By the two-scale homogenization approach we justify a two-scale model of ion transport through a layered membrane, with flows being driven by a pressure gradient and an external electrical field. By up-scaling, the el...By the two-scale homogenization approach we justify a two-scale model of ion transport through a layered membrane, with flows being driven by a pressure gradient and an external electrical field. By up-scaling, the electroosmotic flow equations in horizontal thin slits separated by thin solid layers are approximated by a homogenized system of macroscale equations in the form of the Poisson equation for induced vertical electrical field and Onsager's reciprocity relations between global fluxes (hydrodynamic and electric) and forces (horizontal pressure gradient and external electrical field). In addition, the two-scale approach provides macroscopic mobility coefficients in the Onsager relations. On this way, the cross-coupling kinetic coefficient is obtained in a form which does involves the ζ -potential among the data provided the surface current is negligible.展开更多
The classical two-scale asymptotic paradigm provides macroscopic and microscopic analyses for the elastodynamic homogenization of periodic composites based on the spatial or/and temporal variable,which offers an appro...The classical two-scale asymptotic paradigm provides macroscopic and microscopic analyses for the elastodynamic homogenization of periodic composites based on the spatial or/and temporal variable,which offers an approximate framework for the asymptotic homogenization analysis of the motion equation.However,in this framework,the growing complexity of the homogenization formulation gradually becomes an obstacle as the asymptotic order increases.In such a context,a compact,fast,and accurate asymptotic paradigm is developed.This work reviews the high-order spatial two-scale asymptotic paradigm with the effective displacement field representation and optimizes the implementation by symmetrizing the tensor to be determined.Remarkably,the modified implementation gets rid of the excessive memory consumption required for computing the high-order tensor,which is demonstrated by representative one-and two-dimensional cases.The numerical results show that(1)the contrast of the material parameters between media in composites directly affects the convergence rate of the asymptotic results for the homogenization of periodic composites,(2)the convergence error of the asymptotic results mainly comes from the truncation error of the modified asymptotic homogenized motion equation,and(3)the excessive norm of the normalized wavenumber vector in the two-dimensional inclusion case may lead to a non-convergence of the asymptotic results.展开更多
In this manuscript,we propose an analytical equivalent linear viscoelastic constitutive model for fiber-reinforced composites,bypassing general computational homogenization.The method is based on the reduced-order hom...In this manuscript,we propose an analytical equivalent linear viscoelastic constitutive model for fiber-reinforced composites,bypassing general computational homogenization.The method is based on the reduced-order homogenization(ROH)approach.The ROH method typically involves solving multiple finite element problems under periodic conditions to evaluate elastic strain and eigenstrain influence functions in an‘off-line’stage,which offers substantial cost savings compared to direct computational homogenization methods.Due to the unique structure of the fibrous unit cell,“off-line”stage calculation can be eliminated by influence functions obtained analytically.Introducing the standard solid model to the ROH method enables the creation of a comprehensive analytical homogeneous viscoelastic constitutive model.This method treats fibrous composite materials as homogeneous,anisotropic viscoelastic materials,significantly reducing computational time due to its analytical nature.This approach also enables precise determination of a homogenized anisotropic relaxation modulus and accurate capture of various viscoelastic responses under different loading conditions.Three sets of numerical examples,including unit cell tests,three-point beam bending tests,and torsion tests,are given to demonstrate the predictive performance of the homogenized viscoelastic model.Furthermore,the model is validated against experimental measurements,confirming its accuracy and reliability.展开更多
Based on microstructure analysis,diffusion theory,and hot deformation experiments,the solidification microstructure and element segregation of the Alloy 625 Plus ingot,the diffusion kinetics of Ti,Nb,and Mo during hom...Based on microstructure analysis,diffusion theory,and hot deformation experiments,the solidification microstructure and element segregation of the Alloy 625 Plus ingot,the diffusion kinetics of Ti,Nb,and Mo during homogenization and the hot deformation behavior of the homogenized ingot were investigated in this study.The results indicate that:(1)the solidified ingot exhibits a typical dendritic microstructure,and significant element segregation occurs,leading to the presence of Ti,Nb,and Mo-rich precipitates in the interdendritic region;(2)Following homogenization,the degree of element segregation in the ingot is significantly reduced.The diffusion coefficients(D)of Ti,Nb,and Mo under various homogenization conditions were calculated.Subsequently,the diffusion constants(D_(0))and activation energies(Q)of Ti,Nb,and Mo were obtained to be 0.01432,0.00397 and 0.00195 cm^(2)/s and 244.851,230.312,and 222.125 kJ/mol,respectively.Finally,the diffusion kinetics formulas for Ti,Nb,and Mo in Alloy 625 Plus were established.After homogenization at 1220℃for 8 h,the alloy exhibits low deformation resistance,a high degree of recrystallization,and optimal deformation coordination ability.Therefore,this represents a rational single-stage homogenization process.展开更多
As primary load-bearing components extensively utilized in engineering applications,beam structures necessitate the design of their microstructural configurations to achieve lightweight objectives while satisfying div...As primary load-bearing components extensively utilized in engineering applications,beam structures necessitate the design of their microstructural configurations to achieve lightweight objectives while satisfying diverse mechanical performance requirements.Combining topology optimization with fully coupled homogenization beam theory,we provide a highly efficient design tool to access desirable periodic microstructures for beams.The present optimization framework comprehensively takes into account for key deformation modes,including tension,bending,torsion,and shear deformation,all within a unified formulation.Several numerical results prove that our method can be used to handle kinds of microstructure design for beam-like structures,e.g.,extreme tension(compression)-torsion stiffness,maximization of minimum critical buckling load,and minimization of structural compliance.When optimizing microstructures for macroscopic performance,we emphasize investigating the influence of shear stiffness on the optimized results.The novel chiral beam-like structures are fabricated and tested.The experimental results indicate that the optimized tension(compression)-torsion structure has excellent buffer characteristics,as compared with the traditional square tube.This proposed optimization framework can be further extended to other physical problems of Timoshenko beams.展开更多
