In this paper,numerical analysis is carried out for a class of history-dependent variationalhemivariational inequalities by arising in contact problems.Three different numerical treatments for temporal discretization ...In this paper,numerical analysis is carried out for a class of history-dependent variationalhemivariational inequalities by arising in contact problems.Three different numerical treatments for temporal discretization are proposed to approximate the continuous model.Fixed-point iteration algorithms are employed to implement the implicit scheme and the convergence is proved with a convergence rate independent of the time step-size and mesh grid-size.A special temporal discretization is introduced for the history-dependent operator,leading to numerical schemes for which the unique solvability and error bounds for the temporally discrete systems can be proved without any restriction on the time step-size.As for spatial approximation,the finite element method is applied and an optimal order error estimate for the linear element solutions is provided under appropriate regularity assumptions.Numerical examples are presented to illustrate the theoretical results.展开更多
Experimental investigations were pedermed on the plastic deformation along bilinear strain paths with various values of corner-angle by subjecting thin-walled tubular specimens of type 302 stainless steel to combined ...Experimental investigations were pedermed on the plastic deformation along bilinear strain paths with various values of corner-angle by subjecting thin-walled tubular specimens of type 302 stainless steel to combined axial and torsional loads. Variations of scalar and vectorial behavior of the stress response are discnssed in the vector space of plastic strain. It is found that the intrinsic geometry of loading path, the plastic strain history and the coapled effect among strain components effect effectively the stress response of the material. The experimental results also show that these effects will disappear gradually with increasing strain.展开更多
One objective of developing machine learning(ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems(BVPs).In the family of ML models,recurrent neural ne...One objective of developing machine learning(ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems(BVPs).In the family of ML models,recurrent neural networks(RNNs)have been extensively applied to capture history-dependent constitutive responses of granular materials,but these multiple-step-based neural networks are neither sufficiently efficient nor aligned with the standard finite element method(FEM).Single-step-based neural networks like the multi-layer perceptron(MLP)are an alternative to bypass the above issues but have to introduce some internal variables to encode complex loading histories.In this work,one novel Frobenius norm-based internal variable,together with the Fourier layer and residual architectureenhanced MLP model,is crafted to replicate the history-dependent constitutive features of representative volume element(RVE)for granular materials.The obtained ML models are then seamlessly embedded into the FEM to solve the BVP of a biaxial compression case and a rigid strip footing case.The obtained solutions are comparable to results from the FEM-DEM multiscale modelling but achieve significantly improved efficiency.The results demonstrate the applicability of the proposed internal variable in enabling MLP to capture highly nonlinear constitutive responses of granular materials.展开更多
Background:The steady-state increase in muscle force generating potential following a lengthening contraction is called residual force enhancement(RFE).In this study,we aimed to test for differences in torque,electrom...Background:The steady-state increase in muscle force generating potential following a lengthening contraction is called residual force enhancement(RFE).In this study,we aimed to test for differences in torque,electromyographic activity(EMG),and the associated neuromuscular efficiency(NME)between isometric voluntary contractions of elbow flexors preceded and not preceded by a lengthening contraction.The dependence of such differences on(i)stretch amplitude,(ii)the region of the force-length(FxL)relationship where contraction occurs,and(iii)the individual's ability to produce(negative)work during the stretch was investigated.Methods:Sixteen healthy adults participated in the study.Elbow flexor torque,angle,and biceps brachii EMG for purely isometric contractions(reference contractions)and for isometric contractions preceded by active stretches of 20°and 40°were measured at the ascending,plateau,and descending regions of subject-specific FxL curves.All contractions were performed in an isokinetic dynamometer.Two-factor(stretch×FxL region)repeated measures analysis of variance ANOVAs was used to analyze the effect of active stretch on EMG,torque,and NME across conditions.The relationships between mechanical work during stretch-calculated as the torque-angular displacement integral-and the changes in EMG,torque,and NME were analyzed using Pearson correlation.Results:In general,torque,EMG,and NME following active stretches differed from the values observed for the purely isometric reference contractions.While although the detailed effects of active stretch on torque and EMG differed between regions of the FxL relationship,NME increased by about 19%for all muscle lengths.Up to 30%of the interindividual variability in torque generating potential change in response to active stretching was accounted for by differences in(negative)work capacity between subjects.Conclusion:Our results suggest that(i)RFE contributes to"flatten"the elbow flexor torque-angle relationship,favoring torque production at lengths where the purely isometric torques are reduced substantially,and(ii)RFE contributes to a reduction in energy cost of torque production during isometric contractions for the entire operating range.展开更多
