本文選題：離散單元法 + 閔可夫斯基和��； 參考：《大連理工大學(xué)》2017年博士論文

【摘要】：顆粒物質(zhì)與人類的生產(chǎn)生活緊密相關(guān),如谷物的存儲和運輸、鐵路道床的沉降、沙丘的遷移以及滑坡泥石流等都屬于顆粒物質(zhì)的研究范疇。顆粒物質(zhì)由離散的個體隨機組合而成,其宏觀表現(xiàn)既有固體的力學(xué)特性又有流體的流動特性,并隨著條件的變化在兩者間相互轉(zhuǎn)化。在對顆粒物質(zhì)宏觀行為的研究中,可采用基于Cosserat連續(xù)體的有限元模型進行數(shù)值模擬,但這種連續(xù)模型在計算顆粒材料微結(jié)構(gòu)的連續(xù)性假設(shè)使其不適用于顆粒物質(zhì)發(fā)生大變形的情況。在對大變形的情況以及顆粒物質(zhì)離散的特性研究中,離散單元法是以顆粒個體為研究對象,通過控制形狀、尺寸、物理屬性來構(gòu)造顆粒單元并通過建立單元間相互作用的本構(gòu)關(guān)系來描述顆粒物質(zhì)的動力過程。該方法無需對顆粒物質(zhì)進行諸多假設(shè)和限制,在研究顆粒物質(zhì)時具有特有的優(yōu)勢。離散單元法研究中,球形單元因其簡單的幾何描述以及成熟的接觸模型成為離散單元法中最經(jīng)典的顆粒單元模型之一。采用球體單元可以滿足對顆粒物質(zhì)研究的一般要求。然而顆粒單元的幾何形態(tài)對其宏觀力學(xué)行為的影響不可忽略,在自然界中顆粒物質(zhì)形態(tài)主要是以非規(guī)則顆粒為主。如何構(gòu)造接近真實顆粒形態(tài)的復(fù)雜單元,進而提高顆粒單元之間接觸過程的計算精度是離散單元法需要解決的重要問題。本文在離散單元球形單元的基礎(chǔ)上,研究了擴展圓盤單元和擴展多面體單元兩種非規(guī)則單元模型,以及這里種單元的應(yīng)用。擴展圓盤單元是由球體和圓盤經(jīng)過閔可夫斯基和運算得到的非規(guī)則單元。在計算擴展圓盤單元間的接觸力時,根據(jù)擴展圓盤單元的幾何特點將單元間的接觸簡化為兩類:面-面接觸和弧面-面接觸。參考渤海蓮葉冰的形狀和冰的物理屬性特征,將擴展圓盤單元作為冰塊單元對海冰進行模擬研究。文中模擬了碎浮冰與直立樁腿結(jié)構(gòu)的碰撞過程,分析了浪高和潮流對冰荷載的影響,研究表明碎浮冰產(chǎn)生的冰荷載明顯低于波浪荷載。為研究平整冰對海洋結(jié)構(gòu)的作用,通過粘結(jié)帶將圓盤冰單元連接以模擬平整冰在潮流作用下與錐體結(jié)構(gòu)發(fā)生接觸碰撞而產(chǎn)生冰荷載的過程。模擬結(jié)果和現(xiàn)場實測數(shù)據(jù)對比分析發(fā)現(xiàn),用這種粘結(jié)破碎冰模型得到的冰荷載特點與現(xiàn)場實測數(shù)據(jù)具有較高的一致性。針對鐵路道砟碎石塊等具有復(fù)雜幾何形態(tài)的顆粒單元,用球形單元和多面體單元進行閔可夫斯基和運算得到擴展多面體單元模型,這種模型有尖銳的棱角和不規(guī)則的形態(tài)。根據(jù)單元模型的特點,將單元間的接觸類型分成三類:面-面接觸,點-面接觸,棱-棱接觸。文中用這種單元模型對鐵路道砟在循環(huán)加載下的道砟箱試驗進行模擬,研究道床沉降與循環(huán)荷載頻率的關(guān)系,構(gòu)造了不同尖銳度的道砟顆粒,研究了道砟顆粒尖銳程度對道床性能的影響。研究結(jié)果表明道砟顆粒尖銳度對道床的初始體密度和道床在循環(huán)荷載下的沉降量有顯著影響。顆粒材料的剪切流動行為廣泛地存在于滑坡、泥石流等自然災(zāi)害以及礦物原料傳輸、泵送等工業(yè)過程中。本文用擴展多面體單元模擬了塊石的滑坡過程,研究了塊石滑坡過程中顆粒堆的能量耗散情況。研究發(fā)現(xiàn)滑動摩擦是顆粒系統(tǒng)耗能的主要原因,在同樣的工況下由于顆粒堆內(nèi)部坍塌的原因,滑坡的移動速度比質(zhì)量塊的滑動速度快。顆粒材料在不同體積分數(shù)、剪切速率和應(yīng)力約束下會表現(xiàn)出不同的流動狀態(tài)并發(fā)生相互轉(zhuǎn)化。本文研究了球形顆粒單元接觸間的滾動阻尼,文中采用試驗和數(shù)值模擬兩種方法研究球形單元滾動阻尼的大小以及滾動阻尼對顆粒單元運動形態(tài)的影響。研究發(fā)現(xiàn)滾動摩擦和滑動阻尼將對顆�；虬l(fā)生滾動或發(fā)生滑動的不同運動形態(tài)有很大影響。對顆粒材料在剪切流動過程中力學(xué)特性的研究有助于加深理解其發(fā)生不同流動狀態(tài)的內(nèi)在機理,為解決相應(yīng)的顆粒材料問題提供理論依據(jù)。為此,本文研制了顆粒材料剪切流動的中型環(huán)剪儀,并對顆粒材料在不同法向約束應(yīng)力和剪切速率下的剪切應(yīng)力和體積膨脹率進行了測試。結(jié)果表明,剪切應(yīng)力和體積膨脹率均隨剪切速率的增加而增大,但增長速率在臨界剪切速率處發(fā)生轉(zhuǎn)變,使其隨剪切速率的平方呈分段式線性增長。通過對顆粒材料在不同剪切速率和慣性數(shù)下有效摩擦系數(shù)變化趨勢的分析,討論了顆粒材料由慢速流向快速流轉(zhuǎn)化的基本規(guī)律,以及在臨界剪切速率處發(fā)生流動狀態(tài)轉(zhuǎn)化的內(nèi)在條件。最后,對本文在擴展離散元模型方面的研究工作進行總結(jié),并指出了后續(xù)工作的研究重點。
[Abstract]:Particulate matter is closely related to the production and life of human beings, such as the storage and transportation of grain, the settlement of the railway bed, the migration of sand dunes, and the landslide and debris flow. The particle material is composed of discrete individuals, and its macroscopic performance has both the mechanical properties of the solid and the fluid flow characteristics. In the study of macroscopic behavior of particulate matter, the finite element model based on Cosserat continuum can be used for numerical simulation in the study of macroscopic behavior of particulate matter. However, this continuous model is not suitable for large deformation of particulate matter by calculating the continuity hypothesis of the micro structure of granular materials. In the study of the discrete properties of particulate matter, the discrete element method is based on the particle individual as the research object. The particle elements are constructed by controlling the shape, size and physical properties, and the dynamic process of the particles is described by establishing the constitutive relation of the interaction between the units. In the study of the granular material, the spherical element is one of the most classical particle element models in the discrete element method because of its simple geometric description and mature contact model in the study of the discrete element method. The influence of morphology on its macroscopic mechanical behavior can not be ignored. In nature, the main form of granular material is irregular particles. How to construct complex elements close to the real particle shape and improve the calculation accuracy of contact process between particles is an important problem to be solved by discrete element method. On the basis of the form element, two irregular element models of the extended disk unit and the extended polyhedron element are studied, and the application of the unit is given. The extended disk unit is an irregular unit which is obtained by the sphere and the disk through Minkowski and the operation. The geometric features