The multiscale computational method with asymptotic analysis and reduced-order homogenization(ROH)gives a practical numerical solution for engineering problems,especially composite materials.Under the ROH framework,a ...The multiscale computational method with asymptotic analysis and reduced-order homogenization(ROH)gives a practical numerical solution for engineering problems,especially composite materials.Under the ROH framework,a partition-based unitcell structure at the mesoscale is utilized to give a mechanical state at the macro-scale quadrature point with pre-evaluated influence functions.In the past,the“1-phase,1-partition”rule was usually adopted in numerical analysis,where one constituent phase at the mesoscale formed one partition.The numerical cost then is significantly reduced by introducing an assumption that the mechanical responses are the same all the time at the same constituent,while it also introduces numerical inaccuracy.This study proposes a new partitioning method for fibrous unitcells under a reduced-order homogenization methodology.In this method,the fiber phase remains 1 partition,but the matrix phase is divided into 2 partitions,which refers to the“12”partitioning scheme.Analytical elastic influence+functions are derived by introducing the elastic strain energy equivalence(Hill-Mandel condition).This research also obtains the analytical eigenstrain influence functions by alleviating the so-called“inclusion-locking”phenomenon.In addition,a numerical approach to minimize the error of strain energy density is introduced to determine the partitioning of the matrix phase.Several numerical examples are presented to compare the differences among direct numerical simulation(DNS),“11”,and“12”partitioning schemes.The numerical simulations show improved++numerical accuracy by the“12”partitioning scheme.展开更多
Sodium metal batteries(SMBs)are promising candidates for next-generation energy storage devices owing to their excellent safety performance and natural abunda nce of sodium.However,the insurmountable obstacles of dend...Sodium metal batteries(SMBs)are promising candidates for next-generation energy storage devices owing to their excellent safety performance and natural abunda nce of sodium.However,the insurmountable obstacles of dendrite formation and quick capacity decay are caused by an unstable and inhomogeneous solid electrolyte interphase that resulted from the immediate interactions between the Na metal anode and organic liquid electrolyte.Herein,a customised glass fibre separator coupled with chitosan(CS@GF)was developed to modulate the sodium ion(Na^(+))flux.The CS@GF separator facilitates the Na+homogeneous deposition on the anode side through redistribution at the chitosan polyactive sites and by inhibiting the decomposition of the electrolyte to robust solid electrolyte interphase(SEI)formation.Multiphysics simulations show that chitosan incorporated into SMBs through the separator can make the local electric field around the anode uniform,thus facilitating the transfer of cations.Na|Na symmetric cells utilising a CS@GF separator exhibited an outstanding cycle stability of over 600 h(0.5 mA cm^(-2)).Meanwhile,the Na|Na_(3)V_(5)(PO_(4))_(3)full cell exhibited excellent fast-charging performance(93.47%capacity retention after 1500 cycles at 5C).This study presents a promising strategy for inhibiting dendrite growth and realizes stable Na metal batteries,which significantly boosts the development of high-performance SMBs.展开更多
Enhancing homogenization efficiency and hot-workability is the key issue for wrought superalloys in the industry.A novel approach for simultaneous accelerating the homogenization kinetics and improving hot-workability...Enhancing homogenization efficiency and hot-workability is the key issue for wrought superalloys in the industry.A novel approach for simultaneous accelerating the homogenization kinetics and improving hot-workability via a simple way of prior hot-deformation was proposed,which was not widely accepted for wrought superalloys.The homogenization efficiency is increased by 40%-70%via performing 10%-20%prior hot-deformation.Both theoretical and experimental analyses revealed that the increment in homogenization efficiency is mainly attributed to the decrease in interdendritic-segregation spacing,and thus the necessary diffusion distance,rather than that of dislocations.In addition,dynamic and static recrystallizations occurred during the prior hot-deformation and diffusion-annealing processes,and the grains were significantly refined even after the homogenization.Furthermore,the size of the precipitates was refined as well.These enhanced the hot-workability of the homogenized ingot for the subsequent cogging process.展开更多
This study conducts a thorough examination of honeycomb sandwich panels with a lattice core,adopting advanced computational techniques for their modeling.The research extends its analysis to investigate the natural fr...This study conducts a thorough examination of honeycomb sandwich panels with a lattice core,adopting advanced computational techniques for their modeling.The research extends its analysis to investigate the natural frequency behavior of sandwich panels,encompassing the comprehensive assessment of the entire panel structure.At its core,the research applies the Representative Volume Element(RVE)theory to establish the equivalent material properties,thereby enhancing the predictive capabilities of lattice structure simulations.Themethodology applies these properties in the core of infinite panels,which are modeled using double periodic boundary conditions to explore their natural frequencies.Expanding beyond mere material characterization,the study introduces a novel approach to defining the material within the panel cores.By incorporating alternate materials such as steel and AlSiC,and by strategically modifying their ratios,the research streamlines the process of material variation without resorting to repetitive 3D operations on the constituent cells.This optimizes not only the computational resources but also offers insights into the structural response under diverse material compositions.Furthermore,the investigation extends its scope to analyze the influence of curvature on the structural behavior of lattice structures.Panels are modeled with varying degrees of curvature,ranging from single to double curvatures,including cylindrical and spherical configurations,across a spectrum of radii.A rigorous analysis is performed to study the effect of curvature on the mechanical performance and stability of lattice structures,offering valuable insights for design optimization and structural engineering applications.By building upon the existing knowledge and introducing innovative methodologies,this study contributes to improving the understanding of lattice structures and their applicability in diverse engineering contexts.展开更多
In recent years,the rapid expansion of heritage tourism within China’s ethnic minority regions has been accompanied by a significant challenge:the homogenization of cultural tourism imagery and experiences.This pheno...In recent years,the rapid expansion of heritage tourism within China’s ethnic minority regions has been accompanied by a significant challenge:the homogenization of cultural tourism imagery and experiences.This phenomenon adversely affects the sustainable development of local tourism industries.To foster the effective integration,preservation,and development of heritage tourism and ethnic cultures,this study presents a case analysis of Xijiang Qianhu Miao Village in Guizhou Province.Drawing upon field research and systematic analysis,the paper critically examines manifestations of homogenization across four key dimensions:cultural image representation,commercial operational models,experiential tourism methodologies,and the depth of cultural engagement.Based on these findings,the study proposes targeted strategies to optimize the cultural tourism experience within this specific context.展开更多
