Extension of the particle finite element method towards quadrilateral-dominated meshes for large-deformation geotechnical problems

Abstract

Particle Finite Element Method (PFEM) simulations frequently suffer from volumetric locking and remeshing-related inaccuracies when conventional first-order triangular finite elements are employed. In this contribution, a variant of the PFEM relying on quadrilateral-dominated meshes is proposed, enabling the use of reduced-integration quadrilateral elements without altering the fundamental PFEM framework.The proposed approach is examined through a set of benchmark simulations designed to provoke volumetric locking, including a Hertzian contact problem, loading of a strip footing on clay, cone penetration tests (CPT) in undrained clay, as well as the back-calculation of a calibration-chamber CPT in Toyoura sand using an advanced constitutive soil model. The performance of linearly and quadratically interpolated displacement-based elements is investigated including a systematic variation of different state-variable mapping techniques.The results demonstrate that quadrilateral-dominated meshes effectively suppress volumetric locking and yield accurate global responses. For linearly interpolated elements, the solution quality is strongly influenced by the employed mapping technique, whereas quadratically interpolated elements show robust behaviour with negligible sensitivity to mapping. The recombination approach further leads to substantial reductions in computational cost, highlighting its potential for efficient large-deformation geotechnical simulations within the PFEM framework.