Nowadays,studies on the mechanism of macro-scopic nonlinear behavior of materials by accumulation of micro-scopic degradation are attracting more attention from researchers.Among numerous approaches,multiscale methods...Nowadays,studies on the mechanism of macro-scopic nonlinear behavior of materials by accumulation of micro-scopic degradation are attracting more attention from researchers.Among numerous approaches,multiscale methods have been proved as powerful and practical approaches in predicting macro-scopic material status by averaging and homogenizing physical information from associated micro-scopic mate-rial behavior.Usually in mechanical problem,the stress,consistent material modulus,and possible mate-rial state variables are quantities in interest through the upscaling process.However,the energy-related quantities are not studied much.Some initiative work has been done in the early year including but not limited to the Hill-Mandel condition in multiscale framework,which gives that the macro-scopic elastic strain energy density can be computed by volumetric averaging of that in the micro-scale.However,in the nonlinear analysis,the energy dissipation is an important quantity to measure the degradation status.In this manuscript,two typical multiscale methods,the first-order computational homogenization(FOCH)and reduced-order homogenization(ROH),are adopted to numerically analyze a fiber-reinforced compos-ite material with capability in material nonlinearity.With numerical experiments,it can be shown that energy dissipation is the same for both approaches.展开更多
This paper deals with modeling of the phenomenon of fretting fatigue in heterogeneous materials using the multi-scale computational homogenization technique and finite element analysis(FEA).The heterogeneous material ...This paper deals with modeling of the phenomenon of fretting fatigue in heterogeneous materials using the multi-scale computational homogenization technique and finite element analysis(FEA).The heterogeneous material for the specimens consists of a single hole model(25% void/cell,16% void/cell and 10% void/cell)and a four-hole model(25%void/cell).Using a representative volume element(RVE),we try to produce the equivalent homogenized properties and work on a homogeneous specimen for the study of fretting fatigue.Next,the fretting fatigue contact problem is performed for 3 new cases of models that consist of a homogeneous and a heterogeneous part(single hole cell)in the contact area.The aim is to analyze the normal and shear stresses of these models and compare them with the results of the corresponding heterogeneous models based on the Direct Numerical Simulation(DNS)method.Finally,by comparing the computational time and%deviations,we draw conclusions about the reliability and effectiveness of the proposed method.展开更多
The paper deals with the numerical modelling of ductile damage responses in heterogeneous materials using the classical second-order homogenization approach.The scale transition methodology in the multiscale framework...The paper deals with the numerical modelling of ductile damage responses in heterogeneous materials using the classical second-order homogenization approach.The scale transition methodology in the multiscale framework is described.The structure at the macrolevel is discretized by the triangular C^(1) finite elements obeying nonlocal continuum theory,while the discretization of microstructural volume element at the microscale is conducted by means of the mixed type quadrilateral finite element with the nonlocal equivalent plastic strain as an additional nodal variable.The ductile damage evolution at the microlevel is modelled by using the gradient enhanced elastoplasticity.The macrolevel softening is governed by two criterions expressed by the increase in homogenized damage variable and the threshold of the local equivalent strain.The softening at each material point at the macrolevel is detected by the critical value of the homogenized damage,where homogenization of the damage variable is performed onlywithin softening area.Due to the nonlocal continuumtheory applied,a realistic softening behaviour is demonstrated after the damage initiation,compared to the widely used first-order homogenization approach.All algorithms derived have been embedded into the finite element code ABAQUS by means of the user subroutines and verified on the standard benchmark problems.The damage evolution at both microlevel and macrolevel has been demonstrated.展开更多
In this paper, a kind of second-order two-scale （SOTS） computation is developed for conductive-radiative heat trans- fer problem in periodic porous materials. First of all, by the asymptotic expansion of the tempera...In this paper, a kind of second-order two-scale （SOTS） computation is developed for conductive-radiative heat trans- fer problem in periodic porous materials. First of all, by the asymptotic expansion of the temperature field, the cell problem, homogenization problem, and second-order correctors are obtained successively. Then, the corresponding finite element al- gorithms are proposed. Finally, some numerical results are presented and compared with theoretical results. The numerical results of the proposed algorithm conform with those of the FE algorithm well, demonstrating the accuracy of the present method and its potential applications in thermal engineering of porous materials.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