Fish gelatin films have emerged as eco-friendly packaging materials due to their biodegradability and excellent film-forming properties.This study investigated the effects of varying homogenization rates(0,6500,9500,1...Fish gelatin films have emerged as eco-friendly packaging materials due to their biodegradability and excellent film-forming properties.This study investigated the effects of varying homogenization rates(0,6500,9500,13,500,17,500,and 21,500 rpm)on the functional and structural properties of fish gelatin films enriched with cinnamon essential oil(CEO).Homogenization reduced droplet sizes and narrowed droplet size distributions in the film-forming emulsion(FFE).At a homogenization rate of 9500 rpm,the films exhibited excellent mechan-ical extensibility,reduced surface irregularities,and enhanced smoothness.The highest(p<0.05)tensile strength and elongation at break were observed at this rate,showing increases of 57%and 14%,respectively,compared to the control film made from non-homogenized FFE.However,further increases in homogenization rates signifi-cantly increased(p<0.05)water vapor permeability and caused CEO droplets aggregation,leading to increased surface irregularities and the formation of pores in the film microstructure.These structural changes were observed through confocal laser scanning microscopy(CLSM),scanning electron microscopy(SEM),and atomic force microscopy(AFM).These findings indicate that the film properties were significantly influenced by the homogenization rate,highlighting its role in tailoring the mechanical and barrier properties of fish gelatin/CEO films for food packaging applications.展开更多
The acuurate prediction of the time-dependent mechanical behavior and deformation mechanisms of second-phase reinforced alloys under size effects is critical for the development of high-strength ductile metals and all...The acuurate prediction of the time-dependent mechanical behavior and deformation mechanisms of second-phase reinforced alloys under size effects is critical for the development of high-strength ductile metals and alloys for dynamic applications.However,solving their responses using high-fidelity numerical methods is computationally expensive and,in many cases,impractical.To address this issue,a dual-scale incremental variational formulation is proposed that incorporates the influence of plastic gradients on plastic evolution characteristics,integrating a strain-rate-dependent strain gradient plasticity model and including plastic gradients in the inelastic dissipation potential.Subsequently,two minimization problems based on the energy dissipation mechanisms of strain gradient plasticity,corresponding to the macroscopic and microscopic structures,are solved,leading to the development of a homogenization-based dual-scale solution algorithm.Finally,the effectiveness of the variational model and tangent algorithm is validated through a series of numerical simulations.The contributions of this work are as follows:first,it advances the theory of self-consistent computational homogenization modeling based on the energy dissipation mechanisms of plastic strain rates and their gradients,along with the development of a rigorous multi-level finite element method(FE2)solution procedure;second,the proposed algorithm provides an efficient and accurate method for evaluating the time-dependent mechanical behavior of second-phase reinforced alloys under strain gradient effects,exploring how these effects vary with the strain rate,and investigating their potential interactions.展开更多
The microstructures of a Ti−5Al−5Mo−5V−1Cr−1Fe alloy with a strain gradient from 0.1 to 1 were obtained by double-cone compression experiments.The deformation microstructures were analyzed by EBSD and TEM.The results ...The microstructures of a Ti−5Al−5Mo−5V−1Cr−1Fe alloy with a strain gradient from 0.1 to 1 were obtained by double-cone compression experiments.The deformation microstructures were analyzed by EBSD and TEM.The results show that the deformation mechanism is dynamic recovery when the strain is less than 0.42.In the strain range of 0.42−0.88,the deformation mechanism is dynamic recrystallization.When the strain exceeds 0.88,the deformation bands appear.The deformation mechanism map combined with the homogenization degree of the microstructure was constructed.The more homogeneous deformed microstructure was obtained at the strain of 0.6 and the temperature of 860°C.The dynamic recrystallization forms new grains and reduces the size difference between the grains,which improves the homogenization degree of the microstructure.展开更多
Obtaining an appropriate grain size is crucial for Al alloys or Al matrix composites prior to processing,as it significantly influences the mechanical properties of components and workability during the manufacturing ...Obtaining an appropriate grain size is crucial for Al alloys or Al matrix composites prior to processing,as it significantly influences the mechanical properties of components and workability during the manufacturing process.TiB_(2)particles are exceptional grain refiners in Al and serve as excellent reinforcement particles for particulate-reinforced aluminum matrix composites.However,the optimal particle content for achieving excellent refinement and strengthening effects depends on the matrix composition and requires further investigation.Additionally,homogenization is essential for mitigating the element segregation in the ingot.Although it is anticipated that adding suitable particles can effectively inhibit undesired grain growth during homogenization,comprehensive investigations on this aspect are currently lacking.Therefore,TiB_(2)/2219Al matrix composites with varying reinforcement contents(0,1,3,5 wt%)were fabricated through traditional casting followed by homogenization treatment to address these research gaps.The effects of reinforcement content and homogenization treatment on the microstructure and mechanical properties of in-situ TiB_(2)/2219Al composites were investigated.The results demonstrate a gradual strengthening of the refining effect with increasing particle concentration.Moreover,composites containing 3 wt%TiB_(2)particles exhibit superior comprehensive mechanical properties in both as-cast and homogenized state.Additionally,potential orientation relationships are observed and calculated between undissolved Al_(2)Cu eutectic phase and submicron or nanometer-sized TiB_(2)particles,resulting in a mixture structure with enhanced bonding strength.This mixture structure is continuously distributed along grain boundaries during solidification,forming a three-dimensional cellular network that acts as primary retarding forces for grain growth during homogenization.Furthermore,the established homogenization kinetic equations were further utilized to analyze the correlation between homogenization time and grain size,as well as the influence of homogenization temperature.展开更多
This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to gene...This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to generate the C-ZrC inclusion model.Finally,the fiber structure is added to construct the microstructure of the three-phase plain weave composite.The reconstructed inclusions can meet the randomness of the shape and have a uniform distribution.Using an algorithm based on asymptotic homogenization and finite element method,the equivalent thermal conductivity prediction of the microstructure finite element model was carried out,and the influence of component volume fraction on material thermal properties was explored.The sensitivity of model parameters was studied,including the size,mesh sensitivity,Gaussian complexity,and correlation length of the RVE model,and the optimal calculation model was selected.The results indicate that the volume fraction of the inclusion phase has a significant impact on the equivalent thermal conductivity of the material.As the volume fraction of carbon fiber and ZrC increases,the equivalent thermal conductivity tensor gradually decreases.This model can be used to explore the impact of materialmicrostructure on the results,and numerical simulations have studied the relationship between structure and performance,providing the possibility of designing microstructure based on performance.展开更多
Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting app...Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting applications.With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components,the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields.Traditional numerical models include homogenized orthotropic models,which simplify overall field calculation but miss detailed multi-physics aspects,and full refinement(FR)ones that are thorough but computationally demanding.Herein,we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils.This approach combines a global homogenization(GH)scheme based on the homogenized electromagnetic T-A model,a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A,and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale.We then identify“dangerous regions”at the macroscopic scale and obtain finer details using a local refinement(LR)scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale.The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature,indicating that the present approach is accurate and efficient.The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.展开更多
The dynamic vibration absorber with inerter and grounded stiffness(IGDVA)is used to control a two-scale system subject to a weak periodic perturbation.The vibration suppression effect is remarkable.The amplitude of th...The dynamic vibration absorber with inerter and grounded stiffness(IGDVA)is used to control a two-scale system subject to a weak periodic perturbation.The vibration suppression effect is remarkable.The amplitude of the main system coupled with absorber is significantly reduced,and the high frequency vibration completely disappears.First,through the slow-fast analysis and stability theory,it is found that the stability of the autonomous system exerts a notable regulating effect on the vibration response of the non-autonomous system.After adding the dynamic vibrator absorber,the center in the autonomous system changes to an asymptotically stable focus,consequently suppressing the vibration in the non-autonomous system.Further research reveals that the parameters of the absorber affect the real parts of the eigenvalues of the autonomous system,thereby regulating the stability of the system.Transitioning from a qualitative standpoint to a quantitative approach,a comparison of the solutions before and after the introduction of the dynamic absorber reveals that,when the grounded stiffness ratio and the mass ratio of the dynamic absorber are not equal,the high-frequency part in the analytical solution disappears.As a result,this leads to a reduction in the amplitude of the trajectory,achieving a vibration reduction effect.展开更多
The reaction order plays a crucial role in evaluating the response rate of acid-rock.However,the conventional two-scale model typically assumes that the reaction order is constant as one,which can lead to significant ...The reaction order plays a crucial role in evaluating the response rate of acid-rock.However,the conventional two-scale model typically assumes that the reaction order is constant as one,which can lead to significant deviations from reality.To address this issue,this study proposes a novel multi-order dynamic model for acid-rock reaction by combining rotating disk experimental data with theoretical derivation.Through numerical simulations,this model allows for the investigation of the impact of acidification conditions on different orders of reaction,thereby providing valuable insights for on-site construction.The analysis reveals that higher response orders require higher optimal acid liquid flow rates,and lower optimal H+diffusion coefficients,and demonstrate no significant correlation with acid concentration.Consequently,it is recommended to increase the displacement and use high-viscosity acid for reservoirs with high calcite content,while reducing the displacement and using low-viscosity acid for reservoirs with high dolomite content.展开更多
By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M...By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.展开更多
A two-scale method is proposed to simulate the essential behavior of bolted connections in structures includingelevated temperatures.It is presented,verified,and validated for the structural behavior of two plates,con...A two-scale method is proposed to simulate the essential behavior of bolted connections in structures includingelevated temperatures.It is presented,verified,and validated for the structural behavior of two plates,connectedby a bolt,under a variety of loads and elevated temperatures.The method consists of a global-scale model thatsimulates the structure(here the two plates)by volume finite elements,and in which the bolt is modelled bya spring.The spring properties are provided by a smallscale model,in which the bolt is modelled by volumeelements,and for which the boundary conditions are retrieved from the global-scale model.To ensure the small-scale model to be as computationally efficient as possible,simplifications are discussed regarding the materialmodel and the modelling of the threads.For the latter,this leads to the experimentally validated application ofa non-threaded shank with its stress area.It is shown that a non-linear elastic spring is needed for the bolt inthe global-scale model,so the post-peak behavior of the structure can be described efficiently.All types of boltedconnection failure as given by design standards are simulated by the twoscale method,which is successfullyvalidated(except for net section failure)by experiments,and verified by a detailed system model,which modelsthe structure in full detail.The sensitivity to the size of the part of the plate used in the small-scale modelis also studied.Finally,multi-directional load cases,also for elevated temperatures,are studied with the two-scale method and verified with the detailed system model.As a result,a computationally efficient finite elementmodelling approach is provided for all possible combined load actions(except for nut thread failure and netsection failure)and temperatures.The two-scale method is shown to be insightful,for it contains a functionalseparation of scales,revealing their relationships,and consequently,local small-scale non-convergence can behandled.Not presented in this paper,but the two-scale method can be used in e.g.computationally expensive two-way coupled fire-structure simulations,where it is beneficial for distributed computing and densely packed boltconfigurations with stiffplates,for which a single small-scale model may be representative for several connections.展开更多
文摘By the two-scale homogenization approach we justify a two-scale model of ion transport through a layered membrane, with flows being driven by a pressure gradient and an external electrical field. By up-scaling, the electroosmotic flow equations in horizontal thin slits separated by thin solid layers are approximated by a homogenized system of macroscale equations in the form of the Poisson equation for induced vertical electrical field and Onsager's reciprocity relations between global fluxes (hydrodynamic and electric) and forces (horizontal pressure gradient and external electrical field). In addition, the two-scale approach provides macroscopic mobility coefficients in the Onsager relations. On this way, the cross-coupling kinetic coefficient is obtained in a form which does involves the ζ -potential among the data provided the surface current is negligible.
