Overcoming volumetric locking in stable node-based smoothed particle finite element method with cubic bubble function and selective integration

Wang, Ze-Yu1,2,3; Jin, Yin-Fu1; Yin, Zhen-Yu2; Wang, Yu-Ze3

2022-09-01

10.1002/nme.7107

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING   Impact Factor & Quartile

0029-5981

1097-0207

The stable node-based smoothed particle finite element method (SNS-PFEM) reduces spatial numerical oscillation from direct nodal integration in NS-PFEM but leads to a severe volumetric locking effect when modeling nearly incompressible materials-related boundary value problems. This study proposes an improved locking-free SNS-PFEM to investigate the performance of the bubble function and selective integration scheme in circumventing volumetric locking. Three locking-free variants of SNS-PFEM: (1) SNS-PFEM with a cubic bubble function (bSNS-PFEM), (2) SNS-PFEM with a selective integration scheme (selective SNS-PFEM), and (3) SNS-PFEM with a cubic bubble function and selective integration scheme (selective bSNS-PFEM)-were gradually developed for comparison. The performance of these three approaches was first successively examined using two examples with elastic materials, that is, an infinite plate with a circular hole and Cook's membrane. The comparisons show that the cubic bubble function and selective integration scheme are both necessary as a locking-free approach for modeling nearly incompressible materials, and the proposed selective bSNS-PFEM performs best among the three variants in terms of accuracy and convergence. Two examples of slope stability analysis and footing penetration on elastoplastic materials were then conducted by SNS-PFEM and the proposed selective bSNS-PFEM. The results indicate that the proposed selective bSNS-PFEM is stable and accurate, even when accompanied by significant deformation. All obtained results indicate that the locking-free selective bSNS-PFEM is a powerful approach for modeling nearly incompressible materials with both material and geometric nonlinearity.

bubble function NS-PFEM selective integration scheme stable nodal integration volumetric locking

SCI ; EI

English

Others

Research Grants Council (RGC) of Hong Kong Special Administrative Region Government (HKSARG) of China[R5037-18F] ; Project of Research Institute of Land and Space[CD78] ; Hong Kong Polytechnic University Strategic Importance Fund[ZE2T]

Engineering ; Mathematics

Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications

WOS:000850125700001

WILEY

20223712727082

Elastoplasticity ; Finite element method ; Integral equations ; Integration ; Locks (fasteners) ; Numerical methods ; Slope stability

Roads and Streets:406.2 ; Calculus:921.2 ; Numerical Methods:921.6

ENGINEERING

Web of Science

1.Shenzhen Univ, Coll Civil & Transportat Engn, Shenzhen 518060, Guangdong, Peoples R China
2.Hong Kong Polytech Univ, Dept Civil & Environm Engn, Kowloon, Peoples R China
3.Southern Univ Sci & Technol, Dept Ocean Sci & Engn, Shenzhen, Peoples R China

Wang, Ze-Yu,Jin, Yin-Fu,Yin, Zhen-Yu,et al. Overcoming volumetric locking in stable node-based smoothed particle finite element method with cubic bubble function and selective integration[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING,2022.

Wang, Ze-Yu,Jin, Yin-Fu,Yin, Zhen-Yu,&Wang, Yu-Ze.(2022).Overcoming volumetric locking in stable node-based smoothed particle finite element method with cubic bubble function and selective integration.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING.

Wang, Ze-Yu,et al."Overcoming volumetric locking in stable node-based smoothed particle finite element method with cubic bubble function and selective integration".INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2022).