In this paper,we discuss the numerical accuracy of asymptotic homogenization method(AHM)and multiscale finite element method(MsFEM)for periodic composite materials.Through numerical calculation of the model problems f...In this paper,we discuss the numerical accuracy of asymptotic homogenization method(AHM)and multiscale finite element method(MsFEM)for periodic composite materials.Through numerical calculation of the model problems for four kinds of typical periodic composite materials,the main factors to determine the accuracy of first-order AHM and second-order AHM are found,and the physical interpretation of these factors is given.Furthermore,the way to recover multiscale solutions of first-order AHM and MsFEM is theoretically analyzed,and it is found that first-order AHM and MsFEM provide similar multiscale solutions under some assumptions.Finally,numerical experiments verify that MsFEM is essentially a first-order multiscale method for periodic composite materials.展开更多
The fine-scale heterogeneity of granular material is characterized by its polydisperse microstructure with randomness and no periodicity. To predict the mechanical response of the material as the microstructure evolve...The fine-scale heterogeneity of granular material is characterized by its polydisperse microstructure with randomness and no periodicity. To predict the mechanical response of the material as the microstructure evolves, it is demonstrated to develop computational multiscale methods using discrete particle assembly-Cosserat continuum modeling in micro- and macro- scales,respectively. The computational homogenization method and the bridge scale method along the concurrent scale linking approach are briefly introduced. Based on the weak form of the Hu-Washizu variational principle, the mixed finite element procedure of gradient Cosserat continuum in the frame of the second-order homogenization scheme is developed. The meso-mechanically informed anisotropic damage of effective Cosserat continuum is characterized and identified and the microscopic mechanisms of macroscopic damage phenomenon are revealed. c 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi： 10.1063/2.1301101]展开更多
This paper presents methods for computing a second-order sensitivity matrix and the Hessian matrix of eigenvalues and eigenvectors of multiple parameter structures. Second-order perturbations of eigenvalues and eigenv...This paper presents methods for computing a second-order sensitivity matrix and the Hessian matrix of eigenvalues and eigenvectors of multiple parameter structures. Second-order perturbations of eigenvalues and eigenvectors are transformed into multiple parameter forms,and the second-order perturbation sensitivity matrices of eigenvalues and eigenvectors are developed.With these formulations,the efficient methods based on the second-order Taylor expansion and second-order perturbation are obtained to estimate changes of eigenvalues and eigenvectors when the design parameters are changed. The presented method avoids direct differential operation,and thus reduces difficulty for computing the second-order sensitivity matrices of eigenpairs.A numerical example is given to demonstrate application and accuracy of the proposed method.展开更多
A multiphase computational fluid dynamics(CFD)model coupled with the population balance equation(PBE)was developed in a homogeneous air-kerosene bubble column under elevated pressure(P).The specific pressure drop(ΔP/...A multiphase computational fluid dynamics(CFD)model coupled with the population balance equation(PBE)was developed in a homogeneous air-kerosene bubble column under elevated pressure(P).The specific pressure drop(ΔP/L),gas holdup(α_(G)),and Sauter mean diameter(d_(32))were experimentally measured in the bubble column with 1.8 m height and 0.1 m inner diameter,which was operated at a superficial gas velocity of 12.3 mm·s^(-1),and P=1-35 bar(1 bar=10^(5) Pa).A modified drag coefficient model was proposed to consider the effect of bubble swarm and pressure on hydrodynamics of the bubble column.The Luo breakage model was modified to account for liquid density,viscosity,surface tension and gas density.TheΔP/L,α_(G),and d_(32) obtained from the CFD model were compared with experimental data,and the gas density-dependent parameters of the CFD model were identified.With increasing P from 1 to 35 bar,theα_(G) varied from 5.4%to 7.2% and the d32 decreased from 2.3 to 1.5 mm.The CFD-PBE model is applicable to predict hydrodynamics of pressurized bubble columns for gas-organic liquid in the homogeneous regime.展开更多
The second-order random walk has recently been shown to effectively improve the accuracy in graph analysis tasks.Existing work mainly focuses on centralized second-order random walk(SOW)algorithms.SOW algorithms rely ...The second-order random walk has recently been shown to effectively improve the accuracy in graph analysis tasks.Existing work mainly focuses on centralized second-order random walk(SOW)algorithms.SOW algorithms rely on edge-to-edge transition probabilities to generate next random steps.However,it is prohibitively costly to store all the probabilities for large-scale graphs,and restricting the number of probabilities to consider can negatively impact the accuracy of graph analysis tasks.In this paper,we propose and study an alternative approach,SOOP(second-order random walks with on-demand probability computation),that avoids the space overhead by computing the edge-to-edge transition probabilities on demand during the random walk.However,the same probabilities may be computed multiple times when the same edge appears multiple times in SOW,incurring extra cost for redundant computation and communication.We propose two optimization techniques that reduce the complexity of computing edge-to-edge transition probabilities to generate next random steps,and reduce the cost of communicating out-neighbors for the probability computation,respectively.Our experiments on real-world and synthetic graphs show that SOOP achieves orders of magnitude better performance than baseline precompute solutions,and it can efficiently computes SOW algorithms on billion-scale graphs.展开更多
基金the National Natural Science Foundation of China(Grant No.11988102)is gratefully acknowledged.