文摘The classical two-scale asymptotic paradigm provides macroscopic and microscopic analyses for the elastodynamic homogenization of periodic composites based on the spatial or/and temporal variable,which offers an approximate framework for the asymptotic homogenization analysis of the motion equation.However,in this framework,the growing complexity of the homogenization formulation gradually becomes an obstacle as the asymptotic order increases.In such a context,a compact,fast,and accurate asymptotic paradigm is developed.This work reviews the high-order spatial two-scale asymptotic paradigm with the effective displacement field representation and optimizes the implementation by symmetrizing the tensor to be determined.Remarkably,the modified implementation gets rid of the excessive memory consumption required for computing the high-order tensor,which is demonstrated by representative one-and two-dimensional cases.The numerical results show that(1)the contrast of the material parameters between media in composites directly affects the convergence rate of the asymptotic results for the homogenization of periodic composites,(2)the convergence error of the asymptotic results mainly comes from the truncation error of the modified asymptotic homogenized motion equation,and(3)the excessive norm of the normalized wavenumber vector in the two-dimensional inclusion case may lead to a non-convergence of the asymptotic results.
基金support by the National Key R&D Program of China(Grant No.2023YFA1008901)the National Natural Science Foundation of China(Grant Nos.11988102,12172009)is gratefully acknowledged.
文摘In this manuscript,we propose an analytical equivalent linear viscoelastic constitutive model for fiber-reinforced composites,bypassing general computational homogenization.The method is based on the reduced-order homogenization(ROH)approach.The ROH method typically involves solving multiple finite element problems under periodic conditions to evaluate elastic strain and eigenstrain influence functions in an‘off-line’stage,which offers substantial cost savings compared to direct computational homogenization methods.Due to the unique structure of the fibrous unit cell,“off-line”stage calculation can be eliminated by influence functions obtained analytically.Introducing the standard solid model to the ROH method enables the creation of a comprehensive analytical homogeneous viscoelastic constitutive model.This method treats fibrous composite materials as homogeneous,anisotropic viscoelastic materials,significantly reducing computational time due to its analytical nature.This approach also enables precise determination of a homogenized anisotropic relaxation modulus and accurate capture of various viscoelastic responses under different loading conditions.Three sets of numerical examples,including unit cell tests,three-point beam bending tests,and torsion tests,are given to demonstrate the predictive performance of the homogenized viscoelastic model.Furthermore,the model is validated against experimental measurements,confirming its accuracy and reliability.
基金Project(52174303)supported by the National Natural Science Foundation of ChinaProject(2023JH2/101700302)supported by the Joint Program of Science and Technology Plans in Liaoning Province,China。
文摘Based on microstructure analysis,diffusion theory,and hot deformation experiments,the solidification microstructure and element segregation of the Alloy 625 Plus ingot,the diffusion kinetics of Ti,Nb,and Mo during homogenization and the hot deformation behavior of the homogenized ingot were investigated in this study.The results indicate that:(1)the solidified ingot exhibits a typical dendritic microstructure,and significant element segregation occurs,leading to the presence of Ti,Nb,and Mo-rich precipitates in the interdendritic region;(2)Following homogenization,the degree of element segregation in the ingot is significantly reduced.The diffusion coefficients(D)of Ti,Nb,and Mo under various homogenization conditions were calculated.Subsequently,the diffusion constants(D_(0))and activation energies(Q)of Ti,Nb,and Mo were obtained to be 0.01432,0.00397 and 0.00195 cm^(2)/s and 244.851,230.312,and 222.125 kJ/mol,respectively.Finally,the diffusion kinetics formulas for Ti,Nb,and Mo in Alloy 625 Plus were established.After homogenization at 1220℃for 8 h,the alloy exhibits low deformation resistance,a high degree of recrystallization,and optimal deformation coordination ability.Therefore,this represents a rational single-stage homogenization process.
基金supported by the National Natural Science Foundation of China(grant number 11902015)the Open Fund of Deceleration and Landing Laboratory of the Fifth Academy of Aerospace Science and Technology Group(grant number EDL19092138)the Ministry of Education Chunhui Plan(HZKY20220014).
文摘As primary load-bearing components extensively utilized in engineering applications,beam structures necessitate the design of their microstructural configurations to achieve lightweight objectives while satisfying diverse mechanical performance requirements.Combining topology optimization with fully coupled homogenization beam theory,we provide a highly efficient design tool to access desirable periodic microstructures for beams.The present optimization framework comprehensively takes into account for key deformation modes,including tension,bending,torsion,and shear deformation,all within a unified formulation.Several numerical results prove that our method can be used to handle kinds of microstructure design for beam-like structures,e.g.,extreme tension(compression)-torsion stiffness,maximization of minimum critical buckling load,and minimization of structural compliance.When optimizing microstructures for macroscopic performance,we emphasize investigating the influence of shear stiffness on the optimized results.The novel chiral beam-like structures are fabricated and tested.The experimental results indicate that the optimized tension(compression)-torsion structure has excellent buffer characteristics,as compared with the traditional square tube.This proposed optimization framework can be further extended to other physical problems of Timoshenko beams.
基金funded by the National Key R&D Program of China(Grant No.2023YFA1008901)the National Natural Science Foundation of China(Grant Nos.11988102,12172009)“The Fundamental Research Funds for the Central Universities,Peking University”.
