As part of a collaborative research project with the Institute for Mechanics at TU Darmstadt (Ralf Müller) and EAFIT University (Colombia, Juan M. Rodríguez), the Particle Finite Element Method (PFEM) is being implemented into the finite element program numgeo, developed at the Institute of Geotechnics (IfG). The work is carried out within the framework of the DFG project 517723402 (project page), which focuses on the development of a dynamic PFEM for geotechnical applications. The present contribution represents the first publication arising from this project.

The article systematically investigates the accuracy of PFEM simulations using selected benchmark problems. These include a hydro-mechanically coupled problem in the form of one-dimensional Terzaghi consolidation, a dynamic problem describing the propagation of a compression wave in a soil column, and a static Hertzian contact problem. Particular emphasis is placed on the influence of different mapping methods, which govern the transfer of state variables between computational meshes during remeshing.

In addition to the classical extrapolation and interpolation approach, more advanced mapping strategies are analysed, including a hybrid method, an element-wise transfer approach, and field-based methods using radial basis functions. Furthermore, an extension of PFEM from linearly to quadratically interpolated triangular elements is presented.

The results show overall good agreement with corresponding reference solutions. It is demonstrated that the accuracy of PFEM strongly depends on the choice of mapping method and element formulation. In particular, for linearly interpolated elements, the classical mapping approach leads to smoothing of, for example, stress fields and thus to a tendency towards an overly compliant material response, especially in regions with high gradients, such as contact zones (see Fig. 1).

The use of higher-order mapping methods significantly improves the accuracy and, in many cases, proves to be more efficient than pure mesh refinement. The introduction of quadratically interpolated elements further reduces mapping-induced errors and enables high solution accuracy even on relatively coarse meshes.

Overall, the results demonstrate that the PFEM implementation in numgeo is capable of accurately capturing dynamic as well as hydro-mechanically coupled problems, as well as contact problems.

Check out the full article here.