發(fā)布時(shí)間：2018-08-23 14:33

【摘要】：顆粒材料與人們的日常生活息息相關(guān),廣泛存在于自然界并在實(shí)際工程中被大量地應(yīng)用,例如粒狀藥劑、砂礫、堆石料等。顆粒材料是由大量離散固體顆粒構(gòu)成的,具有非常復(fù)雜的性質(zhì),其力學(xué)行為的理論研究和數(shù)值模擬受到眾多學(xué)者的廣泛關(guān)注。 剪脹性是顆粒材料的重要宏觀力學(xué)行為之一,一般通過(guò)引入剪脹角來(lái)表征其影響。在進(jìn)行工程計(jì)算分析時(shí),對(duì)剪脹角ψ一般有三種處理方式：(1)ψ=0°;(2)ψ=?μ,?μ為材料的內(nèi)摩擦角；(3)0°ψ≡constφμ。以上三種處理方式都有著各自的弊端：第一種處理方式?jīng)]有考慮顆粒材料的剪脹性；第二種處理方式則夸大了顆粒材料的剪脹性,并且與塑性能量耗散理論也存在一定的矛盾；第三種處理方式是前兩種處理方式的折中,是一種過(guò)于依賴工程經(jīng)驗(yàn)的方法。同時(shí)以上三種處理方式中剪脹角均為常數(shù),這將導(dǎo)致剪脹會(huì)隨剪切應(yīng)變的增大而呈線性增加,而此與顆粒材料達(dá)到臨界狀態(tài)后其塑性體積不再增加的實(shí)際情況也是不相符的。本文借鑒了Houlsby提出的剪脹角相關(guān)公式,將其與Drucker-Prager準(zhǔn)則結(jié)合并引入到了Cosserat連續(xù)體模型之中,形成了一個(gè)能考慮剪脹角演化的宏觀連續(xù)體模型并運(yùn)用Fortran語(yǔ)言獨(dú)立開(kāi)發(fā)了程序代碼將其數(shù)值實(shí)現(xiàn),最后通過(guò)數(shù)值算例對(duì)顆粒材料結(jié)構(gòu)的承載力以及應(yīng)變局部化現(xiàn)象進(jìn)行了研究。 同時(shí)顆粒破碎也是顆粒材料的一個(gè)重要特性,其對(duì)顆粒材料的宏觀力學(xué)響應(yīng)也有著影響。顆粒破碎所引起的最直觀變化為顆粒粒徑的改變,經(jīng)典連續(xù)體模型大多無(wú)法對(duì)其加以描述,而Cosserat連續(xù)體模型中包含的特征長(zhǎng)度參數(shù)則在一定程度上反映了細(xì)觀結(jié)構(gòu)內(nèi)的平均顆粒粒徑。本文中借鑒Hardin提出的顆粒破碎相關(guān)公式,將表征顆粒材料破碎程度的相對(duì)破碎率與Cosserat連續(xù)體模型中的特征長(zhǎng)度參數(shù)關(guān)聯(lián)了起來(lái),同時(shí)還提出了破碎應(yīng)力閾值對(duì)相對(duì)破碎率的計(jì)算進(jìn)行了適當(dāng)修正,形成了一個(gè)能考慮顆粒破碎的宏觀連續(xù)體模型并運(yùn)用Fortran語(yǔ)言獨(dú)立開(kāi)發(fā)了程序代碼將其數(shù)值實(shí)現(xiàn),最后通過(guò)數(shù)值算例對(duì)顆粒材料結(jié)構(gòu)的承載力以及應(yīng)變局部化現(xiàn)象進(jìn)行了研究。 此外,顆粒材料多尺度模型的建立為顆粒材料的研究提供了一種新的途徑。本文中使用了宏觀Cosserat連續(xù)體模型-細(xì)觀離散顆粒模型兩尺度模型,該模型在宏觀尺度上依賴于宏觀有限元網(wǎng)格,能有效地解決規(guī)模較大的問(wèn)題；同時(shí)在細(xì)觀尺度上將顆粒材料視為離散顆粒集合體,以便于更真實(shí)地描述顆粒材料的離散特性。此種方法是由計(jì)算均勻化理論發(fā)展而來(lái),其核心為基于表征元的宏細(xì)觀信息的傳遞,而細(xì)觀數(shù)值樣本尺寸的選取合適與否則關(guān)系到細(xì)觀數(shù)值樣本是否能被視作為表征元。本文基于Miehe提出的宏細(xì)觀信息的傳遞格式詳細(xì)研究了細(xì)觀數(shù)值樣本尺寸對(duì)顆粒材料結(jié)構(gòu)的宏觀剛度、極限承載力以及殘余承載力產(chǎn)生的影響,并根據(jù)數(shù)值分析結(jié)果提出了相應(yīng)的指數(shù)-對(duì)數(shù)型擬合公式以便于確定合適的細(xì)觀數(shù)值樣本尺寸,同時(shí)還研究了加載過(guò)程中細(xì)觀尺度上細(xì)觀數(shù)值樣本構(gòu)形及位移殘差場(chǎng)的演化。
[Abstract]:Particle material is closely related to people's daily life and widely exists in nature and is widely used in practical engineering, such as granular reagent, gravel, rockfill and so on. Particle material is composed of a large number of discrete solid particles with very complex properties. The theoretical study and numerical simulation of its mechanical behavior have been studied by many scholars. Widespread concern.
Dilatancy is one of the most important macroscopic mechanical behaviors of granular materials, which is usually characterized by the introduction of dilatancy angle. The first method does not consider the dilatancy of granular materials; the second method exaggerates the dilatancy of granular materials and contradicts the theory of plastic energy dissipation; the third method is a compromise between the first two methods, which is a method