文摘The multiscale computational method with asymptotic analysis and reduced-order homogenization(ROH)gives a practical numerical solution for engineering problems,especially composite materials.Under the ROH framework,a partition-based unitcell structure at the mesoscale is utilized to give a mechanical state at the macro-scale quadrature point with pre-evaluated influence functions.In the past,the“1-phase,1-partition”rule was usually adopted in numerical analysis,where one constituent phase at the mesoscale formed one partition.The numerical cost then is significantly reduced by introducing an assumption that the mechanical responses are the same all the time at the same constituent,while it also introduces numerical inaccuracy.This study proposes a new partitioning method for fibrous unitcells under a reduced-order homogenization methodology.In this method,the fiber phase remains 1 partition,but the matrix phase is divided into 2 partitions,which refers to the“12”partitioning scheme.Analytical elastic influence+functions are derived by introducing the elastic strain energy equivalence(Hill-Mandel condition).This research also obtains the analytical eigenstrain influence functions by alleviating the so-called“inclusion-locking”phenomenon.In addition,a numerical approach to minimize the error of strain energy density is introduced to determine the partitioning of the matrix phase.Several numerical examples are presented to compare the differences among direct numerical simulation(DNS),“11”,and“12”partitioning schemes.The numerical simulations show improved++numerical accuracy by the“12”partitioning scheme.
基金funded by the Key Research and Development Program of Shandong Province(2023CXPT069)Opening Funds of the State Key Laboratory of Building Safety and Built Environment(BSBE2022-EET-06)Innovation Project of Guangwei Group Academician Workstation(GWYS-2022-04)。
文摘Sodium metal batteries(SMBs)are promising candidates for next-generation energy storage devices owing to their excellent safety performance and natural abunda nce of sodium.However,the insurmountable obstacles of dendrite formation and quick capacity decay are caused by an unstable and inhomogeneous solid electrolyte interphase that resulted from the immediate interactions between the Na metal anode and organic liquid electrolyte.Herein,a customised glass fibre separator coupled with chitosan(CS@GF)was developed to modulate the sodium ion(Na^(+))flux.The CS@GF separator facilitates the Na+homogeneous deposition on the anode side through redistribution at the chitosan polyactive sites and by inhibiting the decomposition of the electrolyte to robust solid electrolyte interphase(SEI)formation.Multiphysics simulations show that chitosan incorporated into SMBs through the separator can make the local electric field around the anode uniform,thus facilitating the transfer of cations.Na|Na symmetric cells utilising a CS@GF separator exhibited an outstanding cycle stability of over 600 h(0.5 mA cm^(-2)).Meanwhile,the Na|Na_(3)V_(5)(PO_(4))_(3)full cell exhibited excellent fast-charging performance(93.47%capacity retention after 1500 cycles at 5C).This study presents a promising strategy for inhibiting dendrite growth and realizes stable Na metal batteries,which significantly boosts the development of high-performance SMBs.
基金supported by the National Natural Science Foundation of China(No.51804232)Beijing Municipal Natural Science Foundation(No.2212041)+1 种基金supported by the Interdisciplinary Research Project for Young Teachers of USTB(Fundamental Research Funds for the Central Universities)(FRF-IDRY-20-020)GIMRT Program of the Institute for Materials Research,Tohoku University(202303-RDKGE-0518).
文摘Enhancing homogenization efficiency and hot-workability is the key issue for wrought superalloys in the industry.A novel approach for simultaneous accelerating the homogenization kinetics and improving hot-workability via a simple way of prior hot-deformation was proposed,which was not widely accepted for wrought superalloys.The homogenization efficiency is increased by 40%-70%via performing 10%-20%prior hot-deformation.Both theoretical and experimental analyses revealed that the increment in homogenization efficiency is mainly attributed to the decrease in interdendritic-segregation spacing,and thus the necessary diffusion distance,rather than that of dislocations.In addition,dynamic and static recrystallizations occurred during the prior hot-deformation and diffusion-annealing processes,and the grains were significantly refined even after the homogenization.Furthermore,the size of the precipitates was refined as well.These enhanced the hot-workability of the homogenized ingot for the subsequent cogging process.
文摘This study conducts a thorough examination of honeycomb sandwich panels with a lattice core,adopting advanced computational techniques for their modeling.The research extends its analysis to investigate the natural frequency behavior of sandwich panels,encompassing the comprehensive assessment of the entire panel structure.At its core,the research applies the Representative Volume Element(RVE)theory to establish the equivalent material properties,thereby enhancing the predictive capabilities of lattice structure simulations.Themethodology applies these properties in the core of infinite panels,which are modeled using double periodic boundary conditions to explore their natural frequencies.Expanding beyond mere material characterization,the study introduces a novel approach to defining the material within the panel cores.By incorporating alternate materials such as steel and AlSiC,and by strategically modifying their ratios,the research streamlines the process of material variation without resorting to repetitive 3D operations on the constituent cells.This optimizes not only the computational resources but also offers insights into the structural response under diverse material compositions.Furthermore,the investigation extends its scope to analyze the influence of curvature on the structural behavior of lattice structures.Panels are modeled with varying degrees of curvature,ranging from single to double curvatures,including cylindrical and spherical configurations,across a spectrum of radii.A rigorous analysis is performed to study the effect of curvature on the mechanical performance and stability of lattice structures,offering valuable insights for design optimization and structural engineering applications.By building upon the existing knowledge and introducing innovative methodologies,this study contributes to improving the understanding of lattice structures and their applicability in diverse engineering contexts.
基金supported by Beijing Institute of Graphic Communication Research Platform Construction Project(KYCPT202501).
文摘In recent years,the rapid expansion of heritage tourism within China’s ethnic minority regions has been accompanied by a significant challenge:the homogenization of cultural tourism imagery and experiences.This phenomenon adversely affects the sustainable development of local tourism industries.To foster the effective integration,preservation,and development of heritage tourism and ethnic cultures,this study presents a case analysis of Xijiang Qianhu Miao Village in Guizhou Province.Drawing upon field research and systematic analysis,the paper critically examines manifestations of homogenization across four key dimensions:cultural image representation,commercial operational models,experiential tourism methodologies,and the depth of cultural engagement.Based on these findings,the study proposes targeted strategies to optimize the cultural tourism experience within this specific context.
