Investigation of Solution Accuracy in PFEM Simulations Using Benchmark Problems

ABSTRACT The simulation of large topological changes, such as those occurring in Cone Penetration Testing (CPT) and vibratory pile driving, remains a major challenge in computational geomechanics. Excessive mesh distortions render classical approaches like the Finite Element Method (FEM) unsuitable, emphasizing the need for alternative methodologies. The Particle Finite Element Method (PFEM) combines standard FEM with continuous remeshing techniques, offering a robust framework specifically designed for simulating large topological changes. However, the remeshing process, combined with the mapping of state variables from integration points to nodes, can cause changes in these variables, potentially violating admissible states in constitutive models and compromising the accuracy and stability of the simulation. This study investigates static and dynamic benchmark simulations, such as one‐dimensional consolidation and wave propagation as well as a Hertzian contact problem, to evaluate the influence of such mapping‐induced variations on the accuracy and reliability of PFEM‐based solutions. The results provide insights into the application of PFEM to more complex boundary value problems, particularly those involving advanced constitutive models, such as hypoplasticity with intergranular strain extension or Sanisand, which are highly sensitive to changes in their state variables.