Unidirectional solidification of pivalic acid （PVA）-ethanol （Eth） mixture was performed to examine whether an allowable range of primary dendrite spacing definitely exists at a given growth velocity and how the ra...Unidirectional solidification of pivalic acid （PVA）-ethanol （Eth） mixture was performed to examine whether an allowable range of primary dendrite spacing definitely exists at a given growth velocity and how the range is history-dependent. PVA-0.59 wt pct Eth was unidirectionally solidified in the range of growth velocity 0.5-64 μm/s at the temperature gradient of 2.3 K/ram. Sequential change in growth velocity was imposed to determine the upper and lower limits for the allowable range of stable spacing. An allowable range of the steady state primary spacing was observed at a given growth velocity, and the extent of the range seems to be dependent on the degree to which step-increase or step-decrease in growth velocity is accomplished. As the degree of sequential change in growth velocity increases, the history-dependence of the selection for the primary dendrite spacing tends to disappear.展开更多
In order to investigate the response of cellular spacing to the variation of growth velocity under near-rapid directional solidification condition, Al-0.53wt%Zn alloy is directionally solidified with Bridgman apparatu...In order to investigate the response of cellular spacing to the variation of growth velocity under near-rapid directional solidification condition, Al-0.53wt%Zn alloy is directionally solidified with Bridgman apparatus. The results show that at the given temperature gradient the obtained microstrvctures are all cells and there exists a wide distribution range of cellular spacing. The maximum, λmax, minimum, λmin, and average cellular spacing, λ, as functions of growth rate, V, can be given by λmax=948.51V-0.4961, λmin= 661.16V-0.5015 and λ=412.41V-0.5049, respectively. The experimental results are compared with that predicted by KGT model, and a good agreement is found. Moreover,it is found that the average cellular spacing is also remarkably history-dependent.展开更多
In this paper,we study a new class of differential quasivariational-hemivariational inequalities of the elliptic type.The problem consists of a system coupling the Cauchy problem for an ordinary differential equation ...In this paper,we study a new class of differential quasivariational-hemivariational inequalities of the elliptic type.The problem consists of a system coupling the Cauchy problem for an ordinary differential equation with the variational-hemivariational inequalities,unilateral constraints,and history-dependent operators.First,based on the Minty formulation and the continuity of the solution map of a parametrized quasivariational-hemivariational inequality,and a fixed point theorem for a history-dependent operator,we prove a result on the well-posedness.Next,we examine optimal control problems for differential quasivariational-hemivariational inequalities,including a time-optimal control problem and a maximum stay control problem,for which we show the existence of solutions.In all the optimal control problems,the system is controlled through a distributed and boundary control,a control in initial conditions,and a control that appears in history-dependent operators.Finally,we illustrate the results by considering a nonlinear controlled system for a time-dependent elliptic equation with unilateral constraints.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11671098 and 91630309)Higher Education Discipline Innovation Project(111 Project)(Grant No.B08018)Institute of Scientific Computation and Financial Data Analysis,Shanghai University of Finance and Economics for the support during his visit。
文摘In this paper,numerical analysis is carried out for a class of history-dependent variationalhemivariational inequalities by arising in contact problems.Three different numerical treatments for temporal discretization are proposed to approximate the continuous model.Fixed-point iteration algorithms are employed to implement the implicit scheme and the convergence is proved with a convergence rate independent of the time step-size and mesh grid-size.A special temporal discretization is introduced for the history-dependent operator,leading to numerical schemes for which the unique solvability and error bounds for the temporally discrete systems can be proved without any restriction on the time step-size.As for spatial approximation,the finite element method is applied and an optimal order error estimate for the linear element solutions is provided under appropriate regularity assumptions.Numerical examples are presented to illustrate the theoretical results.
文摘Experimental investigations were pedermed on the plastic deformation along bilinear strain paths with various values of corner-angle by subjecting thin-walled tubular specimens of type 302 stainless steel to combined axial and torsional loads. Variations of scalar and vectorial behavior of the stress response are discnssed in the vector space of plastic strain. It is found that the intrinsic geometry of loading path, the plastic strain history and the coapled effect among strain components effect effectively the stress response of the material. The experimental results also show that these effects will disappear gradually with increasing strain.
基金supported by the National Natural Science Foundation of China(NSFC)(Grant No.12072217).
文摘One objective of developing machine learning(ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems(BVPs).In the family of ML models,recurrent neural networks(RNNs)have been extensively applied to capture history-dependent constitutive responses of granular materials,but these multiple-step-based neural networks are neither sufficiently efficient nor aligned with the standard finite element method(FEM).Single-step-based neural networks like the multi-layer perceptron(MLP)are an alternative to bypass the above issues but have to introduce some internal variables to encode complex loading histories.In this work,one novel Frobenius norm-based internal variable,together with the Fourier layer and residual architectureenhanced MLP model,is crafted to replicate the history-dependent constitutive features of representative volume element(RVE)for granular materials.The obtained ML models are then seamlessly embedded into the FEM to solve the BVP of a biaxial compression case and a rigid strip footing case.The obtained solutions are comparable to results from the FEM-DEM multiscale modelling but achieve significantly improved efficiency.The results demonstrate the applicability of the proposed internal variable in enabling MLP to capture highly nonlinear constitutive responses of granular materials.
