It is well known that coarse-grained super-elastic NiTi shape memory alloys(SMAs)exhibit localized rather than homogeneous martensite transformation(MT),which,however,can be strongly influenced by either internal size...It is well known that coarse-grained super-elastic NiTi shape memory alloys(SMAs)exhibit localized rather than homogeneous martensite transformation(MT),which,however,can be strongly influenced by either internal size(grain size,GS)or the external size(geometric size).The coupled effect of GS and geometric size on the functional properties has not been clearly understood yet.In this work,the super-elasticity,one-way,and stress-assisted two-way shape memory effects of the polycrystalline NiTi SMAs with different aspect ratios(length/width for the gauge section)and different GSs are investigated based on the phase field method.The coupled effect of the aspect ratio and GS on the functional properties is adequately revealed.The simulated results indicate that when the aspect ratio is lower than about 4:1,the stress biaxiality and stress heterogeneity in the gauge section of the sample become more and more obvious with decreasing the aspect ratio,which can significantly influence the microstructure evolution in the process involving external stress.Therefore,the corresponding functional property is strongly dependent on the aspect ratio.With decreasing the GS and the aspect ratio(to be lower than 4:1),both the aspect ratio and GS can affect the MT or martensite reorientation in each grain and the interaction among grains.Thus,due to the strong internal constraint(i.e.,the constraint of grain boundary)and the external constraint(i.e.,the constraint of geometric boundary),the capabilities of the functional properties of NiTi SMAs are gradually weakened and highly dependent on these two factors.展开更多
Phase equilibrium modeling using internally consistent thermodynamic dataset and associated activity-composition(a-x)models are very helpful for quantifying P-T evolution for eclogite,which is the basis for decipherin...Phase equilibrium modeling using internally consistent thermodynamic dataset and associated activity-composition(a-x)models are very helpful for quantifying P-T evolution for eclogite,which is the basis for deciphering the geodynamic processes in subduction zones.In this study,we apply different versions of datasets(ds55 and ds62)and associated a-x relations to a wellestablished LT-HP eclogite at Huwan in the classic western Dabie orogen to constrain its P-T evolution.The eclogite comprises garnet+omphacite+amphibole+white mica+epidote+quartz+chlorite+rutile/ilmenite/sphene.Garnet porphyroblasts show mono-variation in the end members(spessartine from 17 mol%to 0,pyrope from 2 mol%to 18 mol%,almandine from 47 mol%to 64mol%and grossular from 35 mol%to 18 mol%)from core to rim.Phase diagrams combined with compositional isopleth thermobarometry show that dataset ds62 and associated a-x relations yield P_(max)of~33 kbar at~560℃,conflicting with our petrological observations and previous studies.On the other hand,phase equilibrium modeling using dataset ds62 and a revised symmetric garnet a-x model irrespective of Fe^(3+)(O)gives P_(max)of~27 kbar at~560℃,consistent with the results using dataset ds55 and associated a-x relations.Therefore,we recommend a symmetric model for garnet involving py,alm,gr and spss,without Fe~(3+)components,instead of the asymmetric garnet a-x relations involving py,alm,gr,spss and kho by White et al.(2014),for calculating phase diagrams for LT-(U)HP eclogite when using dataset ds62.In this study,the defined P-T path is characterized by a segment of the prograde evolution showing a first moderate slope,followed by gentle then steep slopes,representing the thermal structure evolution recorded by slab surface during continental subduction.Our work combined with previous studies conclude that in western Dabie,the Huwan HP eclogite belt to the north and the Hong'an HP eclogite belt to the south belong to the same HP slice overlying the Xinxian UHP slice.展开更多
As the demand for advanced material design and performance prediction continues to grow,traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy,par...As the demand for advanced material design and performance prediction continues to grow,traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy,particularly when addressing high-dimensional and complex data in multicomponent systems.To overcome these challenges,this study proposes an innovative model,LSGWO-BP,which integrates an improved Grey Wolf Optimizer(GWO)with a backpropagation neural network(BP)to enhance the accuracy and efficiency of quasi-phase equilibrium predictions within the KKS phase-field framework.Three mapping enhancement strategies were investigated–Circle-Root,Tent-Cosine,and Logistic-Sine mappings-with the Logistic mapping further improved via Sine perturbation to boost global search capability and convergence speed in large-scale,complex data scenarios.Evaluation results demonstrate that the LSGWO-BP model significantly outperforms conventional machine learning approaches in predicting quasi-phase equilibrium,achieving a 14%–28%reduction in mean absolute error(MAE).Substantial improvements were also observed in mean squared error,root mean squared error,and mean absolute percentage error,alongside a 7%–33%increase in the coefficient of determination(R2).Furthermore,the model exhibits strong potential for microstructural simulation applications.Overall,the study confirms the effectiveness of the LSGWO-BP model in materials science,especially in enhancing phase-field modeling efficiency and enabling accurate,intelligent prediction for multicomponent alloy systems,thereby offering robust support for microstructure prediction and control.展开更多
In this study,a powerful thermo-hydro-mechanical(THM)coupling solution scheme for saturated poroelastic media involving brittle fracturing is developed.Under the local thermal non-equilibrium(LTNE)assumption,this sche...In this study,a powerful thermo-hydro-mechanical(THM)coupling solution scheme for saturated poroelastic media involving brittle fracturing is developed.Under the local thermal non-equilibrium(LTNE)assumption,this scheme seamlessly combines the material point method(MPM)for accurately tracking solid-phase deformation and heat transport,and the Eulerian finite element method(FEM)for effectively capturing fluid flow and heat advection-diffusion behavior.The proposed approach circumvents the substantial challenges posed by large nonlinear equation systems with the monolithic solution scheme.The staggered solution process strategically separates each physical field through explicit or implicit integration.The characteristic-based method is used to stabilize advection-dominated heat flows for efficient numerical implementation.Furthermore,a fractional step approach is employed to decompose fluid velocity and pressure,thereby suppressing pore pressure oscillation on the linear background grid.The fracturing initiation and propagation are simulated by a rate-dependent phase field model.Through a series of quasi-static and transient simulations,the exceptional performance and promising potential of the proposed model in addressing THM fracturing problems in poro-elastic media is demonstrated.展开更多
