Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry.To study the mechanical behavior of a typical ductile cast iron(GJS-450)with nodular graphite,uni-axial quasi-static and dynamic tensile tests at strain rates of 10^(-4),1,10,100,and 250 s^(-1)were carried out.In order to investigate the influence of stress state on the deformation and fracture parameters,specimens with various geometries were used in the experiments.Stress strain curves and fracture strains of the GJS-450 alloy in the strain rate range of 10^(-4)to 250 s^(-1)were obtained.A strain rate-dependent plastic flow model was proposed to describe the mechanical behavior in the corresponding strain-rate range.The available damage model was extended to take the strain rate into account and calibrated based on the analysis of local fracture strains.Simulations with the proposed plastic flow model and the damage model were conducted to observe the deformation and fracture process.The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys.The predictions with the proposed plastic flow and damage models at various strain rates agree well with the experimental results,which illustrates that the rate-dependent plastic flow and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.The proposed plastic flow and damage models can be used to describe the deformation and fracture analysis of materials with similar properties.

Molecular dynamics study on temperature and strain rate dependences of mechanical tensile properties of ultrathin nickel nanowires

Based on the EAM potential, a molecular dynamics study on the tensile properties of ultrathin nickel nanowires in the （100〉 orientation with diameters of 3.94, 4.95 and 5.99 nm was presented at different temperatures and strain rates. The temperature and strain rate dependences of tensile properties were investigated. The simulation results show that the elastic modulus and the yield strength are gradually decreasing with the increase of temperature, while with the increase of the strain rate, the stress--strain curves fluctuate more intensely and the ultrathin nickel nanowires rupture at one smaller and smaller strain. At an ideal temperature of 0.01 K, the yield strength of the nanowires drops rapidly with the increase of strain rate, and at other temperatures the strain rate has a little influence on the elastic modulus and the yield strength. Finally, the effects of size on the tensile properties of ultrathin nickel nanowires were briefly discussed.

Application of thermodynamics-based rate-dependent constitutive models of concrete in the seismic analysis of concrete dams

This paper discusses the seismic analysis of concrete dams with consideration of material nonlinearity. Based on a consistent rate-dependent model and two thermodynamics-based models, two thermodynamics-based rate-dependent constitutive models were developed with consideration of the influence of the strain rate. They can describe the dynamic behavior of concrete and be applied to nonlinear seismic analysis of concrete dams taking into account the rate sensitivity of concrete. With the two models, a nonlinear analysis of the seismic response of the Koyna Gravity Dam and the Dagangshan Arch Dam was conducted. The results were compared with those of a linear elastic model and two rate-independent thermodynamics-based constitutive models, and the influences of constitutive models and strain rate on the seismic response of concrete dams were discussed. It can be concluded from the analysis that, during seismic response, the tensile stress is the control stress in the design and seismic safety evaluation of concrete dams. In different models, the plastic strain and plastic strain rate of concrete dams show a similar distribution. When the influence of the strain rate is considered, the maximum plastic strain and plastic strain rate decrease.

DISSIPATION-BASED CONSISTENT RATE-DEPENDENT MODEL FOR CONCRETE

An energy-dissipation based viscoplastic consistency model is presented to describe the performance of concrete under dynamic loading. The development of plasticity is started with the thermodynamic hypotheses in order that the model may have a sound theoretical background. Independent hardening and softening and the rate dependence of concrete are described separately for tension and compression. A modified implicit backward Euler integration scheme is adopted for the numerical computation. Static and dynamic behavior of the material is illustrated with certain numerical examples at material point level and structural level, and compared with existing experimental data. Results validate the effectiveness of the model.

