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1.
We relate the micromechanics of vortex evolution to that of force chain buckling and, on this basis, formulate the conditions for strain localization in a continuum model of dense granular media. Using the traditional bifurcation analysis of shear bands, we show that kinematic vortex fields are in fact solutions to the boundary value problem satisfying null boundary conditions. To establish an empirical basis for our study, we first develop a method to identify the location of the core and boundary of each vortex from a given displacement field in two dimensions. We then employ this method to characterize the residual deformation field (i.e., the deviation of particle motions from the continuum deformation) in a physical experiment and a discrete element simulation of dense granular samples submitted to biaxial compression. Vortices in the failure regime are essentially confined to the shear band. Primary vortices, the clear majority, rotate in the same direction as the shear band; secondary vortices, the so-called wakes, rotate in the opposite direction. Primary vortices align in spatial succession along the central axis of the band; wakes form next to the band boundaries, in between and beside two adjacent primary vortices. Force chain buckling, the governing mechanism for shear bands, is responsible for vortex formation in the failure regime. Vortex dynamics are consistent with stick-slip dynamics. From quiescent conditions of jamming or stick, vortical motions arise from force chain buckling and associated relative particle rotations and sliding; these in turn precipitate intermittent periods of unjamming or slip, evident in the attendant drops in stress ratio and bursts in both kinetic energy and local nonaffine deformation. A kinematic vortex field inside shear bands is proposed that is consistent with the equations of continuum mechanics and the underlying instability of force chain buckling: such a field is periodic with a repeating unit cell comprising a primary vortex at the center of the band, with two trailing wakes close next to the band boundaries.  相似文献   

2.
结合颗粒物质力学理论,通过离散元法实现铁粉末压制过程模拟并通过压制方程进行验证,针对粉末体系中的力链演化问题,提出力链特征定量分析方式,进一步通过分析不同颗粒间摩擦系数、侧壁摩擦系数与颗粒运动状态转变的方式,探讨摩擦特性对力链量化特征的影响,从而建立摩擦行为与力链演化间的联系. 研究结果表明:随颗粒间摩擦系数增大,整体力链数目变少,力链方向系数、承载不均匀度及单位屈曲度均变大,而随侧壁摩擦系数增大,力链特征差异较小,则颗粒间摩擦系数较侧壁摩擦系数对力链特征演化具有更显著影响. 同时发现,颗粒接触状态的改变与力链特征演化间具有对应性. 研究成果将进一步拓展粉末压制中考虑摩擦行为及力链演化过程在内的粉体致密化行为理论.   相似文献   

3.
离散颗粒流动堆积行为离散元模拟及实验研究   总被引:2,自引:0,他引:2  
工程应用中存在许多颗粒流动堆积问题.首先设计了一系列测量方法,通过大量的实验和统计分析,得到了颗粒的多种物理参数.并以工程中高炉炉顶称量料罐为背景,采用离散元方法模拟不同物理条件下离散颗粒的流动堆积行为,得出料罐内颗粒系统中颗粒之间力的分布不均匀,而且强力链分布主要与料罐的左下壁方向平行.同时,设计并制作了具有多参数调节的离散颗粒料罐实验模型,进行了相应的物理实验,实测结果与数值模拟吻合良好.  相似文献   

4.
张炜  萧伟健  袁传牛  张宁  刘焜 《力学学报》2022,54(9):2489-2500
为阐明粒径分布对铁粉压制中体系内部细观力学行为的影响, 基于离散元理论, 通过改变铁粉颗粒粒径分布建立压制模型, 结合力链提取方法, 通过对力链空间分布、力链数目、力链长度和力链方向性的分析, 探究粒径分布对力链演化的影响机理. 研究结果表明: 不同粒径分布的粉体压制时形成的力链空间分布具有差异, 粒径分布范围越小, 形成的力链分布越集中, 反之, 粒径分布范围越大, 形成的力链分布越松散且均匀; 在粉末压制时, 粒径分布对力链数目也有影响, 具体表现为随着粉体的粒径分布范围变大, 力链总数逐渐减少; 粉体的粒径分布对颗粒形成短力链的数目起着显著影响, 而对力链长度的影响较为有限; 随着粒径分布范围的增大, 力链的方向由均匀分布逐渐集中在特定角度方向, 表现出一定各向异性, 形成的交叉力链网络结构有利于提高粉体致密化程度. 本文为从粉体粒径分布影响层面拓展粉末压制细观力学理论提供基础, 亦为进一步结合粉体粒径分布及体系内力链演变过程改善粉末致密化行为提供指导.   相似文献   