Ab st ra ct Nanocrystalline materials exhibit unique properties due to their extremely high grain boundary(GB) density.However,this high-density characteristic induces grain coarsening at elevated temperatures,thereby...Ab st ra ct Nanocrystalline materials exhibit unique properties due to their extremely high grain boundary(GB) density.However,this high-density characteristic induces grain coarsening at elevated temperatures,thereby limiting the widespread application of nanocrystalline materials.Recent experimental observations revealed that GB segregation and second-phase pinning effectively hinder GB migration,thereby improving the stability of nanocry stalline materials.In this study,a mouified phase-field model that integrates mismatch strain,solute segregation and precipitation was developed to evaluate the influence of lattice misfit on the thermal stability of nanocrystalline alloys.The simulation results indicated that introducing a suitable mismatch strain can effectively enhance the microstructural stability of nanocrystalline alloys.By synergizing precipitation with an appropriate lattice misfit,the formation of second-phase particles in the bulk grains can be suppressed,thereby facilitating solute segregation/precipitation at the GBs.This concentrated solute segregation and precipitation at the GBs effectively hinders grain migration,thereby preventing grain coarsening.These findings provide a new perspective on the design and regulation of nanocrystalline alloys with enhanced thermal stability.展开更多
The subtropical North and South Pacific Meridional Modes(NPMM and SPMM)are well known precursors of El Niño-Southern Oscillation(ENSO).However,relationship between them is not constant.In the early 1980,the relat...The subtropical North and South Pacific Meridional Modes(NPMM and SPMM)are well known precursors of El Niño-Southern Oscillation(ENSO).However,relationship between them is not constant.In the early 1980,the relationship experienced an interdecadal transition.Changes in this connection can be attributed mainly to the phase change of the Pacific decadal oscillation(PDO).During the positive phase of PDO,a shallower thermocline in the central Pacific is responsible for the stronger trade wind charging(TWC)mechanism,which leads to a stronger equatorial subsurface temperature evolution.This dynamic process strengthens the connection between NPMM and ENSO.Associated with the negative phase of PDO,a shallower thermocline over southeastern Pacific allows an enhanced wind-evaporation-SST(WES)feedback,strengthening the connection between SPMM and ENSO.Using 35 Coupled Model Intercomparison Project Phase 6(CMIP6)models,we examined the NPMM/SPMM performance and its connection with ENSO in the historical runs.The great majority of CMIP6 models can reproduce the pattern of NPMM and SPMM well,but they reveal discrepant ENSO and NPMM/SPMM relationship.The intermodal uncertainty for the connection of NPMM-ENSO is due to different TWC mechanism.A stronger TWC mechanism will enhance NPMM forcing.For SPMM,few models can simulate a good relationship with ENSO.The intermodel spread in the relationship of SPMM and ENSO owing to SST bias in the southeastern Pacific,as WES feedback is stronger when the southeastern Pacific is warmer.展开更多
In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heighte...In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heightened concerns regarding insulation failures. Meanwhile, the underlying mechanism behind discharge breakdown failure and nanofiller enhancement under high-frequency electrical stress remains unclear. An electric-thermal coupled discharge breakdown phase field model was constructed to study the evolution of the breakdown path in polyimide nanocomposite insulation subjected to high-frequency stress. The investigation focused on analyzing the effect of various factors, including frequency, temperature, and nanofiller shape, on the breakdown path of Polyimide(PI) composites. Additionally, it elucidated the enhancement mechanism of nano-modified composite insulation at the mesoscopic scale. The results indicated that with increasing frequency and temperature, the discharge breakdown path demonstrates accelerated development, accompanied by a gradual dominance of Joule heat energy. This enhancement is attributed to the dispersed electric field distribution and the hindering effect of the nanosheets. The research findings offer a theoretical foundation and methodological framework to inform the optimal design and performance management of new insulating materials utilized in high-frequency power equipment.展开更多
The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifur...The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.展开更多
A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same che...A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same chemical potential, but with different compositions. The interface diffusion and boundary diffusion are also considered in the model. As an example, the model is applied to the sintering process with Fe-Cu powders. The free energy of each phase is described by the well-developed thermodynamic models, together with the published optimized parameters. The microstructure and solute distribution during the sintering process can both be obtained quantitively.展开更多
It is of great significance to accurately and rapidly identify shale lithofacies in relation to the evaluation and prediction of sweet spots for shale oil and gas reservoirs.To address the problem of low resolution in...It is of great significance to accurately and rapidly identify shale lithofacies in relation to the evaluation and prediction of sweet spots for shale oil and gas reservoirs.To address the problem of low resolution in logging curves,this study establishes a grayscale-phase model based on high-resolution grayscale curves using clustering analysis algorithms for shale lithofacies identification,working with the Shahejie For-mation,Bohai Bay Basin,China.The grayscale phase is defined as the sum of absolute grayscale and relative amplitude as well as their features.The absolute grayscale is the absolute magnitude of the gray values and is utilized for evaluating the material composition(mineral composition+total organic carbon)of shale,while the relative amplitude is the difference between adjacent gray values and is used to identify the shale structure type.The research results show that the grayscale phase model can identify shale lithofacies well,and the accuracy and applicability of this model were verified by the fitting relationship between absolute grayscale and shale mineral composition,as well as corresponding re-lationships between relative amplitudes and laminae development in shales.Four lithofacies are iden-tified in the target layer of the study area:massive mixed shale,laminated mixed shale,massive calcareous shale and laminated calcareous shale.This method can not only effectively characterize the material composition of shale,but also numerically characterize the development degree of shale laminae,and solve the problem that difficult to identify millimeter-scale laminae based on logging curves,which can provide technical support for shale lithofacies identification,sweet spot evaluation and prediction of complex continental lacustrine basins.展开更多
