Discrete element and finite element coupling simulation and experiment of hot granule medium pressure forming

The granule medium of discreteness is supposed to be continuous（Drucker-Prager model） in the existing finite element simulation analysis on the hot granule medium pressure forming（HGMF） process, so the granule medium may produce tensile stress in the process of pressure-transferring and flowing, which does not coincide with the reality. The analysis method, discrete element and finite element（DE-FE） coupling simulation, is proposed to solve the problem. The material parameters of simulation model are obtained by the pressure-transfer performance test of granule medium and the hot uniaxial tensile test of sheet metal. The DE-FE coupling simulation platform is established by adopting Visual Basic language. The features in the process that AA7075-T6 conical parts are formed by the HGMF process are analyzed and verified by the process test. The studies show that the results of DE-FE coupling simulation coincide well with the test results, which provides a new analysis method to solve the mechanics problem in the coupling of discrete and continuum.

EFFICIENT NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF FLEXIBLE ROD HIT BY RIGID BALL

Impact dynamics of flexible solids is important in engineering practice. Obtaining its dynamic response is a challenging task and usually achieved by numerical methods. The objectives of the study are twofold. Firstly, the discrete singular convolution （DSC） is used for the first time to analyze the impact dynamics. Secondly, the efficiency of various numerical methods for dynamic analysis is explored via an example of a flexible rod hit by a rigid ball. Three numerical methods, including the conventional finite element （FE） method, the DSC algorithm, and the spectral finite element （SFE） method, and one proposed modeling strategy, the improved spectral finite element （ISFE） method, are involved. Numerical results are compared with the known analytical solutions to show their efficiency. It is demonstrated that the proposed ISFE modeling strategy with a proper length of con- ventional FE yields the most accurate contact stress among the four investigated models. It is also found that the DSC algorithm is an alternative method for collision problems.

Tunnel failure in hard rock with multiple weak planes due to excavation unloading of in-situ stress

Natural geological structures in rock(e.g.,joints,weakness planes,defects)play a vital role in the stability of tunnels and underground operations during construction.We investigated the failure characteristics of a deep circular tunnel in a rock mass with multiple weakness planes using a 2D combined finite element method/discrete element method(FEM/DEM).Conventional triaxial compression tests were performed on typical hard rock(marble)specimens under a range of confinement stress conditions to validate the rationale and accuracy of the proposed numerical approach.Parametric analysis was subsequently conducted to investigate the influence of inclination angle,and length on the crack propagation behavior,failure mode,energy evolution,and displacement distribution of the surrounding rock.The results show that the inclination angle strongly affects tunnel stability,and the failure intensity and damage range increase with increasing inclination angle and then decrease.The dynamic disasters are more likely with increasing weak plane length.Shearing and sliding along multiple weak planes are also consistently accompanied by kinetic energy fluctuations and surges after unloading,which implies a potentially violent dynamic response around a deeply-buried tunnel.Interactions between slabbing and shearing near the excavation boundaries are also discussed.The results presented here provide important insight into deep tunnel failure in hard rock influenced by both unloading disturbance and tectonic activation.

Hybrid finite-discrete element modelling of asperity degradation and gouge grinding during direct shearing of rough rock joints

A hybrid finite-discrete element method was implemented to study the fracture process of rough rock joints under direct shearing. The hybrid method reproduced the joint shear resistance evolution process from asperity sliding to degradation and from gouge formation to grinding. It is found that, in the direct shear test of rough rock joints under constant normal displacement loading conditions, higher shearing rate promotes the asperity degradation but constraints the volume dilation, which then results in higher peak shear resistance, more gouge formation and grinding, and smoother new joint surfaces. Moreover, it is found that the joint roughness affects the joint shear resistance evolution through influencing the joint fracture micro mechanism. The asperity degradation and gouge grinding are the main failure micro-mechanism in shearing rougher rock joints with deeper asperities while the asperity sliding is the main failure micro-mechanism in shearing smoother rock joints with shallower asperities. It is concluded that the hybrid finite-discrete element method is a valuable numerical tool better than traditional finite element method and discrete element method for modelling the joint sliding, asperity degradation, gouge formation, and gouge grinding occurred in the direct shear tests of rough rock joints.

