弹性、弹塑性材料显式模拟计算中的准静态加载速度研究

摘 要：动力学显式算法采用时间积分原理，其较静力学隐式算法在强非线性问题中的适用性更广。为将此方法应用到岩土等非线性材料的计算中，考虑到显式算法中动能的影响会导致结果波动，分析动力学显式算法在模拟计算中的准静态加载速度的选取十分必要,如何在缩短模拟消耗时间与结果准确性之间寻求平衡是本文研究重点。研究中提出以加载-位移曲线的波动比来评价准静态计算效果，首先开展弹性材料的平面应变模拟试验以分析弹模、密度、泊松比、围压4个参数对准静态加载速度取值的影响，结果表明：弹模、泊松比、围压的增大会提高准静态加载速度；密度的增大则会减小准静态加载速度。通过对各影响因素与准静态加载速度的相关性分析给出了准静态加载速度取值的经验公式。最后，选取能够反映砂土复杂力学特性的弹塑性本构模型，开展其平面应变模拟试验，对比分析准静态加载速度经验公式在弹性材料与弹塑性材料中的适用性差异，并提出应用建议公式。     

Exploring the undrained cyclic behavior of methane-hydrate-bearing sediments using CFD–DEM

Based on the mechanical experimental results of methane hydrate (MH), a bond contact model considering the rate-dependency of MH is proposed. A CFD–DEM scheme considering fluid compressibility is used to simulate a series of undrained cyclic shear tests of numerical methane-hydrate-bearing sediment (MHBS) samples. The dynamic behavior, including stress–strain relationship, dynamic shear modulus, and damping ratio, is investigated. In addition, the force chains, contact fabric and averaged pure rotation rate (APR) are examined to investigate the relationships between micromechanical variables and macromechanical responses in the DEM MH samples. The effects of temperature, confining pressure and MH saturation are also analyzed. Due to the micro-structural strengthening by the MH bonds, no obvious change in microscopic quantities is observed, and the samples remain at the elastic stage under the applied low-shear stress level. When confining pressure and MH saturation increase, the dynamic elastic modulus increases, while the damping ratio decreases. An increasing temperature (leading to weakening of MH bonds) can lower the dynamic elastic modulus, but has almost no impact on the damping ratio. On the contrary, an increasing cyclic shear stress level lowers the damping ratio, but has almost no effect on the dynamic elastic modulus.     

Compression analysis of rectangular elastic layers bonded between rigid plates

An elastic layer bonded between two rigid plates has higher compression stiffness than the elastic layer without bonding. While the finite element method can be applied to calculate the stiffness, the compression stiffness of bonded rectangular layers derived through a theoretical approach in this paper provides a convenient way for parametric study. Based on two kinematics assumptions, the governing equation for the mean pressure is derived from the equilibrium equations. Using the approximate shear boundary condition, the mean pressure is solved and the compression stiffness of the bonded rectangular layer is then established in an explicit single-series form. Through the solved pressure, the horizontal displacements are derived from the corresponding equilibrium equations, from which the shear stress on the bonding surface can be found. It is found that the effect of the rectangular aspect on the compression stiffness is significant only when Poisson’s ratio is near 0.5. For the smaller Poisson’s ratio, the compression stiffness of the rectangular layer can be approximated by the formula for the infinite-strip layer of the same shape factor.     

Computations of size effects in granular bodies within micro-polar hypoplasticity during plane strain compression

The numerical investigations of size effects in granular bodies during a plane strain compression test are performed. To describe a mechanical behaviour of a cohesionless granular material during a monotonous deformation path in a plane strain compression test, a micro-polar hypoplastic constitutive model was used. It includes particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. In the paper, deterministic and statistical size effects in geometrically similar granular specimens are analysed. The deterministic calculations were carried out with a uniform distribution of the initial void ratio. To investigate a statistical size effect, in order to reduce the number of realizations without loosing the accuracy of the calculations, a Latin hypercube method was applied to generate Gaussian truncated random fields in a granular specimen. The results show that the statistical size effect is significantly stronger than the deterministic one. The shear resistance decreases and the rate of softening increases with increasing specimen size. The effect of the boundary roughness on shear localization is pronounced.     

Numerical analysis of effective elastic properties of geomaterials containing voids using 3D random fields and finite elements

The purpose of the study is to investigate the influence of porosity and void size on effective elastic geotechnical engineering properties with a 3D model of random fields and finite element. The random field theory is used to generate models of geomaterials containing spatially random voids with controlled porosity and void size. A “tied freedom” analysis is developed to evaluate the effective Young’s modulus and Poisson’s ratio in an ideal block material of finite elements. To deliver a mean and standard deviation of the elastic parameters, this approach uses Monte-Carlo simulations and finite elements, where each simulation leads to an effective value of the property under investigation. The results are extended to investigate an influence of representative volume element (RVE). A comparison of the effective elastic stiffness of 2D and 3D models is also discussed.     

