基于Cosserat连续体模型的颗粒材料宏细观力学行为数值模拟

发布时间：2018-08-23 14:33

【摘要】：颗粒材料与人们的日常生活息息相关,广泛存在于自然界并在实际工程中被大量地应用,例如粒状药剂、砂砾、堆石料等。颗粒材料是由大量离散固体颗粒构成的,具有非常复杂的性质,其力学行为的理论研究和数值模拟受到众多学者的广泛关注。剪胀性是颗粒材料的重要宏观力学行为之一,一般通过引入剪胀角来表征其影响。在进行工程计算分析时,对剪胀角ψ一般有三种处理方式：(1)ψ=0°;(2)ψ=?μ,?μ为材料的内摩擦角；(3)0°ψ≡constφμ。以上三种处理方式都有着各自的弊端：第一种处理方式没有考虑颗粒材料的剪胀性；第二种处理方式则夸大了颗粒材料的剪胀性,并且与塑性能量耗散理论也存在一定的矛盾；第三种处理方式是前两种处理方式的折中,是一种过于依赖工程经验的方法。同时以上三种处理方式中剪胀角均为常数,这将导致剪胀会随剪切应变的增大而呈线性增加,而此与颗粒材料达到临界状态后其塑性体积不再增加的实际情况也是不相符的。本文借鉴了Houlsby提出的剪胀角相关公式,将其与Drucker-Prager准则结合并引入到了Cosserat连续体模型之中,形成了一个能考虑剪胀角演化的宏观连续体模型并运用Fortran语言独立开发了程序代码将其数值实现,最后通过数值算例对颗粒材料结构的承载力以及应变局部化现象进行了研究。同时颗粒破碎也是颗粒材料的一个重要特性,其对颗粒材料的宏观力学响应也有着影响。颗粒破碎所引起的最直观变化为颗粒粒径的改变,经典连续体模型大多无法对其加以描述,而Cosserat连续体模型中包含的特征长度参数则在一定程度上反映了细观结构内的平均颗粒粒径。本文中借鉴Hardin提出的颗粒破碎相关公式,将表征颗粒材料破碎程度的相对破碎率与Cosserat连续体模型中的特征长度参数关联了起来,同时还提出了破碎应力阈值对相对破碎率的计算进行了适当修正,形成了一个能考虑颗粒破碎的宏观连续体模型并运用Fortran语言独立开发了程序代码将其数值实现,最后通过数值算例对颗粒材料结构的承载力以及应变局部化现象进行了研究。此外,颗粒材料多尺度模型的建立为颗粒材料的研究提供了一种新的途径。本文中使用了宏观Cosserat连续体模型-细观离散颗粒模型两尺度模型,该模型在宏观尺度上依赖于宏观有限元网格,能有效地解决规模较大的问题；同时在细观尺度上将颗粒材料视为离散颗粒集合体,以便于更真实地描述颗粒材料的离散特性。此种方法是由计算均匀化理论发展而来,其核心为基于表征元的宏细观信息的传递,而细观数值样本尺寸的选取合适与否则关系到细观数值样本是否能被视作为表征元。本文基于Miehe提出的宏细观信息的传递格式详细研究了细观数值样本尺寸对颗粒材料结构的宏观刚度、极限承载力以及残余承载力产生的影响,并根据数值分析结果提出了相应的指数-对数型拟合公式以便于确定合适的细观数值样本尺寸,同时还研究了加载过程中细观尺度上细观数值样本构形及位移残差场的演化。
[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.
【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：O347.7;TU4

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