While the Finite Element Method (FEM) has proven efficient for simulating various civil engineering problems, its results are usually limited to small deformation problems. Alternatives for modelling large deformations exist in different forms, with the most common being remeshing techniques and coupling between particle methods and finite element methods. Particle methods allow for both small and large deformations; in particular, the Material Point Method (MPM) shares similarities with FEM. In soil mechanics, large deformations often found after material failure, leading to a complex material response that is difficult to capture with conventional FEM alone. Typical examples include the deformations of soil during landslides and other mass movements, as well as those encountered with soil penetration during testing or sampling, pile driving, and deep compaction; among others. Accurate numerical models for such scenarios demand methods capable of tracking both small and large deformations during and after failure. Both a finite element program (numgeo) and an MPM program have been developed at the Chair of Geotechnics at Bauhaus-Universität Weimar. The aim of this project is to combine both methods into a standalone implementation based on the numgeo framework. The conceptual part of the theoretical coupling between methods has been developed by the supervisors using isogeometric formulations. This concept has been validated in Python and it needs to be effectively implemented into the numgeo framework using modern Fortran. The objectives of the project are: 1) The efficient implementation of isogeometric shape functions of the B-spline type within numgeo. 2) Implementing numerical integration at arbitrary material point locations within numgeo. 3) The generation of the necessary datasets to effectively and efficiently enable MPM integration for simple 1D and 2D models within numgeo. |
