Particle Mechanics and Micropolar Continua

工程问题通常在宏观尺度上以柯西连续统为基础进行描述。然而，如果发生剪切带等微观结构过程，这些过程可能会控制宏观行为，因此必须考虑扩展连续统模型。为了捕获宏观尺度上的微观响应，该建议涉及具有独特微观结构的连续体的研究，该连续体被假设由由平移和旋转自由度控制的刚性颗粒组成的颗粒物质。在微观结构的代表性基本体积（REV）上应用基于颗粒中心的均质化可以产生宏观应力和应变。该过程还揭示了非对称应力和耦合应力的存在，例如，在剪切区，尽管材料没有被力偶加载。显然，我们得出结论，这种微观结构行为只能通过微极性方法来扩展连续统理论来捕获。该项目的目标是多方面的。一方面，内部有限元模拟工具PANDAS的能力将从二维（2-d）扩展到全三维（3-d）计算具有弹塑性材料特性的微极材料的初边值问题（IBVP）。另一方面，将基于具有弹塑性接触力的球形和椭球形粒子的仿真工具PASIMODO建立粒子力学。这两种方法都将根据对霍斯顿和卡尔斯鲁厄沙子以及冷箱沙子的实验室测试进行校准。Hostun砂的原料数据来自Grenoble的3SR实验室，Karlsruhe砂的数据来自我们的实验室，而cold-box砂的实验数据将由Mahnken教授（Paderborn）提供。此外，我们打算将整个校准过程分为两个基本步骤，分别处理均匀和非均匀实验，后者采取直到剪切区出现。从该程序在连续尺度上的首次试验中，我们期望通过反分析方法从均匀试验中找到标准材料参数，从非均匀试验中找到微极性参数。此外，由于粒子系综的形状、大小和分散性对力学行为有至关重要的影响，预计粒子模型只能通过反分析方法进行完全校准。校正后，我们期望粒子模型一方面可以代替连续介质模型。另一方面，可以定义一个重叠区域，其中粒子和连续体模型同时存在，并且连续体模型的信息可以传递到粒子模型中，使得粒子模型在连续体方法中充当嵌套的微观结构。

Engineering problems are usually described at the macroscopic scale on the basis of a Cauchy continuum. However, if microstructural processes like shear banding occur, these processes might govern the macroscopic behaviour such that extended continuum models have to be considered.To capture the microscopic response on the macroscale, the proposal concerns the investigation of continua with a distinct microstructure, which is assumed to consist of granular matter of rigid particles governed by translational and rotational degrees of freedom. Applying a particle-centre-based homogenisation over Representative Elementary Volumes (REV) of the microstructure yields macroscopic stresses and strains. This procedure also reveals the existence of non-symmetric stresses and couple stresses, for example, in shear zones, although the material has not been loaded by force couples. Obviously, it is concluded that this kind of microstructural behaviour can only be captured by an extension of the continuum theory by a micropolar approach.The goal of the project is manifold. One the one hand, the capabilities of the in-house finite-element simulation tool PANDAS will be extended from two-dimensional (2-d) to fully three-dimensional (3-d) computations of initial-boundary-value problems (IBVP) of micropolar material with elasto-plastic material properties. On the other hand, particle mechanics will be set up on the basis of the simulation tool PASIMODO based on spherically and ellipsoidally shaped particles with elasto-plastic contact forces. Both approaches will be calibrated on the basis of laboratory tests on Hostun and Karlsruhe sand as well as cold-box sand. The raw material data of Hostun sand stems from the laboratoire 3SR in Grenoble and the data for Karlsruhe sand is taken in our laboratory, while experimental data for cold-box sand will be provided by Prof. Mahnken (Paderborn).We furthermore intend to split the overall calibration procedure in two basic steps addressing homogeneous and inhomogeneous experiments, the latter taken until a shearing zone occurs. From first tests of this procedure on the continuum scale, we expect to find the standard material parameters from homogeneous and the micropolar parameters from inhomogeneous tests by the methods of back analysis. It is furthermore expected that the particle model can only be fully calibrated by the methods of back analysis, since the shape, the size and the dispersity of the particle ensemble has a crucial influence on the mechanical behaviour.After calibration, we expect that the particle model can be used, on the one hand, as a substitute for the continuum model. On the other hand, one can define an overlapping area where the particle and the continuum model exist at the same time and where information of the continuum model can be transferred to the particle model such that the particle model acts as a nested microstructure within the continuum approach.