The Tianshan Mountains of Central Asia,highly sensitive to climate change,has been comprehensively assessed for its ecosystem vulnerability across multiple aspects.However,studies on the region's main river system...The Tianshan Mountains of Central Asia,highly sensitive to climate change,has been comprehensively assessed for its ecosystem vulnerability across multiple aspects.However,studies on the region's main river systems and hydropower resources remain limited.Thus,examining the impact of climate change on the runoff and gross hydropower potential(GHP)of this region is essential for promoting sustainable development and effective management of water and hydropower resources.This study focused on the Kaidu River Basin that is situated above the Dashankou Hydropower Station on the southern slope of the Tianshan Mountains,China.By utilizing an ensemble of bias-corrected global climate models(GCMs)from Coupled Model Intercomparison Project Phase 6(CMIP6)and the Variable Infiltration Capacity(VIC)model coupled with a glacier module(VIC-Glacier),we examined the variations in future runoff and GHP during 2017-2070 under four shared socio-economic pathway(SSP)scenarios(SSP1-2.6,SSP2-4.5,SSP3-7.0,and SSP5-8.5)compared to the baseline period(1985-2016).The findings indicated that precipitation and temperature in the Kaidu River Basin exhibit a general upward trend under the four SSP scenarios,with the fastest rate of increase in precipitation under the SSP2-4.5 scenario and the most significant changes in mean,maximum,and minimum temperatures under the SSP5-8.5 scenario,compared to the baseline period(1980-2016).Future runoff in the basin is projected to decrease,with rates of decline under the SSP1-2.6,SSP2-4.5,SSP3-7.0,and SSP5-8.5 scenarios being 3.09,3.42,7.04,and 7.20 m^(3)/s per decade,respectively.The trends in GHP are consistent with runoff,with rates of decline in GHP under the SSP1-2.6,SSP2-4.5,SSP3-7.0,and SSP5-8.5 scenarios at 507.74,563.33,1158.44,and 1184.52 MW/10a,respectively.Compared to the baseline period(1985-2016),the rates of change in GHP under the SSP1-2.6,SSP2-4.5,SSP3-7.0,and SSP5-8.5 scenarios are-20.66%,-20.93%,-18.91%,and-17.49%,respectively.The Kaidu River Basin will face significant challenges in water and hydropower resources in the future,underscoring the need to adjust water resource management and hydropower planning within the basin.展开更多
Ice particles could form under the continuous impingement of incoming supercooled droplets in icing conditions,which will change the surface roughness to enhance the further heat and mass transfer during icing process...Ice particles could form under the continuous impingement of incoming supercooled droplets in icing conditions,which will change the surface roughness to enhance the further heat and mass transfer during icing process.A fixed-grid porous enthalpy method based on the improved Discrete Phase Model(DPM)and Volume of Fluid(VOF)integrated algorithm is developed to solve the multiphase heat transfer problem to give more detailed demonstration of the formation of initial ice roughness.The algorithms to determine the criterion of transformation from DPM to VOF and the allocation of source items during transformation are improved to the general DPM-VOF algorithm.Two verification cases,namely two glycerine-solution droplets impact and single droplet freeze,are conducted to verify the accuracy and reliability of the enthalpy-DPMVOF method,where the simulation results match well with experiment phenomena.Ice roughness on a NACA0012 airfoil is precisely captured and the effects on convective heat transfer characteristics are preliminarily revealed.The results illustrate that the enthalpy-DPM-VOF method could successfully capture the characteristics of motion and the phase change process of droplet,as well as balance the calculation accuracy and efficiency.展开更多
Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary ...Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model. The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification. With the increase of growing time, the grains begin to coalesce and impinge the adjacent grains. When the dendrites start to impinge, the dendrite growth is obviously inhibited.展开更多
Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials...Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials is of great significance and necessity,which demands an accurate and efficient numerical tool in general cases because of the complexity of the arising boundary-value or initial-boundary value problems.In this paper,a phase field model is adopted and applied for the numerical simulation of the crack nucleation and propagation in brittle linear elastic two-phase perforated/particulate composites under a quasi-static tensile loading.The phase field model can well describe the initiation,propagation and coalescence of the cracks without assuming the existence and the geometry of the initial cracks in advance.Its numerical implementation is realized within the framework of the finite element method(FEM).The accuracy and the efficiency of the present phase field model are verified by the available reference results in literature.In the numerical examples,we first study and discuss the influences of the hole/particle size on the crack propagation trajectory and the force-displacement curve.Then,the effects of the hole/particle shape on the crack initiation and propagation are investigated.Furthermore,numerical examples are presented and discussed to show the influences of the hole/particle location on the crack initiation and propagation characteristics.It will be demonstrated that the present phase field model is an efficient tool for the numerical simulation of the crack initiation and propagation problems in brittle two-phase composite materials,and the corresponding results may play an important role in predicting and preventing possible hazardous crack initiation and propagation in engineering applications.展开更多
Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking p...Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites during solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms. When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.展开更多
