砂土强度和剪胀性的颗粒力学分析

砂土强度和剪胀性一直是土力学强度和变形研究的难点和重点,对其进一步认识的关键取决于对砂土颗粒状微观结构的洞察。砂土的颗粒性和散碎性使其适合采用颗粒力学来研究。该文从颗粒力学角度出发,利用平面离散元模拟砂土变形,建立并标定了砂土单元实验的一个颗粒力学模型。在此基础上,通过颗粒力学参数影响分析,研究了砂土无侧限双轴试验的三种表观强度指标(临界状态强度、峰值强度和特征应力强度)、剪胀性及剪切模量的颗粒力学影响因素。研究结果表明:砂土临界状态强度仅受砂土颗粒摩擦系数的影响,是材料属性,符合临界状态土力学理论;砂土峰值强度和特征应力强度不但与砂土颗粒摩擦系数相关,还与围压水平和相对密实度有关。峰值强度不受砂土颗粒自身刚度性质的影响,而特征应力强度受颗粒刚度性质的影响较大,但后者的影响规律不是简单的正比或反比的关系。砂土剪切模量主要受其颗粒自身刚度性质的影响,就目前研究来看,它与砂土相对密实度的关系并不显著。用颗粒力学方法对剪胀性的深入研究比较困难,主要是因为诸多颗粒力学参数(砂土颗粒摩擦系数和刚度、砂土样品的孔隙率及围压水平)均与之相关。该文尝试研究了砂土剪胀性与其颗粒转角的关系。最后,用该文标定的颗粒力学模型,研究了无重地基极限承载力普朗德尔-瑞斯纳问题,通过颗粒力学计算结果与普朗德尔-瑞斯纳解的对比,深化了对砂土地基极限承载力的理解,也为计算颗粒力学方法在岩土工程尺度上的应用提供了参考。     

砂土统一本构模型研究及其三维数值实现

基于广义塑性理论与临界状态概念,研究提出了一个统一三维砂土本构模型,通过一组参数实现了砂土由压缩至剪切过程中状态参量的统一表述。基于ABAQUS提供的用户自定义材料子程序UMAT接口,利用Fortran语言编程实现了该三维弹塑性本构关系模型在软件中的二次开发。分别利用Toyoura砂、Fuji River砂以及Tokachi砂的剪切试验数据与数值模拟结果进行对比,结果表明:提出的有限元计算模型可以有效反映加载过程中不同围压和砂土初始密度对应力-应变曲线的影响,能够准确描述密砂的剪胀特性与应变软化特性以及松砂的剪缩特性与应变硬化特性,从而更加真实地反映三维应力状态下土的变形和强度特性。研究成果进一步扩展了ABAQUS在岩土工程中的应用范围,能够为岩土工程领域的数值分析计算提供更加快捷的解决方案。     

A simple non-associated flow model for sand

 This paper proposes a simple non-associated plasticity model for sand. The yield surface is taken to be a member of a recently derived family of yield loci, requiring the specification of a single parameter in addition to the stress ratio at the peak value of deviatoric stress on the yield surface in deviatoric:mean effective stress space. This simple equation, can easily be fitted to given sand data. The flow rule also has a simple equation, such that the critical state is not at the top of the yield locus in stress space. The equation of the flow rule requires the specification of the critical state dissipation constant, plus one additional parameter. This permits realistic modelling of the undrained behaviour of sand in states looser and denser than critical. The parameter controlling the flow rule can, for convenience, be taken to be equal to the parameter governing the shape of the yield surface. However, since the two parameters are not required to be equal, the flow rule can easily be adjusted to model more accurately the rate of change of direction of the plastic strain increment vector with changing stress ratio around the yield surface. The model resembles more complex models based on the mathematical theory of envelopes, but the equations of the yield loci and flow rules are much simpler. The contribution in this paper is therefore to provide a model similar to those derived based on micro mechanical considerations, but which is more useful to geotechnical engineers, in that the number of parameters is kept to a minimum, the constitutive equations are simple, and the flow rule can easily be controlled. The model is easy to apply in geotechnical analysis, and would be easy to implement in a finite element program. Received: 11 January 2002     