simplify the contact between the units into two categories: surface to surface contact and arc surface contact. Referring to the shape of the Bohai lotus Ye Bing and the physical properties of ice, the extended disk unit is used as an ice unit to simulate the sea ice. The collision process between the broken ice and the upright pile is simulated in this paper, and the wave height and the flow to the ice are analyzed. The study shows that the ice load produced by the crushed ice is obviously lower than the wave load. In order to study the effect of the ice on the ocean structure, the disc ice unit is connected by the bond zone to simulate the ice load caused by the contact collision of the flat ice with the cone structure under the action of the tide. The simulation results are compared with the field measured data. It is found that the ice load characteristics of the broken ice model are in good agreement with the field measured data. For the particle units with complex geometric shapes such as the railway ballast fragments, the spherical element and the polyhedron element are used for Minkowski and the extended polyhedral element model. This model has a sharp point. Sharp edges and irregular forms. According to the characteristics of the unit model, the contact types between units are divided into three types: face to face contact, point to surface contact, and prism contact. In this paper, the ballast box test of railway ballast under cyclic loading is simulated with this element model, and the relationship between the bed settlement and the frequency of cyclic loading is studied. The impact of the sharpness of ballast particles on the performance of ballast particles has been studied. The results show that the sharpness of ballast particles has a significant influence on the initial body density of the ballast bed and the settlement of the ballast bed under cyclic loading. The shear flow behavior of the granular materials is widely distributed in natural disasters such as landslides, debris flows and minerals. During the industrial process of raw material transmission and pumping. This paper simulates the landslide process of block stone with extended polyhedron element and studies the energy dissipation of the granular pile in the process of block stone landslide. It is found that the sliding friction is the main reason for the energy dissipation of the granular system. In the same working condition, the cause of the collapse of the particle heap and the speed of the landslide movement The sliding velocity of the mass is faster than the mass block. The particle material will show different flow states and transform each other under the different volume fraction, shear rate and stress constraint. In this paper, the rolling damping between the contact of spherical particles is studied. In this paper, two methods of experiment and numerical simulation are used to study the size of the rolling damping of the spherical element. It is found that the rolling friction and the sliding damping will have a great influence on the particle or the different motion patterns of the particles or rolling or sliding. The study of the mechanical properties of the granular material during the shear flow will help to deepen the understanding of the internal mechanism of the different flow state. This paper provides a theoretical basis for solving the corresponding particle material problem. Therefore, this paper has developed a medium ring shear apparatus for the shear flow of granular materials. The shear stress and volume expansion rate of the granular materials under different normal stress and shear rates were tested. The results showed that the shear stress and volume expansion rate increased with the shear rate. In addition, the growth rate is changed at the critical shear rate, which makes it linearly increase with the square of shear rate. By analyzing the change trend of the effective friction coefficient under different shear rate and inertia number, the basic law of the transformation from slow flow to fast flow is discussed, and the critical shear rate is discussed. The internal conditions for the transformation of the flow state at the cutting rate. Finally, the research work on the extended discrete element model is summarized, and the focus of the follow-up work is pointed out.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2017
【分類號】：O347.7
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本文編號：2081054