among pore structures, the multiscale behaviors of fracture, and the discontinuous essence of crack propagation. Crack paths in random porous media are accurately predicted by simply inputting the images of targets, without inputting any additional input physical information. The prediction model enjoys an outstanding performance with a prediction accuracy of 90.25% and possesses a robust generalization capability. The accuracy of the present model is a record so far, and the prediction is accomplished within a second. This study opens an avenue to high-throughput evaluation of the fracture behaviors of heterogeneous materials with complex geometries.

Integrating TiNx to Fe-based amorphous coating by reactive plasma spray for ameliorating multi-scale mechanical behavior and corrosion-abrasion resistance

Ocean engineering components are subjected to intense corrosion and abrasion. To address these challenges, the Fe-based amorphous composite coating was engineered for compatibility with these harsh conditions. The Fe-based amorphous composite coating, incorporating TiNx, demonstrated improved nanomechanical properties, offering enhanced resistance against external forces. The integration of TiNx acted as a structural backbone, limiting crack propagation within the amorphous matrix. Although the corrosion resistance of this composite coating was slightly reduced, it demonstrated improved durability subjected to hydraulic machinery corrosion abrasion working condition. Notably, under conditions of higher tribological pair speeds and increased sand concentrations, this composite coating exhibited significantly lower weight loss increase and reduced wear rates escalation compared to coatings made entirely from Fe-based amorphous material. Moreover, the composite coating exhibited diminished susceptibility to erosion damage, with reduced size and severity of erosion craters. These underlying mechanisms are thoroughly discussed in the paper.

Time-dependent damage characteristics of shale induced by fluid–shale interaction: a lab-scale investigation

The shale’s multi-scale mechanical behaviors were investigated to understand the time-dependent damage characteristics induced by shale–fluid interaction. The test results indicate that, as fluid–shale interaction proceeds, the mechanical strength of shale has undergone a weakened to an enhanced process as interaction proceeds, and the size distribution of fragments tends to be more uniform, leading to a positive correlation between the mechanical strength and fractal dimension. Within 2 weeks of fluid–shale interaction show a decreasing trend for the fractal dimension of fragments in post-failure and cause less than 2 mm for the dominant size of fragments. The dominant size increases to greater than 30 mm when the fluid–shale interaction is over 2 weeks. Finally, the correlation dimension associated with ring counts of acoustic emission (AE) at each loading stage is determined in terms of the G-P algorithm to predict the damage degree of shale.

Multifractal of acoustic emission for the multi-scale fracture behavior of diatomite modified concrete

It has been attempted to determine how supplemental cementitious materials (SCMs) affects concrete's resistance to fracture. Nevertheless, acoustic emission (AE) has not been used to investigate the impact of diatomite, an SCMs, on the fracture characteristics of concrete. In this investigation, the aim was to assess the fracture behavior of concrete with variable loadings of diatomite (0 %, 1 %, 2 %, 3 %). Three-point bending is performed along with continuous AE monitoring for concrete with various contents of diatomite to obtain AE information. The fracture behavior (fracture parameters, fracture mode, multi-scale fracture and damage) is determined by analyzing AE parameters and corresponding statistical indicators such as Multifractal Detrended Fluctuation Analysis(MF-DFA) and Weibull theory. The results show that the addition of diatomite enhances the fracture property of concrete especially the optimal 2 % content. Then, the high RA value and tensile crack ratio suggest the improvement of the tensile resistance of diatomite. Moreover, a novel quantitative index called multifractal parameter is proposed to evaluate the multi-scale fracture. The finding contributes to a novel method for quantifying multi-scale cracking. The low multifractal parameter in diatomite modified concrete implies a small cracking scale in comparison with the ordinary concrete. Finally, the presence of diatomite slowed down the development of fracture damage in concrete.