基于亚塑性理论建立土体各向异性本构模型的一种新途径

在归纳整理连续介质的材料力学性质的基础上,引出土体本构关系的两种描述框架,即弹塑性理论和亚塑性理论,并对其相互关系进行了分析,指出亚塑性理论适宜用来构建土体的本构模型,并提出了一种基于亚塑性理论的建立土体各向异性本构模型的新途径,该途径通过将一各向异性破坏准则嵌入亚塑性模型来确定各向异性参数,有别于以往通过拟合实验数据来确定各向异性参数的方法。该途径为目前各种分析平台提供了一种考虑主应力轴旋转效应的可能。     

Mesoscale simulations of a dart penetrating sand

Historically, hydrodynamic calculations have utilized continuum constitutive models to simulate the coupled dynamic response of a solid projectile penetrating a heterogeneous target system such as concrete, foam or a granular porous medium. Continuum models fail to capture the complicated grain level response within the heterogeneous target which can result in asymmetric loading of the projectile leading to variations in projectile performance. These grain level effects can be crucial to predicting the penetration depth or overall effectiveness of the projectile. In order to assess the possibility of using mesoscale simulations to resolve the grain level dynamics, hydrodynamic simulations were performed for an 11.4 cm long, 0.9 cm diameter dart penetrating a bed of porous granular dry sand with an initial velocity of 366 m/s. Simulations were performed using the Eulerian hydrocode CTH in a two-dimensional planar configuration. The goal of the mesoscale simulations is to determine the viability of using these techniques as an alternative to continuum models and to assess the effects of grain level variability such as anisotropic material distributions and variations in the dynamic yield and fracture strength. The results indicate that variations in the size distribution of aggregate added and the fracture strength of the sand system can have a significant effect on penetration performance of the dart; whereas variations in the dynamic strength of the sand had little effect on the dart penetration.     

Using the design of experiment to model the effect of silica sand and cement on crushing properties of carbonate sand

In this study, an experimental investigation into the effects of adding a limited proportion of silica sand and cement on crushing properties of simulated carbonate sand is presented. Silica sand in the proportion of 20, 30 and 50% and cement in the proportion of 2 and 4% by dry weight were the fractions added to the base soil. Cemented samples with different dry density 14 and 16 kN/m³ have been considered. Predictive models for the crushing parameter (C_r) are elaborated using the design of experiment method, considering silica sand fraction, cement fraction and effective normal stresses parameters. A good correlation between the values given by the experimental tests and those given by the model was observed. The main effects of the addition of silica sand and cement are reduction of particles crushing, leading to a soil exhibiting less contraction during shearing. Addition of a fraction of silica sand and/or cement enhances the resistance of the particles to crushing occurring during shear. The greatest resistance in crushing is produced when both a fraction of cement and silica sand are added to the soil and mixed at a denser state.     

Water retention curve of snow with different grain sizes

The water retention curve (WRC), which shows the relationship between volumetric water content (θ_v) and suction (h), is fundamental for characterizing hydraulic properties. Thus, to model water movement through the snow cover, a formulation for the WRC as a function of snow characteristics must be established. In order to examine the dependence of the WRC on the grain size of snow, we measured the WRCs of snow (550 kg m⁻³) of various grain sizes in gravity drainage column experiments. Our experiments revealed many similarities between the WRCs of snow and sand. Thus, we applied two soil physics models, the Brooks and Corey model (BC model) and the van Genuchten model (VG model), which are standard models in soil physics to analyze the WRC of snow. Two parameters in both models that affected the shape of the WRC had a strong relationship with sample grain size. The parameter related to the value of the reverse of air entry suction increased with an increase in grain size, whereas the parameter related to the gradient of θ_v versus h (dθ_v / dh) decreased with an increase in grain size. From these results, we obtained linear equations between those two parameters and grain size. Our results suggest that the WRC of snow can be described as a function of grain size using soil physics models.     