文摘Nowadays,studies on the mechanism of macro-scopic nonlinear behavior of materials by accumulation of micro-scopic degradation are attracting more attention from researchers.Among numerous approaches,multiscale methods have been proved as powerful and practical approaches in predicting macro-scopic material status by averaging and homogenizing physical information from associated micro-scopic mate-rial behavior.Usually in mechanical problem,the stress,consistent material modulus,and possible mate-rial state variables are quantities in interest through the upscaling process.However,the energy-related quantities are not studied much.Some initiative work has been done in the early year including but not limited to the Hill-Mandel condition in multiscale framework,which gives that the macro-scopic elastic strain energy density can be computed by volumetric averaging of that in the micro-scale.However,in the nonlinear analysis,the energy dissipation is an important quantity to measure the degradation status.In this manuscript,two typical multiscale methods,the first-order computational homogenization(FOCH)and reduced-order homogenization(ROH),are adopted to numerically analyze a fiber-reinforced compos-ite material with capability in material nonlinearity.With numerical experiments,it can be shown that energy dissipation is the same for both approaches.
文摘This paper deals with modeling of the phenomenon of fretting fatigue in heterogeneous materials using the multi-scale computational homogenization technique and finite element analysis(FEA).The heterogeneous material for the specimens consists of a single hole model(25% void/cell,16% void/cell and 10% void/cell)and a four-hole model(25%void/cell).Using a representative volume element(RVE),we try to produce the equivalent homogenized properties and work on a homogeneous specimen for the study of fretting fatigue.Next,the fretting fatigue contact problem is performed for 3 new cases of models that consist of a homogeneous and a heterogeneous part(single hole cell)in the contact area.The aim is to analyze the normal and shear stresses of these models and compare them with the results of the corresponding heterogeneous models based on the Direct Numerical Simulation(DNS)method.Finally,by comparing the computational time and%deviations,we draw conclusions about the reliability and effectiveness of the proposed method.
文摘The paper deals with the numerical modelling of ductile damage responses in heterogeneous materials using the classical second-order homogenization approach.The scale transition methodology in the multiscale framework is described.The structure at the macrolevel is discretized by the triangular C^(1) finite elements obeying nonlocal continuum theory,while the discretization of microstructural volume element at the microscale is conducted by means of the mixed type quadrilateral finite element with the nonlocal equivalent plastic strain as an additional nodal variable.The ductile damage evolution at the microlevel is modelled by using the gradient enhanced elastoplasticity.The macrolevel softening is governed by two criterions expressed by the increase in homogenized damage variable and the threshold of the local equivalent strain.The softening at each material point at the macrolevel is detected by the critical value of the homogenized damage,where homogenization of the damage variable is performed onlywithin softening area.Due to the nonlocal continuumtheory applied,a realistic softening behaviour is demonstrated after the damage initiation,compared to the widely used first-order homogenization approach.All algorithms derived have been embedded into the finite element code ABAQUS by means of the user subroutines and verified on the standard benchmark problems.The damage evolution at both microlevel and macrolevel has been demonstrated.
基金Project supported by the National Basic Research Program of China(Grant No.2010CB832702)the National Natural Science Foundation of China(Grant No.90916027)
文摘In this paper, a kind of second-order two-scale （SOTS） computation is developed for conductive-radiative heat trans- fer problem in periodic porous materials. First of all, by the asymptotic expansion of the temperature field, the cell problem, homogenization problem, and second-order correctors are obtained successively. Then, the corresponding finite element al- gorithms are proposed. Finally, some numerical results are presented and compared with theoretical results. The numerical results of the proposed algorithm conform with those of the FE algorithm well, demonstrating the accuracy of the present method and its potential applications in thermal engineering of porous materials.
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the National Natural Science Foundation of China(No.11501449 and 11471262)the Center for high performance computing of Northwestern Polytechnical University.