文摘Fish gelatin films have emerged as eco-friendly packaging materials due to their biodegradability and excellent film-forming properties.This study investigated the effects of varying homogenization rates(0,6500,9500,13,500,17,500,and 21,500 rpm)on the functional and structural properties of fish gelatin films enriched with cinnamon essential oil(CEO).Homogenization reduced droplet sizes and narrowed droplet size distributions in the film-forming emulsion(FFE).At a homogenization rate of 9500 rpm,the films exhibited excellent mechan-ical extensibility,reduced surface irregularities,and enhanced smoothness.The highest(p<0.05)tensile strength and elongation at break were observed at this rate,showing increases of 57%and 14%,respectively,compared to the control film made from non-homogenized FFE.However,further increases in homogenization rates signifi-cantly increased(p<0.05)water vapor permeability and caused CEO droplets aggregation,leading to increased surface irregularities and the formation of pores in the film microstructure.These structural changes were observed through confocal laser scanning microscopy(CLSM),scanning electron microscopy(SEM),and atomic force microscopy(AFM).These findings indicate that the film properties were significantly influenced by the homogenization rate,highlighting its role in tailoring the mechanical and barrier properties of fish gelatin/CEO films for food packaging applications.
基金Project supported by the National Natural Science Foundation of China(Nos.11922206,11702089,12272132)the Postgraduate Scientific Research Innovation Project of Hunan Province(No.CX20240388)。
文摘The acuurate prediction of the time-dependent mechanical behavior and deformation mechanisms of second-phase reinforced alloys under size effects is critical for the development of high-strength ductile metals and alloys for dynamic applications.However,solving their responses using high-fidelity numerical methods is computationally expensive and,in many cases,impractical.To address this issue,a dual-scale incremental variational formulation is proposed that incorporates the influence of plastic gradients on plastic evolution characteristics,integrating a strain-rate-dependent strain gradient plasticity model and including plastic gradients in the inelastic dissipation potential.Subsequently,two minimization problems based on the energy dissipation mechanisms of strain gradient plasticity,corresponding to the macroscopic and microscopic structures,are solved,leading to the development of a homogenization-based dual-scale solution algorithm.Finally,the effectiveness of the variational model and tangent algorithm is validated through a series of numerical simulations.The contributions of this work are as follows:first,it advances the theory of self-consistent computational homogenization modeling based on the energy dissipation mechanisms of plastic strain rates and their gradients,along with the development of a rigorous multi-level finite element method(FE2)solution procedure;second,the proposed algorithm provides an efficient and accurate method for evaluating the time-dependent mechanical behavior of second-phase reinforced alloys under strain gradient effects,exploring how these effects vary with the strain rate,and investigating their potential interactions.
基金supported by the National Natural Science Foundation of China(Nos.52441410,52020105013)the State Key Laboratory for Powder Metallurgy,China(No.2022)。
文摘The microstructures of a Ti−5Al−5Mo−5V−1Cr−1Fe alloy with a strain gradient from 0.1 to 1 were obtained by double-cone compression experiments.The deformation microstructures were analyzed by EBSD and TEM.The results show that the deformation mechanism is dynamic recovery when the strain is less than 0.42.In the strain range of 0.42−0.88,the deformation mechanism is dynamic recrystallization.When the strain exceeds 0.88,the deformation bands appear.The deformation mechanism map combined with the homogenization degree of the microstructure was constructed.The more homogeneous deformed microstructure was obtained at the strain of 0.6 and the temperature of 860°C.The dynamic recrystallization forms new grains and reduces the size difference between the grains,which improves the homogenization degree of the microstructure.
基金supported by the National Key Research and Development Program of China(No.2022YFB3400142)the National Natural Science Foundation of China(Nos.52174356,52022017,51927801,51971051,51901034 and U22A20174)+3 种基金the Science and Technology Plan Project of Liaoning Province(Nos.2022010005-JH6/1001 and 2022JH2/1013)the Innovation Foundation of Science and Technology of Dalian(Nos.2020JJ25CY002 and 2020J12GX037)the Major Science and Technology Projects of Longmen Laboratory(No.231100220400)the Fundamental Research Funds for the Central Universities.
文摘Obtaining an appropriate grain size is crucial for Al alloys or Al matrix composites prior to processing,as it significantly influences the mechanical properties of components and workability during the manufacturing process.TiB_(2)particles are exceptional grain refiners in Al and serve as excellent reinforcement particles for particulate-reinforced aluminum matrix composites.However,the optimal particle content for achieving excellent refinement and strengthening effects depends on the matrix composition and requires further investigation.Additionally,homogenization is essential for mitigating the element segregation in the ingot.Although it is anticipated that adding suitable particles can effectively inhibit undesired grain growth during homogenization,comprehensive investigations on this aspect are currently lacking.Therefore,TiB_(2)/2219Al matrix composites with varying reinforcement contents(0,1,3,5 wt%)were fabricated through traditional casting followed by homogenization treatment to address these research gaps.The effects of reinforcement content and homogenization treatment on the microstructure and mechanical properties of in-situ TiB_(2)/2219Al composites were investigated.The results demonstrate a gradual strengthening of the refining effect with increasing particle concentration.Moreover,composites containing 3 wt%TiB_(2)particles exhibit superior comprehensive mechanical properties in both as-cast and homogenized state.Additionally,potential orientation relationships are observed and calculated between undissolved Al_(2)Cu eutectic phase and submicron or nanometer-sized TiB_(2)particles,resulting in a mixture structure with enhanced bonding strength.This mixture structure is continuously distributed along grain boundaries during solidification,forming a three-dimensional cellular network that acts as primary retarding forces for grain growth during homogenization.Furthermore,the established homogenization kinetic equations were further utilized to analyze the correlation between homogenization time and grain size,as well as the influence of homogenization temperature.