High strength steel products with good ductility can be produced via Q&P hot stamping process,while the phase transformation of the process is more complicated than common hot stamping since two-step quenching and...High strength steel products with good ductility can be produced via Q&P hot stamping process,while the phase transformation of the process is more complicated than common hot stamping since two-step quenching and one-step carbon partitioning processes are involved.In this study,an integrated model of microstructure evolution relating to Q&P hot stamping was presented with a persuasively predicted results of mechanical properties.The transformation of diffusional phase and non-diffusional phase,including original austenite grain size individually,were considered,as well as the carbon partitioning process which affects the secondary martensite transformation temperature and the subsequent phase transformations.Afterwards,the mechanical properties including hardness,strength,and elongation were calculated through a series of theoretical and empirical models in accordance with phase contents.Especially,a modified elongation prediction model was generated ultimately with higher accuracy than the existed Mileiko’s model.In the end,the unified model was applied to simulate the Q&P hot stamping process of a U-cup part based on the finite element software LS-DYNA,where the calculated outputs were coincident with the measured consequences.展开更多
The diesel particulate matter(DPM) emission from diesel powered equipment in underground mines can cause health hazards including cancer to the miners. The understanding of the DPM propagation pattern under realistic ...The diesel particulate matter(DPM) emission from diesel powered equipment in underground mines can cause health hazards including cancer to the miners. The understanding of the DPM propagation pattern under realistic mining condition is required for selecting proper DPM control strategies and to improve working practices in underground mines. In this paper, three dimensional simulations of DPM emission from the exhaust tail pipe of a load-haul-dump(LHD) vehicle and its subsequent distribution inside an isolated zone in the typical underground mine are carried out using two different solution models available in Ansys Fluent. The incoming fresh air into the isolated zone is treated as a continuous phase and DPM is treated either as a continuous phase(gas) or as a secondary discrete phase(particle). Species transport model is used when DPM is treated as gas and discrete phase model is used when DPM is assumed to behave like a particle. The distributions of DPM concentration inside the isolated zone obtained from each method are presented and compared. From the comparison results, an accurate and economical solution technique for DPM evaluation can be selected.展开更多
The Precambrian lower crust rocks at the southeastern margin of the North China Craton （NCC） are mainly exposed as granulite xenoliths hosted by Mesozoic dioritic porphyry and metamorphic terrains in the Xuzhou-Suzh...The Precambrian lower crust rocks at the southeastern margin of the North China Craton （NCC） are mainly exposed as granulite xenoliths hosted by Mesozoic dioritic porphyry and metamorphic terrains in the Xuzhou-Suzhou area. Garnet amphiholites and garnet granulites are two kinds of typical lower-crustal xenoliths and were selected to reconstruct different stages of the metamorphic process. In this study, in view of multistage metamorphic evolution and reworking, phase equilibria modeling was used for the first time to better constrain peak P-T conditions of the xenoliths. Some porphyroblastic garnets have a weak zonal structure in composition with homogeneous cores and were surrounded by thin rims with an increase in XMg and a decrease in X Ca （or X Mg）- Clinopyroxene contain varying amounts of Na2O and Al2O3 as well as amphibole of TiO2, while plagioclases are different in calcium contents. Peak metamorphic P-T conditions are calculated by the smallest garnet x（g） （Fe2＋/（Fe2＋＋Mg）） contours and the smallest plagioclase ca（pl） （Ca/（Ca＋Na）） contours in NCFMASHTO （Na2O-CaO-FeO-MgO-Al2O3-SiO2- H20-TiO2-Fe2O3） system, which are consistent with those estimated by conventional geothermobarometry. The new results show that the peak and decompressional P-T conditions for the rocks are 850-900 ℃/ 1.4-1.6 GPa and 820-850 ℃/0.9-1.3 GPa, respectively, suggestive of high and middle-low pressure granulite-facies metamorphism. Combined with previous zircon U-Pb dating and conventional geothermobarometry data, it is indicated that the xenoliths experienced a clockwise P-T-t evolution with nearisothermal deeompressional process, suggestive of the Paleoproterozoic subduction-collision setting. In this regard, the studied region together with Jiao-Liao-Ji belt is further documented to make up a Paleopro- terozoic collisional orogen in the eastern block of the NCC.展开更多
In this paper, we present an improved multi-order parameter model for multi-component model of polycrystalline solidification. We introduce an interpolation function in the phase field dynamical equation to obtain con...In this paper, we present an improved multi-order parameter model for multi-component model of polycrystalline solidification. We introduce an interpolation function in the phase field dynamical equation to obtain controllable grain boundary energy at large undercooling. The same interpolation function is also employed in the kinetics coefficient to allow for better control of grain boundary migration. Temperature dependent phase field parameters and noise terms are consistently coupled into the dynamics of a binary system in a manner that allows for quantitative simulations in the thin interface limit. The model is applied to multi-phase solidification in Al-Cu alloy, where a parabolic fitting method is employed to model the free energy of Al-Cu phases and two-phase nucleation is demonstrated in directional solidification.展开更多
The relations of bulk modulus, shear modulus, Young's modulus and the Poisson's ratio with porosity of foam plastics are determined by a three phase spheroidal model commonly used in Composite Mechanics. The r...The relations of bulk modulus, shear modulus, Young's modulus and the Poisson's ratio with porosity of foam plastics are determined by a three phase spheroidal model commonly used in Composite Mechanics. The results are compared with those using differential scheme. It is shown that the material properties derived from the present model normally are larger than those obtained by differential scheme for foam plastics with identical porosity. The differences in shear moduli and Young's moduli obtained by the two methods are small but they are larger for bulk moduli of incompressible matrix and Poisson's ratios. The Young's moduli of high density foam plastics derived by the present model agree better with experimental ones.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.12202294 and 12022208)the Project funded by China Postdoctoral Science Foundation (Grant No.2022M712243)the Fundamental Research Funds for the Central Universities (Grant No.2023SCU12098).
