【作者】 马炜；

【导师】 刘才山； 黄琳；

【作者基本信息】 北京大学 ， 一般力学与力学基础， 2008， 博士

【摘要】 由大量粒子或粒子团所组成的散体介质广泛存在于生物、化工、材料等各类工程问题当中,揭示其在冲击载荷作用下所呈现的复杂动力学行为以及产生这些动力学行为的物理机制是当前多学科研究领域所关注的重要内容。本文主要从四个方面研究了散体介质的冲击行为:(1)一维球链在冲击载荷作用下波动现象的连续化描述方法,波的结构、传播规律和相关性质的研究。(2)散体介质间库仑摩擦力的描述,以及多刚体系统含库仑摩擦力的动态超静定问题的分析方法和数值算法。(3)散体介质间碰撞过程中法向局部能量耗散现象的描述方法和相应的数值算法。(4)大量散体材料的宏观力学性能分析。一维球链在冲击载荷作用下将呈现明显的连续介质性质:外部冲击载荷在球链中以波的形式存在,并按照确定的波速传播和扩散。为有效描述散体介质的这种自组织行为,本文首先精细分析冲击载荷影响范围内各个质点的动力学响应,进而基于广义Hamilton变分原理将散体介质的波动行为表示为一组三角函数正交基的线性组合,从而建立了散体介质宏观冲击行为的连续化描述方法。在该连续化描述方法的基础上研究了一维球链所激发的波形结构以及波的传播规律和相关性质,并建立了球链中非线性Hertz接触模型和线性接触模型之间的等效关系。通过相关的数值计算结果和实验结果的比较验证了该连续化分析方法的有效性。摩擦对多刚体的动力学行为研究带来巨大的挑战,近年来的研究结果表明摩擦(特别是库仑摩擦中的粘滞现象)是决定散体介质宏观力学行为的主要因素。本文基于变结构动力学的思想,通过引入补充的运动约束方程建立了处理由于库仑摩擦引起的的多刚体系统动态超静定问题的分析方法;同时引入Stronge定义的能量恢复系数建立了考虑局部能量耗散现象的刚体碰撞接触模型。数值算例和相关文献发表的实验结果验证了该方法的有效性。复杂散体介质受到冲击载荷作用下的动力学行为的描述依赖于高效的数值算法。在建立相关接触搜索算法的基础上发展了月壤计算机模拟生成技术;研究了月壤在受到冲击载荷作用下的动力学特性,提出了月壤力学性能的简化分析模型。研究表明月壤的承载能力与冲击速度有关:低速冲击情况下主要体现在粒子的相对密实和位错;高速冲击情况下则体现在月壤内部粒子形成的射流和飞溅。通过与NASA相关实验的对比建立了月壤轴对称问题二维到三维模型的等效规则。更多还原

【Abstract】 Granular materials are formed by amounts of particles and it is useful for shockingprotection. The dynamic behavior of granular materials is neither similar to solid nor?uent and that caused the vigorous interest of many researchers. When shock accruesin granular materials, it will propagate through the granular materials and many inter-esting dynamic phenomena will be caused. This paper started from theoretical researchworks of a 1D chain of beads which was hit at one end of the chain, based on the Hamil-ton variational principle a continuable method has been carried out to analysis the wavepropagating of the chain. Multi-body dynamics with contact and friction is always atough problem, rigid body model and Coulomb’s law will caused many difficulties andinconsistencies. By bring movement restrictions of stick points from Lagrange ana-lytical mechanics into multi-body dynamics and defining contact model with energydissipation, the problem has been solved theoretically and numerically. At last the dy-namic behavior of Lunar soil has been studied from distinct element method(DEM), thelunar soil can be regarded as an ideal elastic-plastic spring under low-velocity impact.Chain of beads is a simple granular materials. When a long line of particles ishit at one end by another particle, dynamical self-organized impulsive waves will begenerated and propagating through the chain, after that the chain will fragmentate. Theimpulsive waves is propagating in constant speed with a wavelength affect area, parti-cles besides this area can not effect the movement of the waves. Based on the Hamiltonvariational principle we develop a continuable method, in this method theoretical re-sults of the waves can be described by the sum of a set of trigonometric functions.From analytical works we get that all the possible structures of the waves are decidedby the mass ratio of the chain, but the stiffness ratio of the chain excite the exact wavestructure.Multi-body dynamics with contact and friction is fundamental for mechanics andengineering, but rigid body model and Coulomb’s law in multi-body dynamics bringmany difficulties and inconsistencies. Contact between rigid bodies is described by lo-cal ?exibility model, it is a double stiffness track basing on Hertz contact law and the restitution coefficient defined by Stronge. Movement restrictions of stick points are ad-ditional conditions to get the static frictions between rigid bodies. Then the movementof the multi-body system with contact and friction can be decided.Lunar soil–a typical granular materials has also been studied in this paper. A com-puter simulation technology has been used to get the numerical model of the lunar soil,dynamic behavior of the numerical model under impact is simulated by distinct elementmethod. Compared numerical results and experiment results we find the relationshipbetween 2D and 3D model of axis symmetry problems. Under low-velocity impact thedynamic behavior of the lunar soil is decided by the denseness and dislocation of theparticles; jet ?ow of particles will be the major phenomena of lunar soil under high-velocity impact.更多还原