文摘In this paper,we discuss the numerical accuracy of asymptotic homogenization method(AHM)and multiscale finite element method(MsFEM)for periodic composite materials.Through numerical calculation of the model problems for four kinds of typical periodic composite materials,the main factors to determine the accuracy of first-order AHM and second-order AHM are found,and the physical interpretation of these factors is given.Furthermore,the way to recover multiscale solutions of first-order AHM and MsFEM is theoretically analyzed,and it is found that first-order AHM and MsFEM provide similar multiscale solutions under some assumptions.Finally,numerical experiments verify that MsFEM is essentially a first-order multiscale method for periodic composite materials.
基金supported by the National Natural Science Foundation of China(11072046,10672033,90715011 and 11102036)the National Basic Research and Development Program(973Program,2010CB731502)
文摘The fine-scale heterogeneity of granular material is characterized by its polydisperse microstructure with randomness and no periodicity. To predict the mechanical response of the material as the microstructure evolves, it is demonstrated to develop computational multiscale methods using discrete particle assembly-Cosserat continuum modeling in micro- and macro- scales,respectively. The computational homogenization method and the bridge scale method along the concurrent scale linking approach are briefly introduced. Based on the weak form of the Hu-Washizu variational principle, the mixed finite element procedure of gradient Cosserat continuum in the frame of the second-order homogenization scheme is developed. The meso-mechanically informed anisotropic damage of effective Cosserat continuum is characterized and identified and the microscopic mechanisms of macroscopic damage phenomenon are revealed. c 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi： 10.1063/2.1301101]
基金Project supported by the 985-Engineering Innovation of Graduate Students of Jilin Universitythe Science and Technology Development Foundation of Jilin Province(20070541)
文摘This paper presents methods for computing a second-order sensitivity matrix and the Hessian matrix of eigenvalues and eigenvectors of multiple parameter structures. Second-order perturbations of eigenvalues and eigenvectors are transformed into multiple parameter forms,and the second-order perturbation sensitivity matrices of eigenvalues and eigenvectors are developed.With these formulations,the efficient methods based on the second-order Taylor expansion and second-order perturbation are obtained to estimate changes of eigenvalues and eigenvectors when the design parameters are changed. The presented method avoids direct differential operation,and thus reduces difficulty for computing the second-order sensitivity matrices of eigenpairs.A numerical example is given to demonstrate application and accuracy of the proposed method.
基金the financial support from the R&D Convergence Program of the Ministry of Science, ICT and Future Planning (MSIP)the National Research Council of Science & Technology (NST) of the Republic of Korea (CRC-14-1KRICT)supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Ministry of Science and ICT (2020R1F1A1066097)
文摘A multiphase computational fluid dynamics(CFD)model coupled with the population balance equation(PBE)was developed in a homogeneous air-kerosene bubble column under elevated pressure(P).The specific pressure drop(ΔP/L),gas holdup(α_(G)),and Sauter mean diameter(d_(32))were experimentally measured in the bubble column with 1.8 m height and 0.1 m inner diameter,which was operated at a superficial gas velocity of 12.3 mm·s^(-1),and P=1-35 bar(1 bar=10^(5) Pa).A modified drag coefficient model was proposed to consider the effect of bubble swarm and pressure on hydrodynamics of the bubble column.The Luo breakage model was modified to account for liquid density,viscosity,surface tension and gas density.TheΔP/L,α_(G),and d_(32) obtained from the CFD model were compared with experimental data,and the gas density-dependent parameters of the CFD model were identified.With increasing P from 1 to 35 bar,theα_(G) varied from 5.4%to 7.2% and the d32 decreased from 2.3 to 1.5 mm.The CFD-PBE model is applicable to predict hydrodynamics of pressurized bubble columns for gas-organic liquid in the homogeneous regime.
文摘The second-order random walk has recently been shown to effectively improve the accuracy in graph analysis tasks.Existing work mainly focuses on centralized second-order random walk(SOW)algorithms.SOW algorithms rely on edge-to-edge transition probabilities to generate next random steps.However,it is prohibitively costly to store all the probabilities for large-scale graphs,and restricting the number of probabilities to consider can negatively impact the accuracy of graph analysis tasks.In this paper,we propose and study an alternative approach,SOOP(second-order random walks with on-demand probability computation),that avoids the space overhead by computing the edge-to-edge transition probabilities on demand during the random walk.However,the same probabilities may be computed multiple times when the same edge appears multiple times in SOW,incurring extra cost for redundant computation and communication.We propose two optimization techniques that reduce the complexity of computing edge-to-edge transition probabilities to generate next random steps,and reduce the cost of communicating out-neighbors for the probability computation,respectively.Our experiments on real-world and synthetic graphs show that SOOP achieves orders of magnitude better performance than baseline precompute solutions,and it can efficiently computes SOW algorithms on billion-scale graphs.
