Particle Manifold Method (PMM) for Multiscale Continuous-Discontinuous Analysis

It is important to consider the microstructure of a material when studying the macroscopic mechanical properties. Although special equipments have been used for micromechanics study through experimental tests, it is limited by instruments and reproducibility. In contrast, numerical methods have advantages on modelling of different scales, both in space and time. The efficiency, economy, reproducibility and flexibility make numerical modelling very convenient to perform micromechanics study. Current numerical methods used in micromechanics can be grouped into continuous methods, discontinuous methods and coupled methods. Continuous methods are good at the stress analysis in the pre-failure stage while the discontinuous methods are good at the motion analysis in the post-failure stage. Combining continuous and discontinuous methods, coupled methods are developed to deal with problems with different features, e.g., multiscale analysis. The numerical manifold method (NMM) is one of the coupled methods which can provide a uniform framework for continuous-discontinuous analysis. In NMM, the mathematical interpolation and the physical integration are separated. The distinct cover system makes NMM very suitable for large deformation analysis considering both continuous and discontinuous behaviors. However, NMM is still a polyhedron-based numerical method. The geometrical operations (topology and contact detection) are the obstacle especially in 3D. Inspired by micro-based numerical methods, the particle manifold method (PMM) is developed as an extension of NMM. PMM uses a mathematical cover system to describe the motion and deformation of a particle-based physical domain. By introducing the concept of particle into NMM, PMM takes the advantages of easy topological and contact operations with particles. Furthermore, the particle representation is much more suitable for micromechanics study. In this thesis, the methodology, formulations and implementation of the method are presented. After establishment of theoretical basement and validation of numerical implementation, four aspects of PMM are further developed. The first aspect of PMM is the particle contact model and its applications. As an important discontinuous feature, the contact problem in PMM is explicitly described by the particle-particle (P-P) model. The P-P model is very simple to implement through the concept of the penalty method. Different constitutive laws can be introduced using the penalty number, which is the only artificial parameter. The P-P model also simplifies the geometrical operation and the description of rough surface. With the P-P model, PMM is used to model P-wave transmission across rock fractures with different properties. Through the comparisons with theoretical solutions, PMM is validated for the modelling of wave transmission across both continuous and discontinuous rock fractures. The second aspect of PMM is the micro failure model and its applications. The failure and