基于Cosserat连续体平均场理论的颗粒材料多尺度计算均匀化

The macroscopic responses of granular materials (such as rock, sand and soil) are closely related to their microscopic structures. The failure behavior of granular materials is characterized by the multi-scale essential. For example, the width of shear bands in large-scale geo-structures is the function of the typical granular size. Hence, this project is focused on the development of micro-macro modeling method for granular materials on the basis of the average-field theory. The discrete element model (and corresponding discrete element method, DEM) and Cosserat continuum model (and corresponding finite element method, FEM) are respectively adopted on the microscopic and macroscopic scales. Hill's lemma for the average-field theory of heterogeneous Cosserat continuum is derived, with which proper boundary conditions for the representative volume element (RVE) are prescribed to satisfy both the micro-macro energy equivalence condition and the basic assumptions of the average-field theory. The micro discrete particle assembly- macro Cosserat continuum two-scale computational homogenization scheme is established, including: the derivation and transformation of stiffness matrix for microscopic discrete particle assembly, the prescription of RVE boundary conditions, the derivation of rate expressions for macro quantities and their consistent tangential modulus etc. With the above study, a set of micro-macro modeling method and simulation tools will be systematically established and applied to the understanding and analysis on the mechanism of the progressive failure behavior for typical geo-materials.

岩石、砂、土等颗粒类工程材料的宏观响应与其微结构密切相关，其破坏形式往往表现出跨尺度特征，如：大型土工结构物中出现的剪切带宽度是颗粒尺寸的函数。本项目以砂土等地质材料为工程背景，基于Cosserat连续体平均场理论，发展颗粒材料的细-宏观多尺度模拟方法。细、宏观尺度上分别采用离散颗粒模型（和离散元法）与Cosserat连续体模型（和有限元法）。在已有工作基础上，深入推导和发展非均质Cosserat连续体平均场理论的Hill定理，并据此给出完备的表征元边界条件，以满足细-宏观信息传递的能量等价条件及相应的平均场理论基本假定。发展和完善细观离散颗粒集合-宏观Cosserat连续体的两尺度计算均匀化模型，系统地建立一套针对颗粒材料的细-宏观多尺度计算均匀化分析方法和计算工具，并将其应用于地质体渐进破坏过程的内在机理的分析。

砂、土等颗粒类材料的宏观响应与其微结构密切相关，其破坏形式往往表现出跨尺度的特征，并且转角自由度以及偶应力相关量对其细宏观破坏行为有着重要的影响。本项目深入研究了非均质Cosserat连续体平均场理论，推导了不同版本的Hill定理，并据此给定了多种形式的表征元边界条件，使得不同尺度间信息传递既能满足细宏观能量等价条件，也不违背平均场理论的基本假定。在此基础上，发展和完善了“离散颗粒集合-Cosserat连续体模型”多尺度计算均匀化方案和计算工具，建立了转角和偶应力相关量的细宏观联系，并将多尺度分析方法拓展和应用于格栅材料的均匀化等领域。