文摘It is well known that coarse-grained super-elastic NiTi shape memory alloys(SMAs)exhibit localized rather than homogeneous martensite transformation(MT),which,however,can be strongly influenced by either internal size(grain size,GS)or the external size(geometric size).The coupled effect of GS and geometric size on the functional properties has not been clearly understood yet.In this work,the super-elasticity,one-way,and stress-assisted two-way shape memory effects of the polycrystalline NiTi SMAs with different aspect ratios(length/width for the gauge section)and different GSs are investigated based on the phase field method.The coupled effect of the aspect ratio and GS on the functional properties is adequately revealed.The simulated results indicate that when the aspect ratio is lower than about 4:1,the stress biaxiality and stress heterogeneity in the gauge section of the sample become more and more obvious with decreasing the aspect ratio,which can significantly influence the microstructure evolution in the process involving external stress.Therefore,the corresponding functional property is strongly dependent on the aspect ratio.With decreasing the GS and the aspect ratio(to be lower than 4:1),both the aspect ratio and GS can affect the MT or martensite reorientation in each grain and the interaction among grains.Thus,due to the strong internal constraint(i.e.,the constraint of grain boundary)and the external constraint(i.e.,the constraint of geometric boundary),the capabilities of the functional properties of NiTi SMAs are gradually weakened and highly dependent on these two factors.
基金financially supported by the National Natural Science Foundation of China(No.41930215)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)。
文摘Phase equilibrium modeling using internally consistent thermodynamic dataset and associated activity-composition(a-x)models are very helpful for quantifying P-T evolution for eclogite,which is the basis for deciphering the geodynamic processes in subduction zones.In this study,we apply different versions of datasets(ds55 and ds62)and associated a-x relations to a wellestablished LT-HP eclogite at Huwan in the classic western Dabie orogen to constrain its P-T evolution.The eclogite comprises garnet+omphacite+amphibole+white mica+epidote+quartz+chlorite+rutile/ilmenite/sphene.Garnet porphyroblasts show mono-variation in the end members(spessartine from 17 mol%to 0,pyrope from 2 mol%to 18 mol%,almandine from 47 mol%to 64mol%and grossular from 35 mol%to 18 mol%)from core to rim.Phase diagrams combined with compositional isopleth thermobarometry show that dataset ds62 and associated a-x relations yield P_(max)of~33 kbar at~560℃,conflicting with our petrological observations and previous studies.On the other hand,phase equilibrium modeling using dataset ds62 and a revised symmetric garnet a-x model irrespective of Fe^(3+)(O)gives P_(max)of~27 kbar at~560℃,consistent with the results using dataset ds55 and associated a-x relations.Therefore,we recommend a symmetric model for garnet involving py,alm,gr and spss,without Fe~(3+)components,instead of the asymmetric garnet a-x relations involving py,alm,gr,spss and kho by White et al.(2014),for calculating phase diagrams for LT-(U)HP eclogite when using dataset ds62.In this study,the defined P-T path is characterized by a segment of the prograde evolution showing a first moderate slope,followed by gentle then steep slopes,representing the thermal structure evolution recorded by slab surface during continental subduction.Our work combined with previous studies conclude that in western Dabie,the Huwan HP eclogite belt to the north and the Hong'an HP eclogite belt to the south belong to the same HP slice overlying the Xinxian UHP slice.
基金supported by the National Natural Science Foundation of China(Grant Nos.52161002,51661020 and 11364024)。
文摘As the demand for advanced material design and performance prediction continues to grow,traditional phase-field models are increasingly challenged by limitations in computational efficiency and predictive accuracy,particularly when addressing high-dimensional and complex data in multicomponent systems.To overcome these challenges,this study proposes an innovative model,LSGWO-BP,which integrates an improved Grey Wolf Optimizer(GWO)with a backpropagation neural network(BP)to enhance the accuracy and efficiency of quasi-phase equilibrium predictions within the KKS phase-field framework.Three mapping enhancement strategies were investigated–Circle-Root,Tent-Cosine,and Logistic-Sine mappings-with the Logistic mapping further improved via Sine perturbation to boost global search capability and convergence speed in large-scale,complex data scenarios.Evaluation results demonstrate that the LSGWO-BP model significantly outperforms conventional machine learning approaches in predicting quasi-phase equilibrium,achieving a 14%–28%reduction in mean absolute error(MAE).Substantial improvements were also observed in mean squared error,root mean squared error,and mean absolute percentage error,alongside a 7%–33%increase in the coefficient of determination(R2).Furthermore,the model exhibits strong potential for microstructural simulation applications.Overall,the study confirms the effectiveness of the LSGWO-BP model in materials science,especially in enhancing phase-field modeling efficiency and enabling accurate,intelligent prediction for multicomponent alloy systems,thereby offering robust support for microstructure prediction and control.
基金supported by National Natural Science Foundation of China(Grant No.42377149)the Research Grants Council of Hong Kong(General Research Fund Project No.17202423).
文摘In this study,a powerful thermo-hydro-mechanical(THM)coupling solution scheme for saturated poroelastic media involving brittle fracturing is developed.Under the local thermal non-equilibrium(LTNE)assumption,this scheme seamlessly combines the material point method(MPM)for accurately tracking solid-phase deformation and heat transport,and the Eulerian finite element method(FEM)for effectively capturing fluid flow and heat advection-diffusion behavior.The proposed approach circumvents the substantial challenges posed by large nonlinear equation systems with the monolithic solution scheme.The staggered solution process strategically separates each physical field through explicit or implicit integration.The characteristic-based method is used to stabilize advection-dominated heat flows for efficient numerical implementation.Furthermore,a fractional step approach is employed to decompose fluid velocity and pressure,thereby suppressing pore pressure oscillation on the linear background grid.The fracturing initiation and propagation are simulated by a rate-dependent phase field model.Through a series of quasi-static and transient simulations,the exceptional performance and promising potential of the proposed model in addressing THM fracturing problems in poro-elastic media is demonstrated.
