Experimental and Theoretical Investigation of Deformation in Granular Materials: A Micromechanics Approach

在野外和实验室中，土壤的变形通常集中在应变局部化过程中形成的剪切带中。虽然这一机制得到了工程师和研究人员的广泛认可，但它仍然难以建模、预测和分析。主要的困难可以归因于这样一个事实，即经典的连续介质力学模型不包括微观结构长度尺度，可以预测不稳定的开始，但它们不能预测剪切带的大小和演变。特别是，经典的塑性理论在后分叉状态下瓦解。本研究的主要目的是建立一个基于微观结构的连续体模型来研究颗粒材料的变形和局部化。该模型基于晶体塑性，但包含两个微观结构长度尺度；一个与塑性曲率（取向重分布）有关，另一个与孔隙率重分布有关，两者都可以通过实验直接量化。该研究的独特之处在于微观结构模型参数是直接从测量中确定的。颗粒状试样通过树脂浸渍硬化，并通过无创x射线计算机断层扫描捕获其微观结构。在剪切变形的各个阶段监测了微观结构模型参数的演变。该模型将被实现为三维有限元代码，并用于识别边值问题中的变形模式、软化和不稳定（剪切带和液化）。实验和分析程序将导致更好地理解分叉和局部化现象，以及分析应变局部化的分析方法，不仅在实验室样品，而且在实际的岩土工程边值问题。这项工作的结果也将对其他类型的材料（如金属和复合材料）的建模产生影响，这些材料表现出变形不稳定性和剪切带。

The deformation of soils in the field and laboratory are commonly observed to concentrate into shear bands formed during strain localization. While this mechanism is widely appreciated by engineers and researchers, it remains difficult to model, predict and analyze. The main difficulty can be attributed to the fact that while classical continuum mechanics models that do not include microstructure length scales can predict the onset of instability, they cannot predict the size and evolution of the shear bands. In particular, the classical theories of plasticity break down in the post-bifurcation regime. The main objective of this study is to develop a microstructure based continuum model to study deformation and localization in granular materials. The model is based on crystal plasticity but includes two microstructure length scales; one associated with the plastic curvature (orientation re-distribution) and the other related to the porosity re-distribution, both of which can be directly quantified by experiments. The study is unique in that the microstructure model parameters are determined directly from measurements. Granular specimens are hardened by impregnation with resin and their microstructure captured by means of non-invasive x-ray computer tomography. Evolution of the microstructure model parameters is monitored at various stages of shear deformation. The model will be implemented into a 3-D finite element code and used to identify deformation patterning, softening, and instabilities (shear banding and liquefaction) in boundary value problems.The experimental and analytical program will lead to a better understanding of the phenomenon of bifurcation and localization and to analytical methods for analyzing strain localization not only in laboratory specimens, but also in practical boundary value problems in geotechnical engineering. The outcome of this work would also have implications to the modeling of other type of materials such as metals and composites that exhibit deformation instabilities and shear banding.