5.
In this paper, to investigate the buckling characteristics of carbon nanotubes, an equivalent beam model is first constructed. The molecular mechanics potentials in a C–C covalent bond are transformed into the form of equivalent strain energy stored in a three dimensional (3D) virtual beam element connecting two carbon atoms. Then, the equivalent stiffness parameters of the beam element can be estimated from the force field constants of the molecular mechanics theory. To evaluate the buckling loads of multi-walled carbon nanotubes, the effects of van-der Waals forces are further modeled using a newly proposed rod element. Then, the buckling characteristics of nanotubes can be easily obtained using a 3D beam and rod model of the traditional finite element method (FEM). The results of this numerical model are in good agreement with some previous results, such as those obtained from molecular dynamics computations. This method, designated as molecular structural mechanics approach, is thus proved to be an efficient means to predict the buckling characteristics of carbon nanotubes. Moreover, in the case of nanotubes with large length/diameter, the validity of Euler’s beam buckling theory and a shell model with the proper material properties defined from the results of present 3D FEM beam model is investigated to reduce the computational cost. The results of these simple theoretical models are found to agree well with the existing experimental results.  相似文献   

6.
In this paper, a model of topology optimization with linear buckling constraints is established based on an independent and continuous mapping method to minimize the plate/shell structure weight. A composite exponential function (CEF) is selected as filtering functions for element weight, the element stiffness matrix and the element geomet-ric stiffness matrix, which recognize the design variables, and to implement the changing process of design variables from“discrete”to“continuous”and back to“discrete”. The buck-ling constraints are approximated as explicit formulations based on the Taylor expansion and the filtering function. The optimization model is transformed to dual programming and solved by the dual sequence quadratic programming algo-rithm. Finally, three numerical examples with power function and CEF as filter function are analyzed and discussed to demonstrate the feasibility and efficiency of the proposed method.  相似文献   

7.
The lateral buckling and helical buckling problem of a circular cylinder constrained by an inclined circular cylinder under a compressive force, torsion, and its own weight is complicated and difficult to obtain an exact analytical solution. Thus, the non-linear differential equation is solved incrementally using the discrete singular convolution (DSC) algorithm together with the Newton–Raphson method. Detailed formulations are worked out. A simple way to numerically simulate the helical buckling is proposed and solution procedures are given. Four examples with various inclined angles, weights per unit length of the inner cylinder, axial applied loads, and boundary conditions are investigated. To verify the formulations and solution procedures, comparisons are firstly made with data obtained using the finite element method. It is verified that under certain circumstance, only lateral or helical buckling alone will occur. On some other circumstance, both lateral buckling and helical buckling may occur and the critical helical buckling loads are higher than the critical lateral buckling loads if frictions are not considered. Some conclusions are made based on the results presented herein.  相似文献   