辽西风积土动剪切模量与阻尼比特性试验研究

研究辽西风积土的动力特性离不开其动剪切模量与阻尼比这两个最基本的参数. 通过一系列动三轴试验, 分析了围压、固结比、振动频率对原状风积土的动剪切模量与阻尼比的影响情况, 并探讨了其产生的机理. 通过试验数据分析表明, 风积土的动剪切模量随围压的增大而增大, 但阻尼比随围压的增大而减小; 动剪切模量随固结比的增大而增大, 阻尼比随固结比的增大而减小; 动剪切模量和阻尼比均随振动频率的增大而增大, 但影响较小, 不如前两个因素明显.     

Structure dependent elastic properties of supergraphene

Complete replacement of aromatic carbon bonds in graphene by carbyne chains gives rise to supergraphene whose mechanical properties are expected to depend on its structure. However, this dependence is to date unclear. In this paper, explicit expressions for the in-plane stiffness and Poisson’s ratio of supergraphene are obtained using a mole-cular mechanics model. The theoretical results show that the in-plane stiffness of supergraphene is drastically (at least one order) smaller than that of graphene, whereas its Pois-son’s ratio is higher than 0.5. As the index number increases (i.e., the length of carbyne chains increases and the bond density decreases), the in-plane stiffness of supergraphene decreases while the Poisson’s ratio increases. By analyzing the relation among the layer modulus, in-plane stiffness and Poisson’s ratio, it is revealed that the mechanism of the faster decrease in the in-plane stiffness than the bond density is due to the increase of Poisson’s ratio. These findings are useful for future applications of supergraphene in nanomechanical systems.     

Stress concentration around a hole in a radially inhomogeneous plate

The stress concentration factor around a circular hole in an infinite plate subjected to uniform biaxial tension and pure shear is considered. The plate is made of a functionally graded material where both Young’s modulus and Poisson’s ratio vary in the radial direction. For plane stress conditions, the governing differential equation for the stress function is derived and solved. A general form for the stress concentration factor in case of biaxial tension is presented. Using a Frobenius series solution, the stress concentration factor is calculated for pure shear case. The stress concentration factor for uniaxial tension is then obtained by superposition of these two modes. The effect of nonhomogeneous stiffness and varying Poisson’s ratio upon the stress concentration factors are analyzed. A reasonable approximation in the practical range of Young’s modulus is obtained for the stress concentration factor in pure shear loading.     

黄河三角洲粉质土的动模量和阻尼比试验研究

结合室内共振柱和动三轴实验,对黄河三角洲饱和原状粉质土体(粉土、粉砂、粉质粘土)动模量和阻尼比的影响因素和发展规律进行了详细的研究。研究表明,在粉粒和粘粒含量对动模量的共同影响中,粉粒含量起着举足起重的作用;侧限压力对归一化剪模比和阻尼比的影响均较显著,相比粘粒含量的影响不大。通过与Seed建议的砂土及饱和粘土的G/Gmax~γ曲线和λ~γ曲线进行对比,结果显示研究区的粉质土相比一般的砂土和饱和粘土而言,其动力变形特性更接近于砂土,但是与砂土也存在着非常明显的差异;其发展规律与其他地区沉积粉质土也较为不同,具有明显的区域性。采用修正了的Hard in-D rnevich模型和对数模型分别对G/Gmax~γ曲线和λ~γ曲线进行拟合,给出了三类粉质土的归一化动力变形G/Gmax~γ/γr关系曲线,对模型中有关参数的影响因素做了初步的探讨。     

偶应力理论下拉力型锚固体的受力特性

锚固体的受力特征及其影响因素是锚固体设计的重要依据,直接影响锚固效果。传统的经典弹性理论没有考虑应变梯度的影响。偶应力理论引进弯曲曲率,考虑了弯曲效应对介质变形特性的影响。基于偶应力理论,建立了平面应变问题的有限元计算模型,研究锚固体锚固段界面上的剪应力分布、锚固体轴力分布、偶应力的尺度效应以及弹性模量和围压对锚固力的影响,并将偶应力理论的计算结果和经典弹性理论的计算结果进行了比较。结果表明,在偶应力理论下,锚固体锚固段界面的剪应力有所减小,特别是峰值处的剪应力减小明显;岩土的弹性模量越大,锚固界面局部剪应力越大;锚固力随着围压的增大而增大,偶应力尺度效应明显。     