A New 3D Meso-mechanical Modeling Method of Coral Aggregate Concrete Considering Interface Characteristics

On the basis of the three-dimensional(3D)random aggregate&mortar two-phase mesoscale finite element model,C++programming was used to identify the node position information of the interface between the aggregate and mortar elements.The nodes were discretized at this position and the zero-thickness cohesive elements were inserted.After that,the crack energy release rate fracture criterion based on the fracture mechanics theory was assigned to the failure criterion of the interface transition zone(ITZ)elements.Finally,the three-phase mesomechanical model based on the combined finite discrete element method(FDEM)was constructed.Based on this model,the meso-crack extension and macro-mechanical behaviour of coral aggregate concrete(CAC)under uniaxial compression were successfully simulated.The results demonstrated that the meso-mechanical model based on FDEM has excellent applicability to simulate the compressive properties of CAC.

A Brief Summary of Finite Element Method Applications to Nonlinear Wave-structure Interactions

We review recent advances in the finite element method (FEM) simulations of interactions between waves and structures. Our focus is on the potential theory with the fully nonlinear or second-order boundary condition. The present paper has six sections. A review of previous work on interactions between waves and ocean structures is presented in Section one. Section two gives the mathematical formulation. In Section three, the finite element discretization, mesh generation and the finite element linear system solution methods are described. Section four presents numerical methods including time marching schemes, computation of velocity, remeshing and smoothing techniques and numerical radiation conditions. The application of the FEM to the wave-structure interactions are presented in Section five followed by the concluding remarks in Section six.

Discrete element simulation of mechanical characteristic of conditioned sands in earth pressure balance shield tunneling

The discrete element method (DEM) was used to simulate the flow characteristic and strength characteristic of the conditioned sands in the earth pressure balance (EPB) tunneling. In the laboratory the conditioned sands were reproduced and the slump test and the direct shear test of the conditioned sands were implemented. A DEM equivalent model that can simulate the macro mechanical characteristic of the conditioned sands was proposed,and the corresponding numerical models of the slump test and the shear test were established. By selecting proper DEM model parameters,the errors of the slump values between the simulation results and the test results are in the range of 10.3%-14.3%,and the error of the curves between the shear displacement and the shear stress calculated with the DEM simulation is 4.68%-16.5% compared with that of the laboratory direct shear test. This illustrates that the proposed DEM equivalent model can approximately simulate the mechanical characteristics of the conditioned sands,which provides the basis for further simulation of the interaction between the conditioned soil and the chamber pressure system of the EPB machine.

Strategies for h-Adaptive Refinement for a Finite Element Treatment of Harmonic Oscillator Schrodinger Eigenproblem

A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, （i） an application of the Kelly error estimator, and （ii） a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver.

Rock Cutting Analysis Employing Finite and Discrete Element Methods

The petroleum industry has shown great interest in the study of drilling optimization on pre-salt formations given the low rates of penetration observed so far. Rate of penetration is the key to economically drill the pre-salt carbonate rock. This work presents the results of numerical modeling through finite element method and discrete element method for single cutter drilling in carbonate samples. The work is relevant to understand the mechanics of drill bit-rock interaction while drilling deep wells and the results were validated with experimental data raised under simulated downhole conditions. The numerical models were carried out under different geometrical configurations, varying the cutter chamfer size and back-rake angles. The forces generated on the cutter are translated into mechanical specific energy as this parameter is often used to measure drilling efficiency. Results indicate that the chamfer size does not change significantly the mechanical specific energy values, characteristic. Results also show there is a significant increase although the cutter aggressiveness is influenced by this geometrical in drilling resistance for larger values of back-rake angle.