基金financially supported by the National Natural Science Foundation of China (Nos.52122408, 51901013,51971018,52101188,52225103,52071023 and U20B2025)the Funds for Creative Research Groups of NSFC (No.51921001)the financial support from the Fundamental Research Funds for the Central Universities (University of Science and Technology Beijing,Nos.FRF-TP-2021-04C1 and 06500135)。
文摘Ab st ra ct Nanocrystalline materials exhibit unique properties due to their extremely high grain boundary(GB) density.However,this high-density characteristic induces grain coarsening at elevated temperatures,thereby limiting the widespread application of nanocrystalline materials.Recent experimental observations revealed that GB segregation and second-phase pinning effectively hinder GB migration,thereby improving the stability of nanocry stalline materials.In this study,a mouified phase-field model that integrates mismatch strain,solute segregation and precipitation was developed to evaluate the influence of lattice misfit on the thermal stability of nanocrystalline alloys.The simulation results indicated that introducing a suitable mismatch strain can effectively enhance the microstructural stability of nanocrystalline alloys.By synergizing precipitation with an appropriate lattice misfit,the formation of second-phase particles in the bulk grains can be suppressed,thereby facilitating solute segregation/precipitation at the GBs.This concentrated solute segregation and precipitation at the GBs effectively hinders grain migration,thereby preventing grain coarsening.These findings provide a new perspective on the design and regulation of nanocrystalline alloys with enhanced thermal stability.
基金Supported by the National Natural Science Foundation of China(NSFC)(No.41976027)。
文摘The subtropical North and South Pacific Meridional Modes(NPMM and SPMM)are well known precursors of El Niño-Southern Oscillation(ENSO).However,relationship between them is not constant.In the early 1980,the relationship experienced an interdecadal transition.Changes in this connection can be attributed mainly to the phase change of the Pacific decadal oscillation(PDO).During the positive phase of PDO,a shallower thermocline in the central Pacific is responsible for the stronger trade wind charging(TWC)mechanism,which leads to a stronger equatorial subsurface temperature evolution.This dynamic process strengthens the connection between NPMM and ENSO.Associated with the negative phase of PDO,a shallower thermocline over southeastern Pacific allows an enhanced wind-evaporation-SST(WES)feedback,strengthening the connection between SPMM and ENSO.Using 35 Coupled Model Intercomparison Project Phase 6(CMIP6)models,we examined the NPMM/SPMM performance and its connection with ENSO in the historical runs.The great majority of CMIP6 models can reproduce the pattern of NPMM and SPMM well,but they reveal discrepant ENSO and NPMM/SPMM relationship.The intermodal uncertainty for the connection of NPMM-ENSO is due to different TWC mechanism.A stronger TWC mechanism will enhance NPMM forcing.For SPMM,few models can simulate a good relationship with ENSO.The intermodel spread in the relationship of SPMM and ENSO owing to SST bias in the southeastern Pacific,as WES feedback is stronger when the southeastern Pacific is warmer.
基金supported in part by the National Key R&D Program of China (No.2021YFB2601404)Beijing Natural Science Foundation (No.3232053)National Natural Science Foundation of China (Nos.51929701 and 52127812)。
文摘In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heightened concerns regarding insulation failures. Meanwhile, the underlying mechanism behind discharge breakdown failure and nanofiller enhancement under high-frequency electrical stress remains unclear. An electric-thermal coupled discharge breakdown phase field model was constructed to study the evolution of the breakdown path in polyimide nanocomposite insulation subjected to high-frequency stress. The investigation focused on analyzing the effect of various factors, including frequency, temperature, and nanofiller shape, on the breakdown path of Polyimide(PI) composites. Additionally, it elucidated the enhancement mechanism of nano-modified composite insulation at the mesoscopic scale. The results indicated that with increasing frequency and temperature, the discharge breakdown path demonstrates accelerated development, accompanied by a gradual dominance of Joule heat energy. This enhancement is attributed to the dispersed electric field distribution and the hindering effect of the nanosheets. The research findings offer a theoretical foundation and methodological framework to inform the optimal design and performance management of new insulating materials utilized in high-frequency power equipment.
基金supported as part of the Computational Materials Sciences Program funded by the U.S.Department of Energy,Office of Science,Basic Energy Sciences,under Award No.DE-SC0020145Y.Z.would like to acknowledge support for his effort by the Simons Foundation through Grant No.357963 and NSF grant DMS-2142500.
文摘The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.
基金Project(2011CB606306)supported by the National Basic Research Program of ChinaProject(51101014)supported by the National Natural Science Foundation of ChinaProject(SKLSP201214)supported by the State Key Laboratory of Solidification Processing in Northwestern Polytechnical University,China
文摘A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same chemical potential, but with different compositions. The interface diffusion and boundary diffusion are also considered in the model. As an example, the model is applied to the sintering process with Fe-Cu powders. The free energy of each phase is described by the well-developed thermodynamic models, together with the published optimized parameters. The microstructure and solute distribution during the sintering process can both be obtained quantitively.
基金supported by the National Natural Science Foundation of China(42122017,41821002)the Independent Innovation Research Program of China University of Petroleum(East China)(21CX06001A).
文摘It is of great significance to accurately and rapidly identify shale lithofacies in relation to the evaluation and prediction of sweet spots for shale oil and gas reservoirs.To address the problem of low resolution in logging curves,this study establishes a grayscale-phase model based on high-resolution grayscale curves using clustering analysis algorithms for shale lithofacies identification,working with the Shahejie For-mation,Bohai Bay Basin,China.The grayscale phase is defined as the sum of absolute grayscale and relative amplitude as well as their features.The absolute grayscale is the absolute magnitude of the gray values and is utilized for evaluating the material composition(mineral composition+total organic carbon)of shale,while the relative amplitude is the difference between adjacent gray values and is used to identify the shale structure type.The research results show that the grayscale phase model can identify shale lithofacies well,and the accuracy and applicability of this model were verified by the fitting relationship between absolute grayscale and shale mineral composition,as well as corresponding re-lationships between relative amplitudes and laminae development in shales.Four lithofacies are iden-tified in the target layer of the study area:massive mixed shale,laminated mixed shale,massive calcareous shale and laminated calcareous shale.This method can not only effectively characterize the material composition of shale,but also numerically characterize the development degree of shale laminae,and solve the problem that difficult to identify millimeter-scale laminae based on logging curves,which can provide technical support for shale lithofacies identification,sweet spot evaluation and prediction of complex continental lacustrine basins.
