Theoretical And Numerical Study Of The Effective Physical Properties And Dynamic Behaviors Of Granular Matter

Granular matter denotes the matter form which consists of a collection of discrete macroscopic grains and widely exists in our nature.Due to their special properties similar to both fluids and solids,granular materials are also massively used in industrial applications,like the pebble beds serving as the solid tritium breeders and neutron multipliers in future fusion reactors.Under such a background,in this thesis the theoretical and numerical investigations of the effective physical properties and dynamic behaviors of granular matter are carried out.In the respect of granular matter's effective physical properties,based on the continuum assumption we mainly derived theoretically the effective density,effective specific heat,effective thermal expansion coefficient and effective thermal conductivity(ETC),while the effective elastic modulus was studied via the numerical method based on the non-continuum mechanics,i.e.the discrete element method(DEM).Generally,granular matter's effective density is the product of system's packing fraction and the density of solid particle itself,and the effective specific heat and thermal expansion coefficient can be respectively regarded as those of solid grains themselves.As for the foundamental mechanical behaviors and elastic modulus of granular matter,we have re-confirmed the nonlinear elastic stress-strain relation,the much smaller elastic modulus of a granular system than that of the solid material and the faster growth of modulus than the p1/3 law predicted by the effective medium theory(EMT).p is the applied pressure.Especially,we also found that the normalized moduli of various granular materials obey a universal distribution,suggesting that granular packings have some invariance in mechanical property.Besides,the effects of cyclic loading and unloading and subtle difference in grain sizes were also explored.For the ETC of monodispersed granular matter,we developed a new prediction model which has comprehensively taken account of three types of heat thransfer(i.e.conduction,convection and radiation)and includes almost all of influcecing factors.Compared with exsisted models,numerical results and available experimental data of various pebble beds,this model was verified to be valid and its accuracy relative to other models was also showed.Based on the verified model,we further theroretically investigated the effects of influencing factos on the ETC of granular matter,and finally provided the criterions that under which conditions the effects of these influencing factors should be considered or neglected.On the aspect of dynamic behaviors of granular matter,through ultilizing DEM to simulate the realistic granular system,we have studied the responses of granular materials to cyclic pressure,the thermal expansion and fluctuation effects in a binary granular mixture and the physical phenomenon that granular matter shows the energy reallocations under vibration and thermal cycling.Similar to the situation under thermal cycling,under the cyclic pressure the granular system was also observed to exhibit the fast compaction,and this prosess still complies with the stretched exponential law.This indicates that the mechanical and thermal cycling excitations have some similarity in the system's density relaxation induced.Moreover,the cyclic pressure was also found to cause the stiffening in packing structure and to weaken the dependence of elastic modulus on applied pressure.At the same time,in force chains consisting of contact forces between grains the "stress" relief also appeared,although the loads exerted on the system are not lowered.Under thermal excitations(temperature changes),the density segeragation occurred inside the mixed granular system and the force networks were degenerated.Besides,it was also observed that friction between grains would inhibit the thermal expansion and thermal fluctuation effects,and its effect shows a threshold characteristic.Under both vibration and thermal cycling,the imporatant phenomenon that the total system energy was reallocated to grains was observed to occur in granular matter.During the whole process,grains carrying with high energy would try to transfer some of their energy to their neighbors with low energy,and these grains finally relocated into a new steadier packing where grains are closer to energy equilibrium.Furthermore,within a granular system the probability distribution of grain energy obeys a more general Maxwell-Boltzmann(M-B)distribution and has a more uniform profile(narrower energy span)than the classical M-B distribution for gases.This seems to mean that compared with the indirect-contact collision,the direct-contact collision may be a more effective channel for the energy interchange between particles.We hope the above study can make people have a better understanding of granular matter while solving some practical engineering problems.