Mixed mode crack propagation in low brittle rock-like materials

Mixed mode fracture is quite common in rock structures. Numerous investigators have used the Brazilian disk specimens with a central crack for investigating modes I, II, and mixed fracture toughness in brittle materials. In this study, analytical, experimental, and numerical investigations were planned and performed on Central Straight Through Crack Brazilian Disk (CSCBD) specimens. Ranking of geometrical parameters effective on the value of stress intensity factors (SIFs) of CSCBD specimens were obtained using stochastic analysis. Furthermore, experimental tests were undertaken in order to evaluate the crack propagation in rock-like material of low brittleness. Finally, numerical modeling was performed to assess the effect of crack length on the failure mode of CSCBD specimens. Analytical analyses revealed that the inclination angle of the crack with respect to the diametrical load has the most important impact on the SIFs among the geometrical parameters of CSCBD specimen. Performed experimental and numerical analyses also confirmed the effect of inclination angle and crack length and their impact on the mode of failure of the tested specimen.     

Discrete element model for crack propagation in brittle materials

We propose a discrete element model for brittle rupture. The material consists of a bidimensional set of closed‐packed particles in contact. We explore the isotropic elastic behavior of this regular structure to derive a rupture criterion compatible to continuum mechanics. We introduce a classical criterion of mixed mode crack propagation based on the value of the stress intensity factors, obtained by the analysis of two adjacent contacts near a crack tip. Hence, the toughness becomes a direct parameter of the model, without any calibration procedure. We verify the consistency of the formulation as well as its convergence by comparison with theoretical solutions of tensile cracks, a pre‐cracked beam, and an inclined crack under biaxial stress. Copyright © 2015 John Wiley & Sons, Ltd.     

模拟三维裂纹问题的多尺度扩展有限元法

扩展有限元法模拟裂纹时独立于网格,因此该方法是目前求解裂纹问题最有效的数值方法。为了在计算代价不大的情况,实现大型结构分析中考虑小裂纹或提高裂纹附近精度,在裂纹附近一般采用小尺度单元,其他区域采用大尺度单元。提出了分析三维裂纹问题的多尺度扩展有限元法,在需要的地方采用小尺度单元。基于点插值构造了六面体任意节点单元。所有尺度单元都采用8节点六面体单元,这样六面体任意节点单元可方便有效地连接不同尺度单元。采用互作用积分法计算三维应力强度因子。边裂纹和中心圆裂纹算例分析结果表明,该方法是正确和有效的。     

A three-dimensional particle finite element model for simulating soil flow with elastoplasticity

Acta Geotechnica - Soil flow is involved in many earth surface processes such as debris flows and landslides. It is a very challenging task to model this large deformational phenomenon because of...     

A new finite element formulation for one-dimensional analysis of elastic-plastic materials

It is well accepted that severe numerical difficulties arise when using the conventional finite element displacement method to analyse incompressible, or nearly incompressible, solids. These effects are caused by the kinematic constraints imposed on the nodal velocities by the constant volume condition. In elastic-plastic analysis, these effects are due to a conflict between the plastic flow rule and the finite element discretization. Although several methods have been proposed to cope with this problem, none has been based on the appropriate choice of displacement interpolation to minimise the constraints. In this paper, a new displacement interpolation, which is able to reduce the imposed constraints, is adopted. Comparisons of the results with those from a conventional linear displacement interpolation are made for predictions of cylindrical and spherical cavity expansion limit pressures in elastic-plastic solids. This study suggests that the proposed displacement interpolation is preferable to the conventional one in the elastic-plastic finite element analysis of one dimensional-axisymmetric problems which involve nearly incompressible material behaviour.     

模拟三维裂纹问题的扩展有限元法

扩展有限元法是一种在常规有限元框架内求解强和弱不连续问题的新型数值方法,其计算网格与不连续面相互独立,因此模拟移动不连续面时无需对网格进行重新剖分。给出了模拟三维裂纹问题的扩展有限元法。在常规有限元位移模式中,基于单位分解的思想加进一个阶跃函数和二维渐近裂尖位移场,反映裂纹处位移的不连续性。用两个水平集函数表示裂纹。采用线性互补法求解裂纹面非线性接触条件,不需要迭代,提高了计算效率。采用两点位移外推法计算裂纹前缘应力强度因子。给出了3个三维弹性静力问题算例,其结果显示了所提方法能获得高精度的应力强度因子,并能有效地处理裂纹面间的接触问题,同时表明扩展有限元结合线性互补法求解不连续问题具有较好的前景。     