A novel constitutive model for Ti–6Al–4V alloy based on dislocation pile-up theory

The mechanical properties of the titanium alloy Ti–6Al–4V, which vary with the specimen size under different temperatures, are studied through the Split Hopkinson Pressure Bar (SHPB) test and the quasi-static tensile test to determine the parameters for the classical Johnson-Cook (JC) constitutive model. Based on the dislocation pile-up theory, the classical JC constitutive model is modified by adding a grain strain term Δσ to consider the influence of grain size. The SHPB and tensile tests are analysed using a finite element method simulation. Compared with the experimental results, the simulation results based on the modified JC model exhibit a much higher calculation accuracy than that of the classical JC model.     

A Comparative Study of Several Material Models for Prediction of Hyperelastic Properties: Application to Silicone-Rubber and Soft Tissues

Abstract:  The correct modelling of constitutive laws is of critical importance for the analysis of mechanical behaviour of solids and structures. For example, the understanding of soft tissue mechanics, because of the nonlinear behaviour commonly displayed by the mechanical properties of such materials, makes common place the use of hyperelastic constitutive models. Hyperelastic models however, depend on sets of variables that must be obtained experimentally. In this study the authors use a computational/experimental scheme, for the study of the nonlinear mechanical behaviour of biological soft tissues under uniaxial tension. The material constants for seven different hyperelastic material models are obtained via inverse methods. The use of Martins's model to fit experimental data is presented in this paper for the first time. The search for an optimal value for each set of material parameters is performed by a Levenberg–Marquardt algorithm. As a control measure, the process is fully applied to silicone-rubber samples subjected to uniaxial tension tests. The fitting accuracy of the experimental stress–strain relation to the theoretical one, for both soft tissues and silicone-rubber (typically nonlinear) is evaluated. This study intents also to select which material models (or model types), the authors will employ in future works, for the analysis of human soft biological tissues.     

Finite fracture mechanics predictions on the apparent fracture toughness of as‐quenched Charpy V‐type AISI 4340 steel specimens

Quenching AISI 4340 steel from 1200 °C leads to much higher fracture toughness in the as‐quenched state than by conventional austenitizing at 870 °C. However, the increase is limited to fracture toughness tests, because Charpy V impact/slow bend tests do not show any betterment due to high‐temperature austenitizing. Different explanations of these contradicting results have been proposed since the beginning of the 1970s. In the present paper, this puzzling phenomenon will be revisited through the coupled stress and energy criterion in the framework of finite fracture mechanics. The approach involves two material parameters, namely the tensile strength and the fracture toughness, and a critical distance (or finite crack advance), which results to be a structural property. The connection between the critical distance, the microstructure characteristic (i.e. the grain size) and the effective radius involved by other models proposed in the past will be outlined, providing an interesting overview on the studies carried out during the last four decades.     

Grain characteristics and engineering properties of coal ash

Ash produced by the coal fired thermal plants is often used as a geo-material where its characteristics and mechanical behavior is important. The present study describes an investigation into the grain characteristics and the engineering properties of coal ash. The results of x-ray diffraction, micrographic observation and grain size distribution are analyzed in relation to maximum and minimum void ratio, permeability, compressibility and frictional properties. The grain size is found to be a significant grain characteristic that may be used for classification of ash as well as interpretation of primary, secondary and index properties. The compressibility and frictional characteristics depend on stress environment and packing with respect to a critical state uniquely identified by material characteristics. The fitting parameters for the selected sets of samples have been evaluated for the Ropar coal ash. This study presents the data and the correlations that are pertinent to a wider community of geo-technical and geo-environmental engineers interested in the utilization of coal ash as a structural fill.     

A generalised Modified Cam clay model for clay and sand incorporating kinematic hardening and bounding surface plasticity

This paper proposes a simple non-associated Modified Cam clay model suitable for clay and sand. The yield surface is taken to be that of Modified Cam clay, which is a simple ellipse. The modified model reduces the amount of shear strain predicted, and for clay requires no new parameters because the flow rule uses a well established empirical result. For sand, the critical state frictional dissipation constant is required in addition to the stress ratio at the peak of the yield surface. This permits realistic modelling of the undrained behaviour of sand in states looser and denser than critical. The model resembles more sophisticated models with yield surfaces of more complex shapes, but is much simpler. More realistic behaviour could be obtained by assuming a yield surface with the same form as the potential if required. The model is suitable for incorporating kinematic hardening for the modelling of cyclic loading of clay. In addition, bounding surface plasticity can be included to distinguish between compacted and overconsolidated sand. The contribution in this paper is therefore to provide a generalised simple model based on Modified Cam clay.The authors are grateful to Mr C.D. Khong for discussions on the bounding surface formulation of the CASM model.     