Mapped Finite Element Discrete Variable Representation

Efficient numerical solver for the SchrSdinger equation is very important in physics and chemistry. The finite element discrete variable representation （FE-DVR） was first proposed by Rescigno and Mc-Curdy [Phys. Rev. A 62, 032706 （2000）] for solving quantum-mechanical scattering problems. In this work, an FE-DVR method in a mapped coordinate was proposed to improve the efficiency of the original FE-DVR method. For numerical demonstration, the proposed approach is applied for solving the electronic eigenfunctions and eigenvalues of the hydrogen atom and vibrational states of the electronic state 3E＋ of the Cs2 molecule which has long-range interaction potential. The numerical results indicate that the numerical efficiency of the original FE-DVR has been improved much using our proposed mapped coordinate scheme.

3D-Parallel Simulation of Contaminant in Waste Disposals

In this work the authors simulate a contaminant transport problem in three dimensions that takes place in the soil of waste disposals. Such problem is modeled by a diffusion-dominated equation. The solution of this equation is addressed by using mixed finite element method for the spatial discretization of the equation. The resulting linear algebraic system is handled by an iterative domain decomposition procedure. This procedure is naturally parallelizable, and permits to implement computational codes in distributed memory machines in order to save on CPU time. Numerical results of the serial and parallel codes were compared with experimental results, and their performance measures were evaluated. The results indicate that the parallelizable procedure is an efficient tool for performing simulations of the problem.

干缩、湿胀作用下黏土岩崩解的FDEM模拟

黏土岩是常见的工程岩体之一,其遇水后的软化和胀缩变形是诱发滑坡、崩岸等地质灾害的重要内因。为深入理解干缩、湿胀过程中黏土岩力学参数的劣化规律和胀缩裂纹的扩展模式。首先,在湿度应力场理论的基础上,推导基于水头的湿度应力瞬态分析方法,其次,开发一种湿度相关的黏聚力单元(可进行湿度扩散计算,且黏聚力单元参数与湿度相关),并通过实验数据对其主要参数进行标定,最后,基于有限离散元方法(FDEM)对黏土岩受荷膨胀和干湿崩解进行模拟,通过与试验对比,验证本文模拟方法的可靠性。研究表明:(1)黏土岩吸水膨胀过程中,也表现出吸水软化的特点,饱和黏土岩单轴抗压强度和弹性模量仅为干燥试样的22%和25%,在进行岩土膨胀分析时不能忽略力学参数受含水率(湿度)的影响;(2)黏土岩吸水膨胀在时效上滞后于吸水软化,在较大荷载(大于膨胀应力)作用下,侧限状态的黏土岩会出现压缩恢复的现象;(3)干湿过程中胀缩裂纹是诱发黏土岩崩解的主要因素,外侧裂纹易贯通形成碎块,内部裂纹则导致试样出现不可逆损伤。本文提出一种新的岩土体胀缩模拟方法,对于膨胀岩地区的边坡、隧道和库岸的工程计算有一定的指导作用。

Ground-borne vibrations due to dynamic loadings from moving trains in subway tunnels

In this study,ground vibrations due to dynamic loadings from trains moving in subway tunnels were investigated using a 2.5D finite element model of an underground tunnel and surrounding soil interactions.In our model,wave propagation in the infinitely extended ground is dealt with using a simple,yet efficient gradually damped artificial boundary.Based on the assumption of invariant geometry and material distribution in the tunnel's direction,the Fourier transform of the spatial dimension in this direction is applied to represent the waves in terms of the wave-number.Finite element discretization is employed in the cross-section perpendicular to the tunnel direction and the governing equations are solved for every discrete wave-number.The 3D ground responses are calculated from the wave-number expansion by employing the inverse Fourier transform.The accuracy of the proposed analysis method is verified by a semi-analytical solution of a rectangular load moving inside a soil stratum.A case study of subway train induced ground vibration is presented and the dependency of wave attenuation at the ground surface on the vibration frequency of the moving load is discussed.