Dynamic tensile strength and failure mechanisms of thermally treated sandstone under dry and water-saturated conditions

To study the tensile strength and failure mechanisms of rock with hydro-thermal coupling damage under different loading rates,a series of static and dynamic splitting tests were conducted on thermally treated sandstone under dry and water-saturated conditions.Experimental results showed that high temperatures effectively weakened the tensile strength of sandstone specimens,and the P-wave velocity declined with increasing temperature.Overall,thermal damage of rock increased gradually with increasing temperature,but obvious negative damage appeared at the temperature of 100℃.The water-saturated sandstone specimens had lower indirect tensile strength than the dry ones,which indicated that water-rock interaction led to secondary damage in heat-treated rock.Under both dry and water-saturated conditions,the dynamic tensile strength of sandstone increased with the increase of strain rate.The water-saturated rock specimens showed stronger rate dependence than the dry ones,but the loading rate sensitivity of thermally treated rock decreased with increasing treatment temperature.With the help of scanning electron microscopy technology,the thermal fractures of rock,caused by extreme temperature,were analyzed.Hydro-physical mechanisms of sandstone under different loading rate conditions after heat treatment were further discussed.

Effects of water saturation and loading rate on direct shear tests of andesite

For estimating the long-term stability of underground framework,it is vital to learn the mechanical and rheological characteristics of rock in multiple water saturation conditions.However,the majority of previous studies explored the rheological properties of rock in air-dried and water saturated conditions,as well as the water effects on compressive and tensile strengths.In this study,andesite was subjected to direct shear tests under five water saturation conditions,which were controlled by varying the wetting and drying time.The tests were conducted at alternating displacement rates under three vertical stresses.The results reveal that the shear strength decreases exponentially as water saturation increases,and that the increase in shear strength with a tenfold increase in displacement rate is nearly constant for each of the vertical stresses.Based on the findings of the shear tests in this study and the compression and tension tests in previous studies,the influences of both water saturation and loading rate on the Hoek-Brown failure criterion for the andesite was examined.These results indicate that the brittleness index of the andesite,which is defined as the ratio of uniaxial compressive strength to tensile strength,is independent of both water saturation and loading rate and that the influences of the water saturation dependence and the loading rate dependence of the failure criterion can be converted between each other.

Modelling and Analysis of Bacteria Dependent Infectious Diseases with Variable Contact Rates

In this research,we proposed a non-linear SIS model to study the effect of variable interaction rates and non-emigrating population of the human habitat on the spread of bacteria-infected diseases.It assumed that the growth of bacteria is logistic with an intrinsic growth rate is a linear function of infectives.In this model,we assume that contact rates between susceptibles and infectives as well as between susceptibles and bacteria depend on the density of the non-emigrating population and the total population of the habitat.The stability theory has been analyzed to analyzed to study the crucial role played by bacteria in the increased spread of an infectious disease.It is shown that as the density of non-emigrating population increases,the spread of an infectious disease increases.It is shown further that as the emigration increases,the spread of the disease decreases in both the cases of contact mentioned above rates,but this spread increases as these contact rates increase.It suggested that the control of bacteria in the human habitat is very useful to decrease the spread of an infectious disease.These results are confirmed by numerical simulation.

A STUDY OF RATE-DEPENDENCE AT ELEVATED TEMPERATURE FOR AN Al-Cu-Mg ALLOY

The hot deformation of an Al-Cu-Mg alloy was studied in the two temperature ranges (room temperature-300℃ and 400℃-480℃). The rate-independent flow curves are typical of elasto-plastic response with significant work hardening followed by strain softening below 300℃. Similar dislocation structures with high density tangled into grain interiors were observed by TEM, which suggests that the process of obstacles arresting mobile dislocations results in this macroscopically rate-independence. At 400-480℃, all rate dependent flow behaviors characterized by a continuous softening after an initial work hardening at a small plastic strain show large tensile elongations. Long dislocation segments around the second phases infer their good mobility to climb across obstacles. Grain boundary morphology observed by TEM suggests that the capacity of the grain boundaries to absorb the dislocations sensitively accounts for the rate-dependent mechanical properties.

