Abstract The Particle Finite Element Method (PFEM) is employed for the simulations of boundary value problems involving large deformations with evolving boundaries and contact interactions. Its accuracy, however, can be compromised by remeshing-induced errors and volumetric locking due to materially incompressibility. This study evaluates the use of quadratically interpolated displacement-based elements in PFEM simulations, comparing them to linearly interpolated stabilised mixed elements, with focus on state variable mapping during remeshing. Several mapping strategies are systematically assessed. Benchmark results show that quadratically interpolated elements suppress volumetric locking without stabilisation and minimal mapping-induced errors, even for coarse meshes and frequent remeshing. Especially for linearly interpolated elements, advanced mapping methods such as the use of Radial Basis Functions (RBF) minimise mapping-induced errors. Robustness of the implementations are demonstrated by application to geotechnical problems, including the penetration of a rigid strip footing and cone penetration tests. The findings demonstrate that quadratically interpolated displacement-based elements provide a reliable, accurate, and computationally efficient choice for PFEM simulations in geotechnical engineering.
Bettmann et al. (Fri,) studied this question.