三维边坡稳定分析的有限元弹塑性迭代解法

针对已知滑动面的三维边坡稳定分析问题,在塑性力学上限定理的基础上,提出了求解安全系数的三维有限元弹塑性迭代解法。对于滑动面的非线性特性,采用常规的矩形（平面）或立方体（空间）单元来描述,应力则符合相关联流动法则的Mohr-Coulomb强度准则。通过对弹塑性增量理论中流动法则的分析,证明了当结构达到极限状态时,滑动面内切向应力的方向与滑体的主滑方向一致,说明最终以滑动面内的切向应力作为滑体滑动力的有效性。通过迭代的方式,逐步降低滑动面材料的抗剪参数,使边坡达到极限状态,不仅快速求得了滑动面的安全系数,且能够得到边坡在接近临界失稳状态时滑动面内切向应力的分布情况和边坡的变形规律,为边坡采取加固措施提供了参考依据。最后,以椭球面滑动和楔形滑动2个经典算例和工程实例,验证了该方法的有效性和正确性。     

一种模拟堆石料的二维多边形离散单元法及程序

在考虑堆石料真实颗粒形状的基础上,将每个颗粒用一个多边形离散单元表示,基于一种线性搜索算法对多边形-多边形之间的接触详情进行检索计算,引入基于势能原理的法向多边形-多边形接触模型及切向库仑摩擦模型,形成了一种多边形离散元计算方法,并开发了相应的PDEM程序。可以从颗粒尺度层面展示颗粒之间的相互作用以及每个颗粒的位移和转动,帮助进一步揭示颗粒的细观特性(形状、大小、材料特性等)对堆石料的宏观强度和变形的影响。最后采用PDEM程序对某粗粒料的二维模型试验进行了数值模拟,得到了与室内试验一致的应力变形规律,展现了其方法和程序用于研究堆石料的有效性。     

基于有限元计算的边坡三维滑裂面搜索

提出一种基于有限元计算的边坡三维滑裂面搜索的方法,根据有限元计算的应力结果,计算可能滑裂面的安全系数,然后用遗传算法搜索出最危险滑裂面,并得出相应的安全系数作为边坡的安全度评价指标。该方法的优越性是只需进行一次有限元计算,不需要假定滑裂面,可以用于具有复杂地貌和地质构造的三维边坡。通过算例,验证该方法的可行性和程序的正确性,以大岗山水电站库区边坡工程实例验证该方法的实用性。     

Improved algorithms for generalized finite element simulations of three-dimensional hydraulic fracture propagation

This paper reports improvements to algorithms for the simulation of 3-D hydraulic fracturing with the Generalized Finite Element Method (GFEM). Three optimizations are presented and analyzed. First, an improved initial guess based on solving a 3-D elastic problem with the pressure from the previous step is shown to decrease the number of Newton iterations and increase robustness. Second, an improved methodology to find the time step that leads to fracture propagation is proposed and shown to decrease significantly the number of iterations. Third, reduced computational cost is observed by properly recycling the linear part of the coupled stiffness matrix. Two representative examples are used to analyze these improvements. Additionally, a methodology to include the leak-off term is presented and verified against asymptotic analytical solutions. Conservation of mass is shown to be well satisfied in all examples.     

基于量纲分析的岩石相似材料抗压强度计算模型

物理相似模型试验是复杂、难采矿技术研究的有效手段,而岩石相似材料物理力学特性的研究是试验有效进行的前提。根据相似原理和岩石的力学特性,论证了岩石相似材料单轴抗压强度的力学代表性。统计并分析了影响岩石相似材料单轴抗压强度的一系列因素,基于量纲分析的方法构建了岩石相似材料单轴抗压强度与砂粒径、配比材料总量、充填材料（砂）用量、水用量、养护方式等重要因素间的无量纲计算模型,结合岩石相似材料配比试验得到了定量关系式。选取3组具有代表性的岩石相似材料配比试验对所建立的单轴抗压强度计算关系式进行验证,其计算结果与实验室实测结果相吻合,平均误差为4.20%,定量关系式在岩石相似材料参数的研究上具有一定的合理性。研究结果可以为相似材料物理力学参数的预测及岩土工程物理模型试验相似材料的高效选取提供参考。     

Shakedown analysis of ballasted track structure using three-dimensional finite element techniques

Acta Geotechnica - Shakedown analysis is an attractive method for determining the capacity of geostructures to sustain repeated loads involving a large number of cycles, e.g. rolling and sliding...     

