2008-08-012024-05-18https://scholars.lib.ntu.edu.tw/handle/123456789/711829摘要：顆粒材料為宏觀粒子之群聚。由於不連續的顆粒描述方法需要大量之計算，且需要採取適當之平均而得到整體宏觀物理量之描述，因此連續體描述法乃為另一有效之分析工具。然而傳統的連續體力學無法提供顆粒材料內部描述複雜顆粒群運動的訊息，因此本研究之目的是針對此單一組成、單相分散之乾性顆粒材料之行為進行下列兩個課題的探討--顆粒材料如何在連續體的架構下進行描述以及顆粒材料之振動床實驗。 本研究將採取不同於其他研究學者之方法，我們由基礎之微連續體的定義著手，擴展Eringen的思維，將微形連續場依據旋轉、剪切與膨脹三大類進行分解，進而簡化微連續體成七種模型。我們相信其中的微膨脹連續體模型將可對應於顆粒材料的Goodman-Cowin理論，而其他類型之模型亦要深入討論，其相關之熱力學分析亦為探討之課題。此外，顆粒床振動實驗中，我們要進行顆粒追隨現象的深入探討，其中探討不同種類之顆粒、準二維或三維條件之檢驗、三種大小不同顆粒之課題為本研究之重點。除以上理論與實驗分析外，我們將要使用分子動力學的方法，對於顆粒進行牛頓運動學的數值模擬。 <br> Abstract: A granular material is a set of macroscopic particles. The discrete method requires a vast amount of numerical calculations and an appropriate averaging mean to find macroscopic physical quantities. On the contrary, the continuum method is an alternative, which provides an effective tool to analyze the motion of granular media. However, the traditional continuum mechanics is not sufficient to provide the detailed description of internal structure, characterizing the intricate relative motion among particles. This project focuses on the two important issues – the discussion of behavior of granular materials under the framework of continuum mechanics and the experimental work on the vibrating bed. We start from the microcontinuum field theory of Eringen and decompose a microcontinuum into seven continua according to the three-types of deformation — rotational, shearing, and dilatancy motions. It is believed that the micro-dilatation continuum model should be corresponding to the Goodman-Cowin theory. The thermodynamics analyses of these seven models will be thoroughly discussed. In addition, we will study the granular follower, specially on the topics of different types of particle, quasi-2d or 3D conditions, and tri-disperse particles condition. Accompanying with the theoretical and experimental analyses, the numerical approach of molecular dynamics will be performed to confirm the validity of our theory.顆粒材料微連續體混合體顆粒振盪Granular materialsMicrocontinuumMixtureGranular oscillation