Multiscale verification method for prediction results of mechanical behaviors in unidirectional fiber reinforced composites

At present, there is almost no reliable multiscale experiment method that can be used to verify the multiscale mechanical behaviors of unidirectional (UD) fiber reinforced composites (FRC). Therefore, a multiscale method was developed for verifying the prediction results of the macro-mechanical properties and micro-damage modes in UD FRC. Firstly, the fiber volume fractions were determined using the fiber content test for three different FRC. Secondly, the random fiber distributed representative volume elements (RFDRVEs) were generated corresponding to these fiber volume fractions. Moreover, the RFDRVEs were used to predict the macro-mechanical properties and micro-damage modes of UD FRC. Ultimately, the standard mechanical tests and scanning electron microscopy (SEM) were applied to verify the accuracy of the prediction for the macro-mechanical properties and micro-damage modes of UD FRC. The results show that the proposed multiscale method is feasible for the verification of the multiscale prediction results based on RFDRVEs.

A unified nonlinear yield criterion for fracture and fault slip in quasi-brittle rocks

The micromechanical damage model has been developed to better describe multiscale fracture behavior in quasi-brittle rocks. While the deduced yield criterion under tension and compression has been carefully investigated in different stress spaces, it fails to capture a smooth transition from extension to shear fracture and overestimates the tensile strength of the rock. This paper introduces a unified nonlinear yield criterion based on a stress-dependent fracture energy parameter. In particular, the effect of the intermediate principal stress is encapsulated. The proposed yield criterion is then validated in the principal stress space based on a detailed parameter calibration procedure. Subsequently, four verification examples corresponding to Beishan granite, Lac du Bonnect granite, Carrara marble and Berea sandstone are carried out to show a desirable predictive capacity of the proposed yield criterion on progressive failure, extension to compressive-shear fracture transition and fault slip in quasi-brittle rocks.

Bending shape memory properties and multi-scale viscoelastic behaviors of knitted-fabric reinforced polymer composites

Knitted fabrics with easily deformable loop structure have the potential in the development of shape memory polymeric composites with large recovery deformations. The knitted fabric reinforced shape memory epoxy polymer composites (SMPC) were prepared in this work. The effects of loop densities, orientations and bending radii on shape memory properties of SMPC were investigated. The shape fixity ratio and shape recovery ratio of SMPC subjected to U-shaped bending radius of 5 mm are above 98 %. The shape recovery force of SMPC can reach up to 5.9 N. The thermodynamic properties of SMP were also characterized to obtain mechanical parameters and a user-defined material subroutine (UMAT) of shape memory epoxy polymer (SMEP) was written. Based on viscoelastic theory and the multi-scale geometrical structures, the macroscopic homogeneous thermodynamic model and mesoscopic thermodynamic model of knitted fabric reinforced SMPC were established to study the macro-scale stress distribution and meso-scale deformation evolution during shape memory process, respectively. The neutral surface position of SMPC during bending deformation is offset inner. The unique anisotropic loop structure of knitted fabric determines the shape memory behavior of the SMPC. Finally, micro-CT characterizations of knitted fabric reinforced SMPC were conducted to further understand the loop deformation mechanism during shape memory process. This study will provide important theoretical and technical support for large deformation structure design and deformation prediction of smart composites.

Mechanical responses and crystal plasticity model of CoCrNi medium-entropy alloy under ramp wave compression