8.
颗粒流动力学及其离散模型评述   总被引:14,自引:0,他引:14  
孙其诚  王光谦 《力学进展》2008,38(1):87-100
颗粒流是由众多颗粒组成的具有内在相互作用的非经典介质流动. 自然界常见颗粒流 都是密集流, 颗粒间接触形成力链, 诸多力链相互交接构成支撑整个颗粒流重量和外载荷的 网络, 其局部构型及强度在外载荷下演化, 是颗粒流摩擦特性和接触应力的来源.本文 介绍球形颗粒间无粘连作用时的Hertz法向接触理论和Mindlin-Deresiewicz切向接触 理论. Campbell依据是否生成较为稳定的力链把颗粒流分为弹性流和惯性流两大 类, 其中弹性-准静态流和惯性-碰撞流分别对应准静态流和快速流, 作为两种极端流动情况通常处理成连续体, 分 别采用摩擦塑性模型和动理论予以描述, 但是表征接触力链的颗粒弹性参数并不出现这两个 模型和理论框架中, 如何进一步考虑颗粒弹性参数将非常困难. 目前离散动力学方法逐渐 成为复现其复杂颗粒流动现象、提取实验不可能获得的内部流动信息进而综合起来探索颗粒 流问题的一种有效工具, 其真实性强于连续介质理论的描述. 软球模型对颗粒间接触力简化 处理, 忽略了切向接触力对法向接触力及其加载历史的依赖, 带来了法向和切向刚度系数 如何标度等更艰难的物理问题, 但由于计算强度小而广泛应用于工程问题中. 硬球模型不考虑 颗粒接触变形, 因而不能描述颗粒流内在接触应变等物理机理, 仅适用于快速颗粒流, 这不 仅仅是由于两体碰撞的限制. 因此基于颗粒接触力学的离散颗粒动力学模型是崭新的模型, 适用于准静态流到快速流整个颗粒流态的模拟, 可以细致考虑接触形变及接触力的细节, 建立更为合理的颗粒流本构关系, 进而有力的促进颗粒流这一非经典 介质流动的研究.  相似文献   

9.
U型波纹管是现代管道系统中最常见的一种位移补偿器 ,它由环板和具有正、负Gauss曲率的半圆环壳组成 ,在管道所传输的介质的压力作用下会发生屈曲。其中环向屈曲最为复杂 ,精确的理论分析非常困难 ,有限元分析也不多见。作者在分析前人工作的基础上 ,以圆环壳段为单元 (特定的旋转壳段单元 ,能自动退化成环板单元 ) ,限于弹性范围和线性化特征值问题 ,对介质压力作用下U型波纹管及其相关结构 (圆环板、圆环壳、半圆环壳 )的环向屈曲问题进行了分析。考虑了结构屈曲前的弯曲 ,计及压力的二次势能 ,导出的应力刚度矩阵和载荷刚度矩阵是非对称的。全部工作分为三部分 :(Ⅰ )基本方程 ,环板的屈曲 ;(Ⅱ )圆环壳、半圆环壳的屈曲 ;(Ⅲ )波纹管平面失稳的机理。本文为第一部分 ,除推导公式外 ,对不同边界和不同内外径之比的环板在径向均匀压力作用下的环向屈曲进行了计算 (轴对称的径向屈曲作为特例得到 ) ,给出了前屈曲应力分布、临界载荷及相应的屈曲模态 ,并将临界压力的值与前人基于vonK偄rm偄n大挠度板的精确解进行了比较 ,吻合良好。  相似文献   

10.
In this paper, a simplified method is proposed for the prediction of creep buckling. This simplified approach relies upon a model which yields an analytical evaluation of creep buckling times for cylinders under external pressure. This model is fully developed herein, and a ‘closed-form’ solution is given for the evaluation of the critical creep collapse time. The collapse mechanism is assumed to be due to the formation of a plastic hinge which induces an unstable post-buckling of the ring. The analytical ‘closed-form’ creep collapse time is then compared to finite element buckling predictions using the quasi-axisymmetric COMU shell element in the INCA code of the CASTEM system. The model is then applied to four different cylinders under external pressure and compared to finite element predictions; the cylinders' radius-to-thickness ratio varies between 50 and 550. It is shown that the proposed model performs well for this type of prediction: in all cases, the times to failure predicted by the model are lower than the finite element predictions. These predictions prove to be rather conservative for thicker cylinders. It is shown that creep buckling is a very dangerous failure mode. If the shape of the structure is observed as a function of time, nothing seems to happen during a very long ‘incubation’ period; when the initial imperfection reaches some critical value, buckling then suddenly occurs. This phenomenon is shown by the two methods of evaluation presented herein.  相似文献   

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