Particle Mechanics and Micropolar Continua

工程问题通常在宏观尺度上用柯西连续统来描述。然而，如果微观结构的过程，如剪切带的发生，这些过程可能会支配宏观行为，使扩展的连续模型必须考虑到。为了捕捉宏观尺度上的微观响应，建议涉及的连续调查与一个独特的微观结构，这是假定由刚性颗粒的颗粒物质的平移和旋转自由度。在微观结构的代表性基本单元（REV）上应用基于颗粒中心的均匀化产生宏观应力和应变。该过程还揭示了非对称应力和力偶应力的存在，例如，在剪切区中，尽管材料没有受到力偶的加载。很明显，可以得出这样的结论，这种微观结构行为只能通过微极方法的连续介质理论的扩展来捕获。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）计算微极材料的弹塑性材料特性的初边值问题（IBVP）。另一方面，颗粒力学将建立在模拟工具PASIMODO的基础上，基于具有弹塑性接触力的球形和椭圆形颗粒。这两种方法都将根据霍斯顿和卡尔斯鲁厄砂以及冷箱砂的实验室测试进行校准。Hostun砂的原材料数据来自格勒诺布尔的3SR实验室，卡尔斯鲁厄砂的数据来自我们的实验室，而冷箱砂的实验数据将由Mahnken教授（Paderborn）提供。此外，我们打算将整个校准程序分为两个基本步骤，分别处理均匀和非均匀实验，后者直到出现剪切区。从第一次测试的过程中的连续尺度上，我们期望找到标准的材料参数从均匀和微极参数从非均匀测试的方法的反分析。此外，预计粒子模型只能通过反分析的方法完全校准，因为粒子系综的形状，尺寸和分散性对力学行为有着至关重要的影响。校准后，我们希望粒子模型可以使用，一方面，作为连续介质模型的替代品。另一方面，可以定义重叠区域，其中颗粒和连续体模型同时存在，并且其中连续体模型的信息可以被传递到颗粒模型，使得颗粒模型充当连续体方法内的嵌套微观结构。

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.