循环荷载作用下低掺量水泥土试样变形性状试验研究

在大量动三轴试验的基础上,深入研究了低掺量水泥土的动力特性。试验结果表明:动应变εd是影响土样动弹模量及阻尼比的最主要因素,随着动应变水平的提高,动弹模量Ed成倍减小而阻尼比λ成倍增大。随着掺灰量的增大,水泥土的动弹模量和阻尼比相应增大。动弹模量随围压σ3增减而增减,阻尼比λ随围压σ3的增加而减小。最大动弹模量Edmax与围压σ3呈指数递增关系;最大阻尼比λmax在7%～30%之间,与围压σ3呈指数递减关系,并建立了相应的经验公式。     

Homogenization of geomaterials containing voids by random fields and finite elements

The paper describes the use of random fields and finite elements to assess the influence of porosity and void size on the effective elastic stiffness of geomaterials. A finite element model is developed involving “tied freedoms” that allows analysis of an ideal block of materials leading to direct evaluation of the effective Young’s modulus and Poisson’s ratio. The influence of block size and representative volume elements (RVE) are discussed. The use of random fields and Monte-Carlo simulations deliver a mean and standard deviation of the elastic parameters that lead naturally to a probabilistic interpretation. The methodology is extended to a foundation problem involving a footing on an elastic foundation containing voids. The approach enables estimates to be made of the probability of excessive settlement.     

Reddy高阶组合梁弯曲的一般解析解法

基于Reddy高阶梁的轴向位移模式,考虑组合梁界面滑移变形,利用最小势能原理建立了Reddy组合梁弯曲问题的控制微分方程和边界条件,,并将控制方程转化为含12个基本未知量的一阶常微分方程组,给出一般求解方法和解表达式。其次,研究了横向均布荷载作用下Reddy简支组合梁的弯曲,所得结果与有限元解吻合良好,说明本文解析解的有效性和可靠性。最后,数值分析了组合梁界面滑移剪切刚度kcs、弹性模量-剪切模量比E/G、梁长-高比L/h和子梁厚度比hs/hc等参数对Reddy简支组合梁弯曲的影响。分析表明：滑移刚度显著影响横截面应力的分布;组合梁长-高比越小、弹性模量-剪切模量比越大或界面滑移刚度越大,组合梁的剪切效应对其挠度影响越显著,此时不宜忽略其剪切变形。     

卸荷条件下粉质粘土变形性状研究

通过室内应力控制的三轴试验研究卸荷条件下土体的应力-应变关系和孔隙水压力变化特征,得到变形模量的确定方法。研究表明:在初始偏压应力固结条件下,无论是轴向压力保持不变而侧向压力不断卸荷,还是轴向压力和侧向压力同时卸荷,其应力-应变关系均表现为较好的双曲线函数关系。而且,侧向固结压力愈大,强度值愈大。在卸荷过程中,随剪切应力的增大和剪切应变的发展,土样呈现剪胀趋势并在后期产生较大的负孔隙水压力。不排水条件下由于负孔隙水压力的存在,土样的表观强度略有增大。     

Macroscopic elastic properties of regular lattices

In this paper we study analytically the elastic properties of the 2-D and 3-D regular lattices consisting of bonded particles. The particle-scale stiffnesses are derived from the given macroscopic elastic constants (i.e. Young's modulus and Poisson's ratio). Firstly a bonded lattice model is presented. This model permits six kinds of relative motion and corresponding forces between each bonded particle pair. By comparing the strain energy distributions between the discrete lattices and the continuum, the explicit relationship between the microscopic and macroscopic elastic parameters can be obtained for the 2-D hexagonal lattice and the 3-D hexagonal close-packed and face-centered cubic structures. The results suggest that the normal stiffness is determined by Young's modulus and the particle size (in 3-D), and that the ratio of the shear to normal stiffness is related to Poisson's ratio. Rotational stiffness depends on the normal stiffness, shear stiffness and particle sizes. Numerical tests are carried out to validate the analytical results. The results in this paper have theoretical implications for the calibration of the spring stiffnesses in the Discrete Element Method.     