基金Lisheng Liu acknowledges the support from the National Natural Science Foundation of China(No.11972267).
文摘This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to generate the C-ZrC inclusion model.Finally,the fiber structure is added to construct the microstructure of the three-phase plain weave composite.The reconstructed inclusions can meet the randomness of the shape and have a uniform distribution.Using an algorithm based on asymptotic homogenization and finite element method,the equivalent thermal conductivity prediction of the microstructure finite element model was carried out,and the influence of component volume fraction on material thermal properties was explored.The sensitivity of model parameters was studied,including the size,mesh sensitivity,Gaussian complexity,and correlation length of the RVE model,and the optimal calculation model was selected.The results indicate that the volume fraction of the inclusion phase has a significant impact on the equivalent thermal conductivity of the material.As the volume fraction of carbon fiber and ZrC increases,the equivalent thermal conductivity tensor gradually decreases.This model can be used to explore the impact of materialmicrostructure on the results,and numerical simulations have studied the relationship between structure and performance,providing the possibility of designing microstructure based on performance.
基金Project supported by the National Natural Science Foundation of China(Nos.11932008 and 12272156)the Fundamental Research Funds for the Central Universities(No.lzujbky-2022-kb06)+1 种基金the Gansu Science and Technology ProgramLanzhou City’s Scientific Research Funding Subsidy to Lanzhou University of China。
文摘Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting applications.With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components,the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields.Traditional numerical models include homogenized orthotropic models,which simplify overall field calculation but miss detailed multi-physics aspects,and full refinement(FR)ones that are thorough but computationally demanding.Herein,we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils.This approach combines a global homogenization(GH)scheme based on the homogenized electromagnetic T-A model,a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A,and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale.We then identify“dangerous regions”at the macroscopic scale and obtain finer details using a local refinement(LR)scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale.The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature,indicating that the present approach is accurate and efficient.The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.
基金Project supported by the National Natural Science Foundation of China(Nos.12172233 and U1934201)。
文摘The dynamic vibration absorber with inerter and grounded stiffness(IGDVA)is used to control a two-scale system subject to a weak periodic perturbation.The vibration suppression effect is remarkable.The amplitude of the main system coupled with absorber is significantly reduced,and the high frequency vibration completely disappears.First,through the slow-fast analysis and stability theory,it is found that the stability of the autonomous system exerts a notable regulating effect on the vibration response of the non-autonomous system.After adding the dynamic vibrator absorber,the center in the autonomous system changes to an asymptotically stable focus,consequently suppressing the vibration in the non-autonomous system.Further research reveals that the parameters of the absorber affect the real parts of the eigenvalues of the autonomous system,thereby regulating the stability of the system.Transitioning from a qualitative standpoint to a quantitative approach,a comparison of the solutions before and after the introduction of the dynamic absorber reveals that,when the grounded stiffness ratio and the mass ratio of the dynamic absorber are not equal,the high-frequency part in the analytical solution disappears.As a result,this leads to a reduction in the amplitude of the trajectory,achieving a vibration reduction effect.
基金financially supported by the National Natural Science Foundation of China(Project No.51874336)the National Key Technologies Research and Development Program of China during the 13th Five-Year Plan Period(Project No.2017ZX005030005)。
文摘The reaction order plays a crucial role in evaluating the response rate of acid-rock.However,the conventional two-scale model typically assumes that the reaction order is constant as one,which can lead to significant deviations from reality.To address this issue,this study proposes a novel multi-order dynamic model for acid-rock reaction by combining rotating disk experimental data with theoretical derivation.Through numerical simulations,this model allows for the investigation of the impact of acidification conditions on different orders of reaction,thereby providing valuable insights for on-site construction.The analysis reveals that higher response orders require higher optimal acid liquid flow rates,and lower optimal H+diffusion coefficients,and demonstrate no significant correlation with acid concentration.Consequently,it is recommended to increase the displacement and use high-viscosity acid for reservoirs with high calcite content,while reducing the displacement and using low-viscosity acid for reservoirs with high dolomite content.
基金supported by the National Natural Science Foundation of China(Grant No.12272144).
文摘By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.
基金supported by the China Scholarship Council (Grant No.2018-0861-0211).
文摘A two-scale method is proposed to simulate the essential behavior of bolted connections in structures includingelevated temperatures.It is presented,verified,and validated for the structural behavior of two plates,connectedby a bolt,under a variety of loads and elevated temperatures.The method consists of a global-scale model thatsimulates the structure(here the two plates)by volume finite elements,and in which the bolt is modelled bya spring.The spring properties are provided by a smallscale model,in which the bolt is modelled by volumeelements,and for which the boundary conditions are retrieved from the global-scale model.To ensure the small-scale model to be as computationally efficient as possible,simplifications are discussed regarding the materialmodel and the modelling of the threads.For the latter,this leads to the experimentally validated application ofa non-threaded shank with its stress area.It is shown that a non-linear elastic spring is needed for the bolt inthe global-scale model,so the post-peak behavior of the structure can be described efficiently.All types of boltedconnection failure as given by design standards are simulated by the twoscale method,which is successfullyvalidated(except for net section failure)by experiments,and verified by a detailed system model,which modelsthe structure in full detail.The sensitivity to the size of the part of the plate used in the small-scale modelis also studied.Finally,multi-directional load cases,also for elevated temperatures,are studied with the two-scale method and verified with the detailed system model.As a result,a computationally efficient finite elementmodelling approach is provided for all possible combined load actions(except for nut thread failure and netsection failure)and temperatures.The two-scale method is shown to be insightful,for it contains a functionalseparation of scales,revealing their relationships,and consequently,local small-scale non-convergence can behandled.Not presented in this paper,but the two-scale method can be used in e.g.computationally expensive two-way coupled fire-structure simulations,where it is beneficial for distributed computing and densely packed boltconfigurations with stiffplates,for which a single small-scale model may be representative for several connections.
