
A Modified Particle Finite Element Method (PFEM) Ensuring Mass Conservation
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Originally conceived within the fluid dynamics community, the Particle Finite Element Method (PFEM) has evolved into a powerful tool for addressing complex nonlinear problems across various fields [1]. By integrating the Lagrangian finite element approach with innovative remeshing techniques, the PFEM effectively captures free-surface evolution and mitigates issues related to mesh distortion caused by large deformations. However, a challenge associated with traditional PFEM is the violation of mass conservation. This occurs when the computational domain is redefined, potentially resulting in discrepancies in the volume of the reconstructed domain, which can lead to unphysical mass conservation violations. In this study, we introduce a modified PFEM that incorporates the concept of material points into the version of a nodal integration based PFEM [2]. This enhancement ensures that mass conservation is consistently upheld. We have developed both explicit and implicit formulations of this improved PFEM, which have been tested on a variety of solid and fluid mechanics problems. The results demonstrate the robustness and efficiency of our approach, highlighting its potential for broader applications. REFERENCES [1] M. Cremonesi, A. Franci, S. Idelsohn, and E. Oñate, A state of the art review of the particle finite element method (PFEM). Archives of Computational Methods in Engineering, 27(5): p. 1709-1735, (2020). [2] Y. Zhang, X. Zhang, H. Nguyen, X. Li, and L. Wang, An implicit 3D nodal integration based PFEM (N-PFEM) of natural temporal stability for dynamic analysis of granular flow and landslide problems. Computers and Geotechnics, 159: p. 105434, (2023).