Micromechanical analysis of state variables for phenomenological constitutive models of soils

为了描述土体中发生在宏观尺度上的某些现象，例如由于荷载反转引起的刚度突变，本构模型使用了唯象状态变量(例如弹塑性中的背应力或亚塑性中的晶间应变概念)，这些变量往往缺乏明确的物理意义。必须在颗粒尺度上寻找控制宏观行为的机制，并因此在连续介质尺度上观察到不同的现象，其中单个粒子的相互作用起关键作用。X射线计算机断层成像(CT)允许在各种加载条件下对自然土壤样本进行3D成像，因此，现在和将来都将成为该项目中使用的工具。为了提取关于颗粒材料结构的信息，可以使用不同的图像分析方法，并且应该针对有限的分辨率来评估其准确性。在当前运行的项目的第一部分中，评估了从3D图像中提取织物描述符的不同方法的能力和准确性，即在这种情况下基于粒子和接触的实体，并提出并验证了改进措施。来自X射线纳米CT的人工和高分辨率图像是这一分析的基础，这表明在任何商业软件中实现的标准方法精度都很低，而且往往会引入巨大的伪影。此外，在运行项目中，还在天然砂土上进行了X射线CT扫描仪的真实力学实验。后续项目的主要重点是开发所获得的实验数据库。为此，将在加载的不同步骤从3D图像中提取各个织物实体，并使用织物张量来捕获。然后，使用不同的变量和不同的阶数来定义不同的组构张量的演变，并将其与宏观应力和应变的演变联系起来。微观结构的演化可以与唯象变量的演化联系在一起，例如，加载方向的变化导致亚塑性的晶间应变，从而可能导致这些概念的微观力学增强。建立微观力学变量之间的联系，如描述结构的组构张量，和宏观力学观察之间的联系，不仅可以增强我们对连续统尺度上发生的不同现象的理解，而且能够以更直接和可靠的方式将这些效应纳入现象学方法。在对天然颗粒高分辨率图像的研究中发现，天然颗粒形状的分形性使得颗粒间接触的几何定义变得非常复杂。该项目的一部分将与Syndey大学合作，调查接触比例的影响。

In order to describe some of the phenomena in soils occurring on the macroscopic scale, e.g. an abrupt change of stiffness due to a load reversal, constitutive models use phenomenological state variables (e.g. back stress in elasto-plasticity or the intergranular strain concept for hypoplasticity) which often lack a clear physical meaning. The mechanisms that control the macroscopic behaviour and, as such, different phenomena, that can be observed on the continuum scale, must be sought at the grain-scale with the interactions of individual particles playing the key-role. X-Ray-computed tomography (CT) allows for a 3D imaging of natural soil samples in various loading conditions and, thus, is and will be the tool used in this project. In order to extract information on the structure of the granular material, different image analysis approaches can be used and their accuracy should be evaluated with respect to the limited resolution. In the first part of the currently running project the ability as well as the accuracy of different approaches to extract fabric descriptors, i.e. in this case particle- and contact-based entities, from 3D images is assessed and enhancements are proposed and validated. Artificial as well as high resolution images coming from x-ray nano-CT serve as the basis of this analysis which shows that the standard approaches, implemented in any commercial software, strongly suffer in accuracy and often introduce huge artefacts. Furthermore, real mechanical experiments in the x-ray CT scanner have been carried out on natural sands in the running project. The main focus of the follow-up project is to exploit the obtained experimental database. For this purpose, the individual fabric entities will be extracted from the 3D images at different steps of the loading and captured using fabric tensors. The evolution of various fabric tensors, defined using different variables and different orders, is then assessed and linked to the evolution of the macroscopic stresses and strains. The evolution of the microstructure can be linked to the evolution of the phenomenological variables, e.g. the intergranular strain for hypoplasticity for changes in loading direction, leading to a possible micromechanical enhancement of these concepts. Establishing a link between micromechanical variables, such as the fabric tensors describing the stucture, and the macromechanical observations cannot only enhance our understanding of different phenomena occurring on the continuum scale, but also enable an incorporation of these effects into phenomenological approaches in a more straight-forward and reliable way. In the study on high-resolution images of natural grains it wasfound, that the fractality of the shape of natural grains makes a geometrical definition of inter-particle contacts highly complicated. In cooperation with University of Syndey a part of this project will investigate the influence of the scaling of the contacts.