Finite Element Analysis of the Stacked Structure of Soft Spherical Shells Under Gravity

doi:10.19596/j.cnki.1001-246x.8578

Abstract

Abstract:

Based on the finite element method of structural mechanics, the two-dimensional stacking structure of soft spherical shells under gravity is studied by using the area of soft spheres and the distribution of the number of adjacent spheres, and the filling rate and potential energy of the stacking structure are analyzed. The results show that the soft spherical shell stacking process is disordered and has no orientation preference. There are different types of stacking structures, and different types correspond to different areas and distributions of adjacent spheres, which exhibit polydispersity characteristics. The area change rate of the stacking structure is positively correlated with the potential energy of the stacking structure. The greater the area change rate results the greater the potential energy, and the potential energy of the structure type decreases with the increase of the modulus. For the stacking structures of bidisperse soft spheres with different radii, there is an approximate linear relationship between the area of the soft spheres and the number of adjacent spheres, and the more number of soft spheres with bigger radii in the structure results in the greater potential energy of the structure. This study helps to improve the understanding of the geometric and topological properties of soft matter packing structures such as cells, and provides a computational basis for the analysis of living tissues and materials with soft spherical shells.

Key words: stacked structure, soft sphere, finite element, potential energy, gravity

Xinghong MAI, Qiaoyue CHEN, Mingming DING. Finite Element Analysis of the Stacked Structure of Soft Spherical Shells Under Gravity[J]. Chinese Journal of Computational Physics, 2023, 40(3): 359-368.

Figures/Tables 17

Fig.1 Schematic diagram of soft spherical shell accumulation model under gravity field

Fig.2 Stacking structure type of 200 Pa (a) stacking structure type A; (b) stacking structure type B; (c) stacking structure type C

Fig.3 Soft sphere area distribution of the same type

Fig.4 Soft sphere area distribution of the same type

Fig.5 Potential energy of the same type of soft spherical shell stacking structure

Fig.6 Area change rate of stacking structure of the same type of soft spherical shell

Fig.7 Filling rate of the same type of soft spherical shell stacking structure

Fig.8 Relationship between potential energy and modulus of type A stacked structure

Fig.9 Relationship between area change rate and modulus of type A stacked structure

Fig.10 Relationship between filling rate and modulus of type A stacked structure

Fig.11 Relationship between the potential energy of double dispersed soft spherical shell stacking structure and the proportion of big and small spheres

Fig.12 Relationship between the area change rate of double dispersed soft spherical shell stacking structure and the proportion of big and small spheres

Fig.13 Area distribution of double dispersed soft spherical shell stacking structure

Fig.14 Adjacent sphere number distribution of double dispersed soft spherical shell stacking structure

Fig.15 Potential energy diagram of double dispersed soft spherical shell stacking structure

Fig.16 Filling rate of double dispersed soft spherical shell stacking structure

Fig.17 The relationship between the average area of soft balls and the number of adjacent balls

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