Particle Mechanics and Micropolar Continua

• Applicant: Professor Dr.-Ing. Wolfgang Ehlers
• Subject Area: Applied Mechanics, Statics and Dynamics ; Mechanics
• Term: from 2015 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 268098820

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.

• DFG Programme: Research Grants