基于非结构化有限元的三维井地电阻率法约束反演

电磁探测反演是典型的不适定问题,易造成反演结果的多解性,不适定性是反演自身固有的特征,没有求解的附加信息这一本质困难是很难克服的,解决该问题的有效方法是研究约束反演。本文采用目前较为主流的高斯牛顿—共轭梯度法(GN-CG),在反演目标函数中直接施加约束条件,将介质电阻率的取值范围作为先验信息和约束条件以外点罚函数法的方式引入到反演目标函数中,与常规三维电阻率反演目标函数相比,增加了不等式约束项的目标函数,理论上可以压制反演的多解性。通过多种理论模型的测试结果表明,本文基于不等式约束的三维井地电阻率反演算法有效地改善了反演结果的精度,以惩罚函数法施加不等式约束条件的方式是现实可行及有效的。     

A finite element porothermoelastic model for dual-porosity media

An existing dual-porosity finite element model has been extended to include thermo-hydro-mechanical coupling in both media. The model relies on overlapping distinct continua for the fluid and solid domains. In addition, conductive and convective heat transfers are incorporated using a single representative thermodynamics continuum. The model is applied to the problem of an inclined borehole drilled in a fractured formation subjected to a three-dimensional state of stress and, a temperature gradient between the drilling fluid and the formation. A sensitivity analysis has been carried out to study the impact of thermal loading, effect of heat transport by pore fluid flow and, the effect of parameters of the secondary medium used to represent the fractures. Copyright © 2004 John Wiley & Sons, Ltd.     

A novel finite element method for seepage analysis

A novel finite element method has been proposed in this paper for the solution of seepage problems economically and accurately. In this method the governing equation and the prescribed boundary conditions are transformed so that they refer to a suitable logarithmically condensed ‘image’ space; the physical problem domain is also mapped into the image space. The transformed equation is then solved in the image space using standard finite elements, subject to the transformed boundary conditions. Because physical space is logarithmically condensed in the image space, the proposed method is capable of dealing with large or very large aspect ratio seepage problems economically and accurately. The validity of the method has been demonstrated by means of a number of examples including anisotropy and non-linearity. In all cases an excellent degree of accuracy was achieved, efficiently and economically.     

A micromorphic elastoplastic model and finite element simulation on failure behaviors of granular materials

One of the purposes in this study is to develop a modified micromorphic continuum model for granular materials on the basis of a micromechanics approach. A symmetric curvature tensor is proposed in this model, and a symmetric couple stress tensor is derived conjugating the symmetric curvature tensor. In addition, a correct derivation is presented to obtain the symmetric stress tensor conjugated with the symmetric strain tensor. The modified model provides a complete deformation mode for granular materials by considering the decomposition for motions (displacement and rotation) of particles. Consequently, the macroscopic constitutive relationships and constitutive moduli are derived in expressions of the microstructural information. Furthermore, the balance equations and boundary conditions are obtained for the modified micromorphic model. By considering the extended Drucker-Prager yield criterion, the micromorphic elastoplastic model is developed. Another purpose of this study is to derive the finite element formulation for the developed micromorphic elastoplastic model. Based on the ABAQUS user element (UEL) interface, numerical simulations investigated the load-displacement relationship and the strain localization behavior of granular materials and investigated the influence of microscopic parameters in the micromorphic model on these macroscopic mechanical responses. Numerical results illustrate the presented model's capability of simulating the strain-softening and strain localization behaviors, and the capability of considering the influence of microstructural information on the macroscopic mechanical behaviors of granular materials.     

A mixed finite element approach for viscoelastic wave propagation

In this paper, we are interested in the modeling of wave propagation in viscoelastic media. We present a family of models which generalize the Zeners model. We achieve its mathematical analysis: existence and uniqueness of solutions, energy decay and propagation with finite speed. For the numerical resolution, we extend a mixed finite element method proposed in [8]. This method combines mass lumping with a centered explicit scheme for time discretization. For the resulting scheme, we prove a discrete energy decay result and provide a sufficient stability condition. For the numerical simulation in open domains we adapt the perfectly matched layers techniques to viscoelastic waves [23]. Various numerical results are presented.     

A mixed finite element method for Hele-Shaw cell equations

A new numerical method to solve the system of equations describing two phase flow in a Hele-Shaw cell is presented. It combines a mixed finite element method, the method of subtraction of the singularity and a front tracking grid in a single computational strategy. This choice of discretization techniques is well motivated by the difficulties present in the system of equations and the physics of the problem. The new method was tested against analytical solutions and also by solving the Saffman–Taylor viscous fingering problem for finite and infinite mobility ratios. In both cases convergence under mesh refinement is achieved for the fingers developed from an initial sinusoidal interface. Finger splitting is observed for low values of the surface tension and high mobility ratio. Different explanations, based in our results, are provided for this phenomenon. This revised version was published online in July 2006 with corrections to the Cover Date.