Visco-elastic behavior through fractional calculus: An easier method for best fitting experimental results

In capturing visco-elastic behavior, experimental tests play a fundamental rule, since they allow to build up theoretical constitutive laws very useful for simulating their own behavior. The main challenge is representing the visco-elastic materials through simple models, in order to spread their use. However, the wide used models for capturing both relaxation and creep tests are combinations of simple models as Maxwell and/or Kelvin, that depend on several parameters for fitting both creep and relaxation tests. This paper, following Nutting and Gemant idea of fitting experimental data through a power law function, aims at stressing the validity of fractional model. In fact, as soon as relaxation test is well fitted by power law decay then the fractional constitutive law involving Caputo’s derivative directly appears. It will be shown that fractional model is proper for studying visco-elastic behavior, since it may capture both relaxation and creep tests, requiring the identification of two parameters only. This consideration is assessed by the good agreement between experimental tests on creep and relaxation and the fractional model proposed. Experimental tests, here reported are performed on two polymers having different chemical physical properties such that the fractional model may cover a wide range of visco-elastic behavior.     

The effect of grain size on the nanocrystalline growth in metals and its simulation by Monte Carlo method

In this study, the thermodynamic stability of the grain boundaries and the grain growth of nanocrystalline Palladium (Pd) at 800 K were investigated. For this purpose, the Gibbs free energy curves of grain boundaries were plotted in terms of the excess volume by the use of Song’s, quasi-harmonic Debye approximation (QDA), and equation of state (EOS) thermodynamic models. The results of the two EOS and Song’s models showed that the excess volume increase up to values more than the critical excess volume, can result in the thermodynamic stability of nanocrystalline Pd. Therefore, according to the prediction of these two models, the nanocrystalline growth in metals was stopped at the grain sizes less than the critical grain size. But, according to the results of the QDA model there was no possibility for the stoppage of the grain growth and thermodynamic stability of the nanocrystalline Pd. To investigate the validity of the mentioned predictions, the Monte Carlo atomic simulation method was employed. The results obtained from the simulation confirmed the grain growth of nanocrystalline Pd within the size of the grains larger than the critical grain size and stoppage within the size of the grains less than the critical grain size.     

Experimental evaluation and extension of a simple critical state model for sand

This paper presents an experimental evaluation of a simple critical state model and its extension in modelling the stress-strain behaviour of sand under a wide range of confining pressures and initial void ratios under both drained and undrained loading conditions. The critical state model concerned is known as CASM developed by Yu [1,2] and CASM is a relatively simple model as it only requires seven model constants, five of which are the same as those used in the modified Cam clay model. All these constants have clear physical meanings and can be easily determined from the results of triaxial tests as demonstrated in this paper. A key advantage of CASM over many other existing critical state models lies on its unified nature as it can be used to model the behaviour of both clay and sand. In addition, the paper also shows how CASM can be further extended in order to simulate a particular undrained behaviour of loose sand, which is the reappearance of hardening after the material experiences a peak shear stress followed by a softening response.     

SIMPLE MODELS FOR PREDICTING STRESS INTENSITY FACTORS FOR TUBULAR JOINTS

Offshore structures are subjected to onerous environmental conditions. These conditions can cause cracking at tubular joints in these jacket structures and increasingly fracture mechanics is being applied to assess the cracks. There are a variety of fracture mechanics approaches to assessing cracks in tubular joints, all of which predict similar trends but give a wide variation of stress intensity factors. This variation is caused by the different models and inconsistent input parameters used. This paper presents a finite element study of a cracked tubular joint using several different structural models and consistent input parameters. The analysis includes both simple representations of a tubular joint, e.g. a plate model, and a full-scale analysis on the joint. A comparison of the full-scale analysis and the simple representations allow conclusions to be drawn on the applicability of simplifications to the problem and also allows errors to be quantified.     