It is of substantial scientific significance and practical value to reveal and understand the multiscale mechanical properties and intrinsic mechanisms of medium-entropy alloys (MEAs) under high strain rates and pressures. In this study, the mechanical responses and deformation mechanisms of an equiatomic CoCrNi MEA are investigated utilizing magnetically driven ramp wave compression (RWC) with a strain rate of 105 s−1. The CoCrNi MEA demonstrates excellent dynamic mechanical responses and yield strength under RWC compared with other advanced materials. Multiscale characterizations reveal that grain refinement and abundant micromechanisms, including dislocation slip, stacking faults, nanotwin network, and Lomer–Cottrell locks, collectively contribute to its excellent performance during RWC. Furthermore, dense deformation twins and shear bands intersect, forming a weave-like microstructure that can disperse deformation and enhance plasticity. On the basis of these observations, we develop a modified crystal plasticity model with coupled dislocation and twinning mechanisms, providing a relatively accurate quantitative description of the multiscale behavior under RWC. The results of simulations indicate that the activation of multilevel microstructures in CoCrNi MEA is primarily attributable to stress inhomogeneities and localized strain during RWC. Our research offers valuable insights into the dynamic mechanical responses of CoCrNi MEA, positioning it as a promising material for use under extreme dynamic conditions.

A multiaxial multiscale compressive thermo-mechanical damage model for Fiber Reinforced Cementitious Composites (FRCC)

In the current study, a multiaxial multiscale compressive stress-strain model for Fiber Reinforced Cementitious Composites (FRCC) was innovatively developed. The proposed model was on the basis of the theory of thermodynamics, multiscale theory and internal variable theory. The free energy function and dissipation function were established to characterize the elastic and plastic deformation of FRCC, respectively. The multiscale behaviors of FRCC in meso-scale and macro-scale was taken into account. In meso-scale, the energy dissipation functions of fiber in tension and bond-slip deformation in the interface transition zone (ITZ) were established. The resistance to cracking of cementitious matrix through the fiber bond stress were taken into account. In macro-scale, the thermo-mechanical coupling contributions of plastic damage, thermal damage, yield surface and hardening evolution were creatively considered in the potential function within thermodynamics framework. The influence of types and volume fractions of fibers on the reinforcement mechanism was discussed. When the temperature is higher than the melting point of fiber, the fiber influence coefficients was employed. The sensitivity of yield surface was discussed. The numerical predictions of this developed model were carried out for validation. The nonlinear stress-strain responses of concrete were accurately captured at temperatures ranges from 20 °C to 800 °C compared with the experimental data, which indicates the accuracy and applicability of the proposed model.

Dynamics-augmented cluster-based network model

In this study we propose a novel data-driven reduced-order model for complex dynamics, including nonlinear, multi-attractor, multi-frequency and multiscale behaviours. The starting point is a fully automatable cluster-based network model (CNM) (Li et al., J. Fluid Mech., vol. 906, 2021, A21) that kinematically coarse grains the state with clusters and dynamically predicts the transitions in a network model. In the proposed dynamics-augmented CNM (dCNM) the prediction error is reduced with trajectory-based clustering using the same number of centroids. The dCNM is first exemplified for the Lorenz system and then demonstrated for the three-dimensional sphere wake featuring periodic, quasi-periodic and chaotic flow regimes. For both plants, the dCNM significantly outperforms the CNM in resolving the multi-frequency and multiscale dynamics. This increased prediction accuracy is obtained by stratification of the state space aligned with the direction of the trajectories. Thus, the dCNM has numerous potential applications to a large spectrum of shear flows, even for complex dynamics.

A review on modeling of graphene and associated nanostructures reinforced concrete

Abstract Concrete is the most popular construction material in infrastructure projects due to its numerous natural advantages. Nevertheless, concrete constructions frequently suffer from low tensile strength and poor durability performance which are always urgent tasks to be solved. The concrete reinforced by various nanomaterials, especially graphene and its associated nanostructures (GANS), shows excellent chemical and physical properties for engineering applications. The influence of GANS on cement composites is a multiscale behavior from the nanoscale to the macroscale, which requires a number of efforts to reveal via numerical and experimental approaches. To meet this need, this study provides a comprehensive overview of the numerical modeling for GANS reinforced concrete in various scales. The background and importance of the topic are addressed in this study, along with the review of its methodologies, findings, and applications. Moreover, the study critically summarizes the performance of GANS reinforced concrete, including its mechanical behavior, transport phenomena, and failure mechanism. Additionally, the primary challenges and future prospects in the research field are also discussed. By presenting an extensive overview, this review offers valuable insights for researchers and practitioners interested in numerical simulation to advance concrete science and engineering.

