Work

A generalized non-hourglass updated Lagrangian formulation for SPH solid dynamics

Year: 2025

Type: article

Abstract: Hourglass modes, characterized by zigzag particle and stress distributions, are a common numerical instability encountered when simulating solid materials with updated Lagrangian smoothed particle hydrodynamics (ULSPH). While recent solutions have effectively addressed this issue in elastic materials using an essentially non-hourglass formulation, extending these solutions to plastic materials with more complex constitutive equations has proven challenging due to the need to express shear forces in the form of a velocity Laplacian . To address this, a generalized non-hourglass formulation is proposed within the ULSPH framework, suitable for both elastic and plastic materials. Specifically, a penalty force is introduced into the momentum equation to resolve the disparity between the linearly predicted and actual velocity differences of neighboring particle pairs, thereby mitigating the hourglass issue. The stability, convergence, and accuracy of the proposed method are validated through a series of classical elastic and plastic cases, with a dual-criterion time-stepping scheme to improve computational efficiency. The results show that the present method not only matches or even surpasses the performance of the recent essentially non-hourglass formulation in elastic cases but also performs well in plastic scenarios.

Source: Computer Methods in Applied Mechanics and Engineering

DOI: 10.1016/j.cma.2025.117948

Authors: Shuaihao Zhang, Dong Wu, Sérgio D.N. Lourenço, Xiangyu Hu

Institutions: Technical University of Munich, University of Hong Kong

Language: English

Topic: Fluid Dynamics Simulations and Interactions

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,830

Funders: Deutsche Forschungsgemeinschaft, Research Grants Council, University Grants Committee, University of Hong Kong