不同晶粒尺寸钛合金高温压缩力学行为研究

为了解不同晶粒尺寸钛合金的高温变形力学行为,对α相平均晶粒尺寸分别为6、12μm和20μm的TC4钛合金进行了高温压缩试验,研究了晶粒尺寸和变形参数对TC4钛合金高温压缩力学行为的影响,建立了不同晶粒尺寸TC4钛合金的高温变形本构方程.研究表明:应变速率为10-4s-1时6μm的细晶钛合金出现超塑现象,应变速率在10-3～10-1s-1范围时,变形初期不同晶粒尺寸钛合金的流动应力符合Hall-Petch关系,由于细晶钛合金流动应力软化速度较快,变形至稳态阶段时细晶钛合金流动应力低于粗晶合金.     

Microstructure-sensitive notch root analysis for dwell fatigue in Ni-base superalloys

Macroscopic viscoplastic constitutive models for γ–γ′ Ni-base superalloys typically do not contain an explicit dependence on the underlying microstructure. Microstructure-sensitive models are of interest in many applications since microstructure can vary in components, whether intentional or not. In such cases, the use of experiments from one microstructure condition to fit macroscopic models may be too limiting. The principal microstructure attributes that can significantly affect the cyclic stress–strain response of γ–γ′ Ni-base superalloys are the grain size and γ′ precipitate volume fraction and size distributions. An artificial neural network (ANN) is used to correlate the material parameters of a macroscale internal state variable cyclic viscoplasticity model with these microstructure attributes using a combination of limited experiments augmented by polycrystal plasticity calculations performed on other (virtual) microstructures within the range characterized experimentally. The trained model is applied to an example of a component fatigue notch root analysis with dwell periods at peak load to demonstrate the methodology and explore the potential impact of microstructure-sensitive constitutive models on life prediction for notched structures subjected to realistic load histories.     

Modeling signalized intersection safety with corridor-level spatial correlations

Intersections in close spatial proximity along a corridor should be considered as correlated due to interacted traffic flows as well as similar road design and environmental characteristics. It is critical to incorporate this spatial correlation for assessing the true safety impacts of risk factors. In this paper, several Bayesian models were developed to model the crash data from 170 signalized intersections in the state of Florida. The safety impacts of risk factors such as geometric design features, traffic control, and traffic flow characteristics were evaluated. The Poisson and Negative Binomial Bayesian models with non-informative priors were fitted but the focus is to incorporate spatial correlations among intersections. Two alternative models were proposed to capture this correlation: (1) a mixed effect model in which the corridor-level correlation is incorporated through a corridor-specific random effect and (2) a conditional autoregressive model in which the magnitude of correlations is determined by spatial distances among intersections. The models were compared using the Deviance Information Criterion. The results indicate that the Poisson spatial model provides the best model fitting. Analysis of the posterior distributions of model parameters indicated that the size of intersection, the traffic conditions by turning movement, and the coordination of signal phase have significant impacts on intersection safety.     

An average stress strain approach to creep analysis of RC uncracked elements

The paper presents a method which enables us to perform creep analysis of RC elements with uncracked cross-sections relying on the evaluation of an average stress strain state in a sense to fulfill Volterra’s integral term in time interval elapsed after loading and the prediction of an actual state at the time considered. The analytically derived expressions for time-dependent stresses, strains and curvatures are very simple, being gained by a newly proposed relation for the ageing coefficient, constitutive law for creep and the classical formulae of strength of materials. The method proposed is mathematically tractable, as well as accounting for the variation of elastic modulus. A validity of the method proposed was proven by direct calculation of the time-dependent parameters in the analysis of various RC elements. The approach gives exact values of the time-dependent stress strain state as those determined using the age-adjusted effective modulus method involving a sophisticated relaxation procedure. The method does not require the introduction of the fictitious restraining actions dramatically simplifying computation and could be used as a simple alternative approach for the exact analysis of RC uncracked elements. Numerical examples and methodology for applicability to RC structures/elements were also developed.