基金funded by the National Natural Science Foundation of China(42067062).
文摘The Tianshan Mountains of Central Asia,highly sensitive to climate change,has been comprehensively assessed for its ecosystem vulnerability across multiple aspects.However,studies on the region's main river systems and hydropower resources remain limited.Thus,examining the impact of climate change on the runoff and gross hydropower potential(GHP)of this region is essential for promoting sustainable development and effective management of water and hydropower resources.This study focused on the Kaidu River Basin that is situated above the Dashankou Hydropower Station on the southern slope of the Tianshan Mountains,China.By utilizing an ensemble of bias-corrected global climate models(GCMs)from Coupled Model Intercomparison Project Phase 6(CMIP6)and the Variable Infiltration Capacity(VIC)model coupled with a glacier module(VIC-Glacier),we examined the variations in future runoff and GHP during 2017-2070 under four shared socio-economic pathway(SSP)scenarios(SSP1-2.6,SSP2-4.5,SSP3-7.0,and SSP5-8.5)compared to the baseline period(1985-2016).The findings indicated that precipitation and temperature in the Kaidu River Basin exhibit a general upward trend under the four SSP scenarios,with the fastest rate of increase in precipitation under the SSP2-4.5 scenario and the most significant changes in mean,maximum,and minimum temperatures under the SSP5-8.5 scenario,compared to the baseline period(1980-2016).Future runoff in the basin is projected to decrease,with rates of decline under the SSP1-2.6,SSP2-4.5,SSP3-7.0,and SSP5-8.5 scenarios being 3.09,3.42,7.04,and 7.20 m^(3)/s per decade,respectively.The trends in GHP are consistent with runoff,with rates of decline in GHP under the SSP1-2.6,SSP2-4.5,SSP3-7.0,and SSP5-8.5 scenarios at 507.74,563.33,1158.44,and 1184.52 MW/10a,respectively.Compared to the baseline period(1985-2016),the rates of change in GHP under the SSP1-2.6,SSP2-4.5,SSP3-7.0,and SSP5-8.5 scenarios are-20.66%,-20.93%,-18.91%,and-17.49%,respectively.The Kaidu River Basin will face significant challenges in water and hydropower resources in the future,underscoring the need to adjust water resource management and hydropower planning within the basin.
基金supported by the National Natural Science Foundation of China(No.51706244)National Science and Technology Major Projects of China(No.2017-VIII-0003-0114)。
文摘Ice particles could form under the continuous impingement of incoming supercooled droplets in icing conditions,which will change the surface roughness to enhance the further heat and mass transfer during icing process.A fixed-grid porous enthalpy method based on the improved Discrete Phase Model(DPM)and Volume of Fluid(VOF)integrated algorithm is developed to solve the multiphase heat transfer problem to give more detailed demonstration of the formation of initial ice roughness.The algorithms to determine the criterion of transformation from DPM to VOF and the allocation of source items during transformation are improved to the general DPM-VOF algorithm.Two verification cases,namely two glycerine-solution droplets impact and single droplet freeze,are conducted to verify the accuracy and reliability of the enthalpy-DPMVOF method,where the simulation results match well with experiment phenomena.Ice roughness on a NACA0012 airfoil is precisely captured and the effects on convective heat transfer characteristics are preliminarily revealed.The results illustrate that the enthalpy-DPM-VOF method could successfully capture the characteristics of motion and the phase change process of droplet,as well as balance the calculation accuracy and efficiency.
基金supported by the Doctor Foundational Research Project in Shenyang Ligong University(Serial Number:0010).
文摘Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model. The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification. With the increase of growing time, the grains begin to coalesce and impinge the adjacent grains. When the dendrites start to impinge, the dendrite growth is obviously inhibited.
基金the National Natural Science Foundation of China(Grants U1333201 and U1833116)。
文摘Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials is of great significance and necessity,which demands an accurate and efficient numerical tool in general cases because of the complexity of the arising boundary-value or initial-boundary value problems.In this paper,a phase field model is adopted and applied for the numerical simulation of the crack nucleation and propagation in brittle linear elastic two-phase perforated/particulate composites under a quasi-static tensile loading.The phase field model can well describe the initiation,propagation and coalescence of the cracks without assuming the existence and the geometry of the initial cracks in advance.Its numerical implementation is realized within the framework of the finite element method(FEM).The accuracy and the efficiency of the present phase field model are verified by the available reference results in literature.In the numerical examples,we first study and discuss the influences of the hole/particle size on the crack propagation trajectory and the force-displacement curve.Then,the effects of the hole/particle shape on the crack initiation and propagation are investigated.Furthermore,numerical examples are presented and discussed to show the influences of the hole/particle location on the crack initiation and propagation characteristics.It will be demonstrated that the present phase field model is an efficient tool for the numerical simulation of the crack initiation and propagation problems in brittle two-phase composite materials,and the corresponding results may play an important role in predicting and preventing possible hazardous crack initiation and propagation in engineering applications.
基金financially supported by the Educational Department of Liaoning Province (No.20060744)the Shenyang Nurturing Young Scientific Technological Talents Items (No.1081230-1-00)
文摘Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites during solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms. When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.