Demographic Structure and the Real Exchange Rate:A Study Based on Cross-Country Data

By creating a two-sector intertemporal and intergenerational small open economy model,this paper investigates how real exchange rate responds to demographic shifts in the long term.The result shows that when the capital density of tradable goods sector exceeds that of non-tradable goods sector in a country,an increase in the country's elderly dependency rate(ODR) will cause its real exchange rate to appreciate.In addition,higher savings rate or per capita labor income means that real exchange rate is more responsive to ODR variations.We conducted an econometric test on our theoretical hypotheses using the data of 214 countries and regions during 1980-2013.Empirical result indicates that an increase of ODR will cause real exchange rate to appreciate.This result is robust and unaffected by sample grouping characteristics and differences.An increase in savings rate will significantly increase the ODR elasticity of real exchange rate.This conclusion is also significant and robust for overall samples and categorized samples(except for developed countries) and generally consistent with our theoretical hypothesis.However,our empirical research generally does not support the hypothesis that higher labor income increases the responsiveness of real exchange rate to ODR.This study is of great significance to unravel the effect of China's ageing population on the longterm variations of renminbi's exchange rate.

Relay-intercropping soybean with maize maintains soil fertility and increases nitrogen recovery efficiency by reducing nitrogen input

Optimized nitrogen(N)management can increase N-use efficiency in intercropping systems.Legume-nonlegume intercropping systems can reduce N input by exploiting biological N fixation by legumes.Measurement of N utilization can help in dissecting the mechanisms underlying N uptake and utilization in legume-nonlegume intercropping systems.An experiment was performed with three planting patterns:monoculture maize(MM),monoculture soybean(SS),and maize-soybean relay intercropping(IMS),and three N application levels:zero N(NN),reduced N(RN),and conventional N(CN)to investigate crop N uptake and utilization characteristics.N recovery efficiency and 15N recovery rate of crops were higher under RN than under CN,and those under RN were higher under intercropping than under the corresponding monocultures.Compared with MM,IMS showed a lower soil N-dependent rate(SNDR)in 2012.However,the SNDR of MM rapidly declined from 86.8%in 2012 to 49.4%in 2014,whereas that of IMS declined slowly from 75.4%in 2012 to 69.4%in 2014.The interspecific N competition rate(NCRms)was higher under RN than under CN,and increased yearly.Soybean nodule dry weight and nitrogenase activities were respectively 34.2%and 12.5%higher under intercropping than in monoculture at the beginning seed stage.The amount(Ndfa)and ratio(%Ndfa)of soybean N2 fixation were significantly greater under IS than under SS.In conclusion,N fertilizer was more efficiently used under RN than under CN;in particular,the relay intercropping system promoted N fertilizer utilization in comparison with the corresponding monocultures.An intercropping system helps to maintain soil fertility because interspecific N competition promotes biological N fixation by soybean by reducing N input.Thus,a maize-soybean relay intercropping system with reduced N application is sustainable and environmentally friendly.

GLOBAL DYNAMICS OF AN SEIR EPIDEMIC MODEL WITH IMMIGRATION OF DIFFERENT COMPARTMENTS

The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation.

The ICM method with objective function transformed by variable discrete condition for continuum structure

ICM （Independent Continuous Mapping） method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuration, by introducing the discrete condition of topological variables and integrating with the original objective, an optimal model with multi-objectives is formulated to make the topological variables approach 0 or 1 as near as possible, and the model reduces the effect of deleting rate on the result. The image-filtering method is employed to eliminate the checkerboard patterns and mesh dependence that occurred in the topology optimization of a continuum structure. The computational efficiency is enhanced through selecting quasi-active displacement constraints and a design region. Numerical examples indicate that this algorithm is robust and practicable, though the number of iterations is slightly increased with respect to the original algorithm.

