Dynamical Behavior Of Granular Materials Under Impact

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.