基金Supported by National Natural Science Foundation of China (Grant Nos. 51775336,U1564203)Program of Shanghai Academic Research Leadership (Grant No. 19XD1401900)
文摘High strength steel products with good ductility can be produced via Q&P hot stamping process,while the phase transformation of the process is more complicated than common hot stamping since two-step quenching and one-step carbon partitioning processes are involved.In this study,an integrated model of microstructure evolution relating to Q&P hot stamping was presented with a persuasively predicted results of mechanical properties.The transformation of diffusional phase and non-diffusional phase,including original austenite grain size individually,were considered,as well as the carbon partitioning process which affects the secondary martensite transformation temperature and the subsequent phase transformations.Afterwards,the mechanical properties including hardness,strength,and elongation were calculated through a series of theoretical and empirical models in accordance with phase contents.Especially,a modified elongation prediction model was generated ultimately with higher accuracy than the existed Mileiko’s model.In the end,the unified model was applied to simulate the Q&P hot stamping process of a U-cup part based on the finite element software LS-DYNA,where the calculated outputs were coincident with the measured consequences.
基金financial support provided by the Western US Mining Safety and Health Training&Translation Center by the National Institute for Occupational Safety and Health(NIOSH)
文摘The diesel particulate matter(DPM) emission from diesel powered equipment in underground mines can cause health hazards including cancer to the miners. The understanding of the DPM propagation pattern under realistic mining condition is required for selecting proper DPM control strategies and to improve working practices in underground mines. In this paper, three dimensional simulations of DPM emission from the exhaust tail pipe of a load-haul-dump(LHD) vehicle and its subsequent distribution inside an isolated zone in the typical underground mine are carried out using two different solution models available in Ansys Fluent. The incoming fresh air into the isolated zone is treated as a continuous phase and DPM is treated either as a continuous phase(gas) or as a secondary discrete phase(particle). Species transport model is used when DPM is treated as gas and discrete phase model is used when DPM is assumed to behave like a particle. The distributions of DPM concentration inside the isolated zone obtained from each method are presented and compared. From the comparison results, an accurate and economical solution technique for DPM evaluation can be selected.
基金financially supported by the National Natural Science Foundation of China (No. 41773020)the National Basic Research Program of China (No. 2015CB856104)the PhD Foundation of the Ministry of Education of China (No. 20133402130008)
文摘The Precambrian lower crust rocks at the southeastern margin of the North China Craton （NCC） are mainly exposed as granulite xenoliths hosted by Mesozoic dioritic porphyry and metamorphic terrains in the Xuzhou-Suzhou area. Garnet amphiholites and garnet granulites are two kinds of typical lower-crustal xenoliths and were selected to reconstruct different stages of the metamorphic process. In this study, in view of multistage metamorphic evolution and reworking, phase equilibria modeling was used for the first time to better constrain peak P-T conditions of the xenoliths. Some porphyroblastic garnets have a weak zonal structure in composition with homogeneous cores and were surrounded by thin rims with an increase in XMg and a decrease in X Ca （or X Mg）- Clinopyroxene contain varying amounts of Na2O and Al2O3 as well as amphibole of TiO2, while plagioclases are different in calcium contents. Peak metamorphic P-T conditions are calculated by the smallest garnet x（g） （Fe2＋/（Fe2＋＋Mg）） contours and the smallest plagioclase ca（pl） （Ca/（Ca＋Na）） contours in NCFMASHTO （Na2O-CaO-FeO-MgO-Al2O3-SiO2- H20-TiO2-Fe2O3） system, which are consistent with those estimated by conventional geothermobarometry. The new results show that the peak and decompressional P-T conditions for the rocks are 850-900 ℃/ 1.4-1.6 GPa and 820-850 ℃/0.9-1.3 GPa, respectively, suggestive of high and middle-low pressure granulite-facies metamorphism. Combined with previous zircon U-Pb dating and conventional geothermobarometry data, it is indicated that the xenoliths experienced a clockwise P-T-t evolution with nearisothermal deeompressional process, suggestive of the Paleoproterozoic subduction-collision setting. In this regard, the studied region together with Jiao-Liao-Ji belt is further documented to make up a Paleopro- terozoic collisional orogen in the eastern block of the NCC.
基金financial support by the National Foundation of China under Grant No. 51875131Nikolas Provatas acknowledges financial support by the Canada Research Chairs (CRC) Programsupported by the China Scholarship Council as a Graduate Trainee at McGill University。
文摘In this paper, we present an improved multi-order parameter model for multi-component model of polycrystalline solidification. We introduce an interpolation function in the phase field dynamical equation to obtain controllable grain boundary energy at large undercooling. The same interpolation function is also employed in the kinetics coefficient to allow for better control of grain boundary migration. Temperature dependent phase field parameters and noise terms are consistently coupled into the dynamics of a binary system in a manner that allows for quantitative simulations in the thin interface limit. The model is applied to multi-phase solidification in Al-Cu alloy, where a parabolic fitting method is employed to model the free energy of Al-Cu phases and two-phase nucleation is demonstrated in directional solidification.
基金Supported by the National Natural Science Foundation of China and Laboratory for Nonlinear Mechanics of Continuous Media,Institute of Mechanics,Chinese Academy of Sciences.
文摘The relations of bulk modulus, shear modulus, Young's modulus and the Poisson's ratio with porosity of foam plastics are determined by a three phase spheroidal model commonly used in Composite Mechanics. The results are compared with those using differential scheme. It is shown that the material properties derived from the present model normally are larger than those obtained by differential scheme for foam plastics with identical porosity. The differences in shear moduli and Young's moduli obtained by the two methods are small but they are larger for bulk moduli of incompressible matrix and Poisson's ratios. The Young's moduli of high density foam plastics derived by the present model agree better with experimental ones.