Hypoplastic constitutive modelling of the wetting induced creep of rockfill materials

Discrete element simulations of one-dimensional compression of breakable granular assemblies were performed to investigate the capability of the exponential compression equation suggested by Bauer.The relationship between the so-called solid hardness and the particle strength was studied so as to provide a physical background for the introduction of a time-dependent solid hardness.A hyperbolic flow rule,describing the relationship between the inclination of the strain path and the stress ratio during wetting,was proposed based on typical triaxial wetting experiments on two different rockfill materials.The flow rule was then extended and incorporated into the transformed stress based hypoplastic model to capture the direction of creep strains.Meanwhile,a new density factor was introduced to the extended model to take into account the dependence of the magnitude of creep strains on the packing density.The stiffness tensor given by the extended model was discussed and the flowchart for the integration of the constitutive equation was designed.The extended model was then embedded into a finite element program and used to simulate the triaxial compression and wetting experiments performed on the aforementioned rockfill materials.Good agreement between the model predictions and the measured results lends sufficient credibility to the extended model in reproducing the stress-stain behaviour under loading and the creep behaviour during wetting.The extended model and the finite element program were also used to investigate the deformation behaviour of an earth-rock dam at the end of construction and during first impounding.The familiar phenomena such as the wetting induced settlement of the upstream shell and the movement of the dam crest towards the upstream were successfully captured by the numerical model,which confirms the feasibility of applying the extended model to dam engineering in the future.

Numerical study on two-phase flow through fractured porous media

Based on the flux equivalent principle of a single fracture, the discrete fracture concept was developed, in which the macroscopic fractures are explicitly described as （n-l） dimensional geometry element. On the fundamental of this simplification, the discrete-fractured model was developed which is suitable for all types of fractured porous media. The principle of discrete-fractured model was introduced in detail, and the general mathematical model was expressed subsequently. The fully coupling discrete-fractured mathematical model was implemented using Galerkin finite element method. The validity and accuracy of the model were shown through the Buckley-Leverett problem in a single fracture. Then the discrete-fractured model was applied to the two different type fractured porous media. The effect of fractures on the water flooding in fractured reservoirs was investigated. The numerical results showed that the fractures made the porous media more heterogeneous and anisotropic, and that the orientation, size, type of fracture and the connectivity of fractures network have important impacts on the two-phase flow.

VARIATIONAL DISCRETIZATION FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY PARABOLIC EQUATIONS

This paper considers the variational discretization for the constrained optimal control problem governed by linear parabolic equations.The state and co-state are approximated by RaviartThomas mixed finite element spaces,and the authors do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control.A priori error estimates are derived for the state,the co-state,and the control.Some numerical examples are presented to confirm the theoretical investigations.

Multi-scale finite element analysis of chloride diffusion in concrete incorporating paste/aggregate ITZs

In this paper,we propose a concurrent multi-scale finite element(FE) model coupling equations of the degree of freedoms of meso-scale model of ITZs and macroscopic model of bulk pastes.The multi-scale model is subsequently implemented and integrated into ABAQUS resulting in easy application to complex concrete structures.A few benchmark numerical examples are performed to test both the accuracy and efficiency of the developed model in analyzing chloride diffusion in concrete.These examples clearly demonstrate that high diffusivity of ITZs,primarily because of its porous microstructure,tends to accelerate chloride penetration along concentration gradient.The proposed model provides new guidelines for the durability analysis of concrete structures under adverse operating conditions.

A NEWTON MULTIGRID METHOD FOR QUASILINEAR PARABOLIC EQUATIONS

A combination of the classical Newton Method and the multigrid method, i.e., a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O（NNk） similar to multigrid method for linear parabolic problems.

Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices

We consider the drift-diffusion （DD） model of one dimensional semiconductor devices, which is a system involving not only first derivative convection terms but also second derivative diffusion terms and a coupled Poisson potential equation. Optimal error estimates are obtained for both the semi-discrete and fully discrete local discontinuous Galerkin （LDG） schemes with smooth solutions. In the fully discrete scheme, we couple the implicit-explicit （IMEX） time discretization with the LDG spatial diseretization, in order to allow larger time steps and to save computational cost. The main technical difficulty in the analysis is to treat the inter-element jump terms which arise from the discontinuous nature of the numerical method and the nonlinearity and coupling of the models. A simulation is also performed to validate the analysis.

A Penalty-Regularization-Operator Splitting Method for the Numerical Solution of a Scalar Eikonal Equation

In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.