too dependent on engineering experience. The dilatancy angle is constant, which leads to the linear increase of dilatancy with the increase of shear strain. This is also inconsistent with the fact that the plastic volume of granular materials does not increase after reaching the critical state. In the Cosserat continuum model, a macroscopic continuum model which can consider the evolution of dilatancy angle is formed, and the program code is developed independently by Fortran language. Finally, the bearing capacity and strain localization of granular material structures are studied by numerical examples.
Particle breakage is also an important characteristic of granular materials, and it also has an effect on the macroscopic mechanical response of granular materials. In this paper, the relative breakage rate of granular materials is correlated with the characteristic length parameter in Cossserat continuum model by using the particle breakage correlation formula proposed by Hardin. At the same time, the breakage stress threshold is proposed to calculate the relative breakage rate. A macroscopic continuum model considering particle breakage is formed with proper modification and the program code is developed independently by Fortran language. Finally, the bearing capacity and strain localization of granular material structures are studied by numerical examples.
In addition, the multi-scale model of granular materials provides a new way for the study of granular materials. In this paper, a two-scale model of macro-Cosserat continuum model and micro-discrete granular model is used. The model relies on macro-finite element meshes at macro-scale, and can effectively solve large-scale problems. In order to describe the discrete characteristics of granular materials more truly, granular materials are considered as discrete aggregates in scale. This method is developed from computational homogenization theory. The core of this method is the transmission of macro-and micro-information based on representation elements, and the selection of the size of meso-numerical samples is related to whether the meso-numerical samples are suitable or not. Based on the transfer scheme of macro-and micro-information proposed by Miehe, the effects of sample size on the macro-stiffness, ultimate bearing capacity and residual bearing capacity of granular material structures are studied in detail, and the corresponding exponential-logarithmic fitting formulas are proposed according to the numerical results. At the same time, the evolution of the configuration and the displacement residual field of the mesoscopic numerical samples in the loading process are studied.
【學(xué)位授予單位】：武漢大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：O347.7;TU4

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本文編號(hào)：2199361