Numeričko modeliranje granularnih materijala

Abstract

Granularne materijale čini skup vema velikog broja sitnih solida (zrna, granula, čestica) čije ponašanje zavisi od energije koju solidi poseduju i predstavljaju nakon vode drugu najmanipulisaniju materiju u inženjerstvu. Za numeričku analizu uređaja za transport, skladištenje i obradu granularnih materijala, neophodno je tačno modeliranje opterećenja kojima granularni materijal deluje na pomenute uređaje. U okviru ove disertacije data je teorijska analiza ponašanja granularnih materijala od mikro nivoa gde je analiziran kontakt između dva zrna, do makro nivoa u kome se analizira ponašanje celokupnog materijala. Metoda diskretnih elemenata je korišćena za modeliranje troosnog testa, eksperimenta koji se najčešće koristi za određivanje materijalnih karakteristika, kao i traka smicanja i vrtolga koji se pri tom javljaju u granularnom materijalu. Opterećenja u granularnom materijalu nisu ravnomerno raspoređena, već najopterećenija zrna formiraju lance sila dok ostala zrna igraju potpornu ulogu. Deformacije granularnog materijala izazivaju kidanje starih i formiranje novih lalnaca sila, a promene opterećenja su analizirane za izabrana zrna. Glatka čestična hidrodinamika je numerička metoda zasnovana na mehanici kontinuuma, a njen bezmrežni karakter omogućava analizu velikih deformacija u realnim problemima, pa je generalisani materijalni model sa kapom ugrađen u program i korišćen za modeliranje granularnih materijala. Metoda konačnih elementata je najčešće korišćena numerička metoda u inženjerstvu, a da bi se koristila za analizu uređaja za transport, skladištenje i obradu granularnih materijala povezana je sa glatkom čestičnom hidrodinamikom po principima fluid-solid interakcije, a kontaktni algoritam između ove dve metode je proširen tretmanom trenja na osnovu Kulonovog zakona. Metodologija analize podrazumeva korišćenje dva programa za pre-procesiranje i jednog za post-procesiranje koji su povezani sa solverima pomoću programa prevodioca. Materijalni model, sprezanje numeričkih metoda i kontaktni algoritam su verifikovani na test primerima, a u poslednjem primeru je dat razvoj materijalnog modela koji uzima u obzir i uticaj temperature na ponašanje materijala.

The granular materials consists of large number of small solids (grains, granules, particles) whose behavior depends on the energy they have and represent the second most manipulated matter in engineering (water is the first). For numerical analysis of devices for transport, storage and processing of granular materials, it is necessary to accurately model load which granular materials exert on the aforementioned devices. As a part of this dissertation the theoretical analysis of granular materials behavior is presented, both at the micro levels where the contact between two grains is analyzed, and a macro level in which the behavior of the whole material is analyzed. Discrete element method was used for modeling of triaxial tests, experiments that are commonly used to determine material characteristics, as well as shear bands and vortexes which occur in the granular material during these tests. Loads in the granular material are not evenly distributed, with most loaded grains forming force chains, while other grains play only a supporting role. Deformation of granular materials causes breaking of old and the formation of new force chains and load changes are analyzed in selected grains. Smoothed particle hydrodynamics is a numerical method based on continuum mechanics, and its meshless character allows analysis of large deformation in real problems, so generalized material model with cap was coded into the program and used to model granular materials. Finite element analysis is the most widely used numerical methods in engineering, but in order to be used for the evaluation of construction for transportation, storage and processing of granular materials it needed to be connected with smoothed particle hydrodynamics using the principles of fluid-solid interactions, and contact algorithm between these two methods is expanded by friction treatment on the basis of Coulomb's law. The methodology of analysis involves the use of two programs for pre-processing and one for post-processing that are connected with the solver using interpreter software. Material model, coupling numerical methods and contact algorithm are verified on tests, and in the last example, the development of material models that take into account the effect of temperature on the behavior of materials is given.