文摘Background:The steady-state increase in muscle force generating potential following a lengthening contraction is called residual force enhancement(RFE).In this study,we aimed to test for differences in torque,electromyographic activity(EMG),and the associated neuromuscular efficiency(NME)between isometric voluntary contractions of elbow flexors preceded and not preceded by a lengthening contraction.The dependence of such differences on(i)stretch amplitude,(ii)the region of the force-length(FxL)relationship where contraction occurs,and(iii)the individual's ability to produce(negative)work during the stretch was investigated.Methods:Sixteen healthy adults participated in the study.Elbow flexor torque,angle,and biceps brachii EMG for purely isometric contractions(reference contractions)and for isometric contractions preceded by active stretches of 20°and 40°were measured at the ascending,plateau,and descending regions of subject-specific FxL curves.All contractions were performed in an isokinetic dynamometer.Two-factor(stretch×FxL region)repeated measures analysis of variance ANOVAs was used to analyze the effect of active stretch on EMG,torque,and NME across conditions.The relationships between mechanical work during stretch-calculated as the torque-angular displacement integral-and the changes in EMG,torque,and NME were analyzed using Pearson correlation.Results:In general,torque,EMG,and NME following active stretches differed from the values observed for the purely isometric reference contractions.While although the detailed effects of active stretch on torque and EMG differed between regions of the FxL relationship,NME increased by about 19%for all muscle lengths.Up to 30%of the interindividual variability in torque generating potential change in response to active stretching was accounted for by differences in(negative)work capacity between subjects.Conclusion:Our results suggest that(i)RFE contributes to"flatten"the elbow flexor torque-angle relationship,favoring torque production at lengths where the purely isometric torques are reduced substantially,and(ii)RFE contributes to a reduction in energy cost of torque production during isometric contractions for the entire operating range.
文摘Unidirectional solidification of pivalic acid （PVA）-ethanol （Eth） mixture was performed to examine whether an allowable range of primary dendrite spacing definitely exists at a given growth velocity and how the range is history-dependent. PVA-0.59 wt pct Eth was unidirectionally solidified in the range of growth velocity 0.5-64 μm/s at the temperature gradient of 2.3 K/ram. Sequential change in growth velocity was imposed to determine the upper and lower limits for the allowable range of stable spacing. An allowable range of the steady state primary spacing was observed at a given growth velocity, and the extent of the range seems to be dependent on the degree to which step-increase or step-decrease in growth velocity is accomplished. As the degree of sequential change in growth velocity increases, the history-dependence of the selection for the primary dendrite spacing tends to disappear.
文摘In order to investigate the response of cellular spacing to the variation of growth velocity under near-rapid directional solidification condition, Al-0.53wt%Zn alloy is directionally solidified with Bridgman apparatus. The results show that at the given temperature gradient the obtained microstrvctures are all cells and there exists a wide distribution range of cellular spacing. The maximum, λmax, minimum, λmin, and average cellular spacing, λ, as functions of growth rate, V, can be given by λmax=948.51V-0.4961, λmin= 661.16V-0.5015 and λ=412.41V-0.5049, respectively. The experimental results are compared with that predicted by KGT model, and a good agreement is found. Moreover,it is found that the average cellular spacing is also remarkably history-dependent.
基金supported by National Natural Science Foundation of China(Grant No.12171070)the Central Guidance on Local Science and Technology Development Fund of Sichuan Province(Grant No.2021ZYD0002)+3 种基金supported by the China Scholarship Council(Grant No.202106070120)supported by the European Union’s Horizon 2020 Research and Innovation Program under the Marie Sk?odowska-Curie Grant(Grant No.823731 CONMECH)the Ministry of Science and Higher Education of Poland(Grant Nos.4004/GGPJII/H2020/2018/0 and 440328/PnH2/2019)the National Science Center of Poland(Grant No.2021/41/B/ST1/01636)。
文摘In this paper,we study a new class of differential quasivariational-hemivariational inequalities of the elliptic type.The problem consists of a system coupling the Cauchy problem for an ordinary differential equation with the variational-hemivariational inequalities,unilateral constraints,and history-dependent operators.First,based on the Minty formulation and the continuity of the solution map of a parametrized quasivariational-hemivariational inequality,and a fixed point theorem for a history-dependent operator,we prove a result on the well-posedness.Next,we examine optimal control problems for differential quasivariational-hemivariational inequalities,including a time-optimal control problem and a maximum stay control problem,for which we show the existence of solutions.In all the optimal control problems,the system is controlled through a distributed and boundary control,a control in initial conditions,and a control that appears in history-dependent operators.Finally,we illustrate the results by considering a nonlinear controlled system for a time-dependent elliptic equation with unilateral constraints.
