Essentially non-hourglass SPH elastic dynamics

More than two decades ago, the numerical instabilities of particle clustering and non-physical fractures encountered in the simulations of typical elastic dynamics problems using updated Lagrangian smoothed particle hydrodynamics (ULSPH) was identified as tensile instability. Despite continuous efforts in the past, a satisfactory resolution for the simulations of these problems has remained elusive. In this paper, the concept of hourglass modes, other than tensile instability, is first explored for the discretization of shear force, arguing that the former may actually lead to the numerical instabilities in these simulations. Based on such concept, we present an essentially non-hourglass formulation by utilizing the Laplacian operator which is widely used in fluid simulations. Together with the dual-criteria time stepping, adopted into the simulation of solids for the first time to significantly enhance computational efficiency, a comprehensive set of challenging benchmark cases is used to showcase that our method achieves accurate and stable SPH elastic dynamics. © 2024 The Author(s)     «

More than two decades ago, the numerical instabilities of particle clustering and non-physical fractures encountered in the simulations of typical elastic dynamics problems using updated Lagrangian smoothed particle hydrodynamics (ULSPH) was identified as tensile instability. Despite continuous efforts in the past, a satisfactory resolution for the simulations of these problems has remained elusive. In this paper, the concept of hourglass modes, other than tensile instability, is first explored...     »

Funding text S\u00E9rgio D.N. Louren\u00E7o would like to express his gratitude to the Research Grants Council Hong Kong for their sponsorship of this research under a Collaborative Research Fund (C6006-20GF). Dong Wu, Chi Zhang and Xiangyu Hu would like to express their gratitude to the German Research Foundation (DFG) for their sponsorship of this research under grant number DFG HU1527/12-4. The computations were performed using research computing facilities offered by Information Technology Services, the University of Hong Kong.     «

Funding text S\u00E9rgio D.N. Louren\u00E7o would like to express his gratitude to the Research Grants Council Hong Kong for their sponsorship of this research under a Collaborative Research Fund (C6006-20GF). Dong Wu, Chi Zhang and Xiangyu Hu would like to express their gratitude to the German Research Foundation (DFG) for their sponsorship of this research under grant number DFG HU1527/12-4. The computations were performed using research computing facilities offered by Information Technology S...     »