Auxetic frameworks inspired by cubic crystals

In this work we show that a structure consisting of a network of bending beams can exhibit a negative Poisson’s ratio. We have shown that the negative Poisson’s ratio behaviour is driven by the (bcc analogous) type III beams, the type II (fcc like) beams result in a structure with a Poisson’s ratio of around zero and type I (simple cubic configuration) beams result in a Poisson’s ratio of nearly +1. The tensile and shear strengths of the type III beams are augmented by addition of type II and type III beams. By tailoring the relative stiffness of the component beams within the structure it is possible to design an auxetic truss structure with specific Poisson’s ratio, tensile and shear moduli.This validates the hypothesis that crystal structures can provide inspiration for macro structures with tailored mechanical properties where the mechanism for negative Poisson’s ratio (auxetic) behaviour at the atomic scale in cubic crystals is replicated by bending beams.     

FE analysis of the in-plane mechanical properties of a novel Voronoi-type lattice with positive and negative Poisson’s ratio configurations

This work presents a novel formulation for a Voronoi-type cellular material with in-plane anisotropic behaviour, showing global positive and negative Poisson’s ratio effects under uniaxial tensile loading. The effects of the cell geometry and relative density over the global stiffness, equivalent in-plane Poisson’s ratios and shear modulus of the Voronoi-type structure are evaluated with a parametric analysis. Empirical formulas are identified to reproduce the mechanical trends of the equivalent homogeneous orthotropic material representing the Voronoi-type structure and its geometry parameters.     

Critical state shear behavior of the soil-structure interface determined by discrete element modeling

The interface between soil and structure can be referred to as a soil-structure system, and its behavior plays an important role in many geotechnical engineering practices. In this study, results are presented from a series of monotonic direct shear tests performed on a sand-structure interface under constant normal stiffness using the discrete element method (DEM). Strain localization and dilatancy behavior of the interface is carefully examined at both macroscopic and microscopic scales. The effects of soil initial relative density and normal stress on the interface shear behavior are also investigated. The results show that a shear band progressively develops along the structural surface as shear displacement increases. At large shear displacement a unique relationship between stress ratio and void ratio is reached in the shear band for a certain normal stress, indicating that a critical state exists in the shear band. It is also found that the thickness and void ratio of the shear band at the critical state decreases with increasing normal stress. Comparison of the DEM simulation results with experimental results provides insight into the shear behavior of a sand-structure interface and offers a means for quantitative modeling of such interfaces based on the critical state soil mechanics.     

含水率和围压对安家岭泥岩峰后力学特性影响的试验研究

为分析含水率和围压对泥岩峰后力学特性的影响,从山西安家岭矿取泥岩,制成不同含水率的5组试样,在YAW2000电液伺服试验机上开展了三轴试验,获得了不同含水率泥岩试样三轴全程应力应变曲线,使用激光共聚焦显微镜观测了泥岩增水过程中微观结构变化。利用试验结果,分析了围压和含水率对泥岩峰值强度、残余强度、弹性模量、破坏应变和脆性模量的影响规律和泥岩增水过程中微观结构的变化规律。引入脆性模量系数和强度退化指数来描述围压对泥岩峰后强度退化过程和残余强度的影响,与FLAC中的SS模型结合,建立了考虑围压影响的泥岩应变软化力学模型,模拟了围压对泥岩应变软化行为的影响。研究结果表明:(1)随着围压增加,泥岩的峰值强度、偏应力峰值、破坏应变和残余强度都增长,峰后强度降低速率趋缓,强度退化指数和脆性模量系数可以较好地描述围压对泥岩残余强度和峰后强度退化过程的影响。(2)泥岩增水过程中,岩样内微裂隙及尺寸增长,泥岩的力学性质劣化。随着含水率增加,泥岩的弹性模量、峰值强度和残余强度降低,破坏应变增长。含水率与泥岩的弹性模量、峰值强度和破坏应变之间近似服从线性关系。(3)本文基于脆性模量系数的岩石应变软化模型能较好地描述三轴压缩泥岩的全程变形行为。     

Stiffness properties of particulate composites containing debonded particles

This paper considers the problem of determining the nonlinear bimodular stiffness properties, i.e., the tensile and compressive Young’s moduli and Poisson’s ratios, and the shear modulus, of particulate composite materials with particle–matrix interfacial debonding. It treats the general case in which some of the particles are debonded while the others remain intact. The Mori–Tanaka approach is extended to formulate the method of solution for the present problem. The resulting auxiliary problem of a single debonded particle in an infinite matrix subjected to a remote stress equal to the average matrix stress, for which Eshelby’s solution does not exist, is solved by the finite element method accounting for the particle–matrix separation and contact at the debonded particle–matrix interface. Because of the nonlinear nature of the problem, an iterative process is employed in calculating the stiffness properties. The predicted stiffness properties are compared to the exact solutions of the stiffness properties of particulate composites with body-centered cubic packing arrangement.