STRESS DISTRIBUTION NEAR GRAIN BOUNDARY IN ANISOTROPIC BICRYSTALS AND TRICRYSTALS

The rate dependent crystallographic finite element program was implemented in ABAQUS as a UMAT for the analysis of the stress distributions near grain boundary in anisotropic bicrystals and tricrystals, taking the different crystallographic orientations into consideration. The numerical results of bicrystals model with the different crystallographic orientations shows that there is a high stress gradient near the grain boundaries. The characteristics of stress structures are dependent on the crystallographic orientations of the two grains. The existing of triple junctions in the tricrystals may result in the stress concentrations,or may not, depending on the crystallographic orientations of the three grains. The conclusion shows that grain boundary with different crystallographic orientations can have different deformation, damage, and failure behaviors. So it is only on the detail study of the stress distribution can the metal fracture be understood deeply.

Load Dependent Series-Parallel Systems with Common Bus Performance Sharing Mechanism

A series-parallel system was proposed with common bus performance sharing in which the performance and failure rate of the element depended on the load it was carrying. In such a system,the surplus performance of a sub-system can be transmitted to other deficient sub-systems. The transmission capacity of the common bus performance sharing mechanism is a random variable. Effects of load on element performance and failure rate were considered in this paper. A reliability evaluation algorithm based on the universal generating function technique was suggested. Numerical experiments were conducted to illustrate the algorithm.

Viscosity Transient Phenomenon in Drop Impact Testing of Soft Material

The authors carried out drop impact tests for several soft materials under a flat frontal impact condition in which a drop hammer with a flat bottom surface strikes a plate-like soft material in the normal direction. The experimental results indicated that the impact force waveforms of soft materials consisted of a thorn-shaped waveform and a subsequent mountain-shaped waveform. The thorn-shaped waveform was strongly affected by the strain rate. In the present study, the occurrence mechanism of this distinctive waveform was discussed from the viewpoint of the viscosity transient phenomenon. A standard linear solid (SLS) model in which the viscosity transient phenomenon was considered was applied to the simulation. Some features of the impact force waveform of soft materials could be explained by the SLS model. Furthermore, the thorn-shape waveform could also be observed in the impact force waveforms of human skin and free-falling hollow balls.

Impact of Demographic Transition on Household Energy Consumption: A Case from China

Understanding how aging population and low fertility affect household energy consumption is important for optimizing household energy consumption and reaching effective policies.This paper studies the impacts of demographic transition on household energy consumption based on panel data of 30 provinces in China from 2005 to 2016.Child-age dependency rate(CDR)and old-age dependency rate(ODR)are selected to track the shifts in age structure.They are introduced into a STIRPAT model to measure their impacts on household energy consumption.Besides,8 representative regions are additionally chosen and investigated to find some regional characteristics.The results show that current demographic transition to aging population expands household energy consumption.The aging population and low fertility cause additional challenges for energy saving and emission reduction.Household energy consumption in less developed areas is more likely to be affected by CDR and ODR.Regions with large population are also more easily influenced by demographic transitions especially CDR.This study emphases the effects of demographic elements on household energy consumption.It indicates that continuous optimization of household energy consumption structures should be based on population dynamics.

Rate-Dependent Weakening of the Shear Force for the Submerged Granular Medium Based on the Experimental Study

An experimental study is conducted to describe rate-dependent shear strength in a submerged granular medium to understand the mystery of submarine landslides with extremely small slide angles and long run-out distances.The experimental apparatus allows a long-span shear strain rate,■,for five orders of magnitude from 10^(-4)to 10^(1)s^(-1).It is observed that(a)submerged sand under higher shear tend to have bigger yield strength;this positive response of rate effect is significantly affected by the magnitudes of shear strain rates.(b)the residual strength of soil is clearly affected negatively by shear strain rate,decreasing as shear strain rate increases;even small variations under lower rate cause notable differences in residual strength,indicating a novel weaking rate-dependent.The yield strength and residual strength are corresponding to the shear state of soil.Hence,it is enough experimentally to explain that as long as the submarine mass flow speeds up,the slope sliding can be kept by only a small amount of force along the slide direction,which can be calculated as the gravity component even with a small slide angle.