Energy dissipation and evolutions of the nonlocal Cahn-Hilliard model and space fractional variants using efficient variable-step BDF2 method

In this work, an energy stable BDF2 scheme with general nonuniform time steps is developed for the nonlocal Cahn-Hilliard model to capture the multi-scale behavior of evolution efficiently and accurately. The fully discrete numerical scheme is demonstrated to inherit main physical properties of the continuous model, namely, mass conservation and energy dissipation. Recently, various variants of the Cahn-Hilliard model with nonlocal operators and fractional Laplacian have attracted great attention in terms of theoretical analysis and numerical approximation, while there is less emphasis on the comparisons among the different variant models. By comparing the impact of various parameters and coarsening behaviors, numerical results suggest that the nonlocal Cahn-Hilliard model bears a strong resemblance to the space fractional Cahn-Hilliard model derived from H−1 gradient flow of the nonlocal energy. Nevertheless, the order of the fractional Laplacian appears to affect only the rate of energy decay, without altering the profile of the solution for the fractional model relating to the H−β (0<β<1) gradient flow of the classical Ginzburg-Landau energy functional in one dimensional case.

Multiscale residual stress and mechanical behavior analysis in machining of Ti-6Al-4V alloy with advanced microscopic characterization

Machining of polycrystalline metal materials results in metallurgical modifications in the machined surface, and it can introduce multiscale residual stresses (macroscale and microscale residual stress), which may be detrimental to the mechanical properties thereby interfering with the service performance of machined parts. However, most of the current studies only focus on the macroscale residual stress, the microscale residual stresses have always been neglected since the limitations of the commonly used techniques for residual stress measurement in machined surfaces. In this study, the recently developed Focused Ion Beam-digital image correlation (FIB-DIC) ring core method was employed to evaluate the time-resolved strain relaxation and multiscale residual stress of the machined surface under different cutting conditions. The quantitative evaluation of residual stress and microstructural effects on hardness of the machined surface was conducted by combining with FIB incremental milling and nanoindentation technique. It has been observed that although the global tensile strain relaxation was captured in the ring-core region, local microscale compressive strain relaxation also occurred. The hardness of the machined surface was determined by the combined effects of microstructure and residual stress induced by machining. Specifically, the grain refinement and compressive residual stress contributed to hardening, while tensile residual stress resulted in softening of the machined surface. Furthermore, it was also observed the hardening/softening effects were enhanced with increasing intensity of tension and compression.

Microscale Mechanical Behaviour Evaluation of Unsaturated Granular Soils via 4D in situ Triaxial Test on μ-CT

Owing to the complex structure and stress history of unsaturated soils, the micro-mechanism of effective stress theory in unsaturated soil mechanics remains unelucidated. In this study, we developed a miniature triaxial test apparatus for a micro-focus computed tomography (μ-CT) scanning system for the microscopic study of the mechanical behaviour of unsaturated soil. By comparing the results from the developed mini-triaxial test device system with those from a conventional triaxial device, its experimental accuracy was verified. Micron-level high-resolution CT images of sheared specimens at different strain stages were obtained using the device for in situ suction-control triaxial compression 4D (3-Dimensional+Dynamic) tests with a μ-CT scanning system. The multiscale evolution behaviours of the physical parameters (porosity and degree of saturation) of the specimens corresponded to the stress–strain relationship revealed by the in situ test. Triaxial shearing drains out the pore water, and the decomposition of the largest water clusters causes the quantity of small-volume liquid clusters to increase, shifting the distribution of the interfacial areas. The degree of saturation scale indicates the presence of liquid bridges within the shear band that provide interparticle cementation effect and thus enhance the global strength of unsaturated granular soil specimens.