Slow Phase Transition-Induced Scan Rate Dependence of Spin Crossover in a Two-Dimensional Supramolecular Fe(III)Complex

Spin crossover(SCO)is commonly accompanied by a synchronous phase transition.A few phase transitioncoupled SCO compounds have been reported,yet the synergy between SCO and phase transition on different time scales has not been explored.Herein,we report an[Fe(H-5-Cl-thsa-Et)(5-Cl-thsa-Et)]·H2O(1·H2O;H2-5-Cl-thsa-Et=5-chloro-salicylaldehyde ethylthiosemicarbazone)Fe(III)complex that displays a two-dimensional supramolecular structure and SCO behavior above room temperature.Its dehydrated form1 exhibits a two-step spin transition with aplateau in the temperature-dependent magnetization(M−T)curve at room temperature and a 51 K thermal hysteresis loop(Tc↑↓=299/248 K)at a rate of 5 K/min.The improved SCOperformance in 1 could be attributed to the stronger intralayer but weaker interlayer interactions,which is supported by single-crystal structural analysis and density functional theory calculations.Remarkably,complex 1 displays an unusual scan rate-dependent SCO behavior at rates of 0.5−30 K/min,in whichM−T curveplateaus appear at lower scan rates(<10 K/min)but vanish at faster scan rates(≥10 K/min).Scan rate-dependent differential scanning calorimetry,powder X-ray diffractometry,timedependent magnetic moment decays,and infrared spectroscopy consistently reveal that the slow structural relaxation is coupled with a slowcrystallographic phase transition,which is the mechanism for the unusual scan rate-dependent SCO.

Analysis of SIRVI model with time dependent coefficients and the effect of vaccination on the transmission rate and COVID-19 epidemic waves

COVID-19 epidemic models with constant transmission rate cannot capture the patterns of the infection data in the presence of pharmaceutical and non-pharmaceutical interventions during a pandemic.Because of this,a new modification of SIR model that contain the vaccination compartment with time dependent coefficients and weak/lossimmunity is explored.Literature review confirms that the effect of vaccination on the time dependent transmission rate is still an open problem.This study answers this open problem.In this study,we first prove the well-posedness and investigate the model dynamics to show their continuous dependence on the model parameters.We then provide an algorithm to derive the time-dependent transmission function for the epidemiologic model and the data of the infected cases.The derived coupled nonlinear differential equations show the effect of vaccination on the transmission rate.Unlike previous studies,we first filter the published data and solve the nonlinear coupled differential equations using the finite difference technique,where the coefficient of the coupled nonlinear differential equations is a function of given data.We then show that time-dependent transmission function can be represented by linear combinations of Gaussian radial base function.We then validate the prediction of our models using numerical simulations,where we used the published data of COVID-19 confirmed cases by the Ministries of Health in Saudi Arabia and Poland.Finally,the numerical solutions of a SIRVI model with time dependent transmission rate show that the waves for currently active cases are in good agreement with the data of Saudi Arabia and Poland.

A unified stochastic damage model for concrete based on multi-scale energy dissipation analysis

This work proposes a unified damage model for concrete within the framework of stochastic damage mechanics. Based on the micro-meso stochastic fracture model(MMSF), the nonlinear energy dissipation process of the microspring from nanoscale to microscale is investigated. In nanoscale, the rate process theory is adopted to describe the crack growth rate;therefore, the corresponding energy dissipation caused by a representative crack propagation can be obtained. The scale gap from nanoscale to microscale is bridged by a crack hierarchy model. Thus, the total energy dissipated by all cracks from the nanoscale to the microscale is gained. It is found that the fracture strain of the microspring can be derived from the above multi-scale energy dissipation analysis. When energy dissipation is regarded as some microdamage to the microspring, the constitutive law of the microspring is no longer linearly elastic, as previously assumed. By changing the expression of the damage evolution law from fracture strain to energy dissipation threshold, the new damage evolution model is derived. The proposed model can not only replicate the original static model but also extend to cases of rate dependence. By deriving the fracture strain under different strain rates, the rate sensitivity of concrete materials can be reflected. The model parameters can be conveniently obtained by identifying them with experimental data. Finally, several numerical examples are presented to verify the proposed model.