Low-resolution spherical harmonics models in application to quasi-quadric particle shapes

Abstract

In this paper a numerical analysis was performed developing low-resolution spherical harmonics (LRSH) models in order to describe particle shapes. The potential of LRSH, limited by the expansion degree L ≤ 3, to describe quasi-regular particle shapes was explored. The term “quasi” is used hereafter to indicate the monomeric, almost regular shaped, particle described by a single continuous function. This approach reflects the shape of a major part of soil minerals. It was shown, that even the simplest case of the suggested low-resolution harmonics technique with L = 1 showed sufficient accuracy. The main drawback of the suggested approach was that the low-resolution harmonics yield particle shapes with nearly sharp angles, there-fore, enhanced analysis of local surface curvatures becomes necessary. An application using quasi-ellipsoidal particles is enclosed.

Keywords:

• soil
• particle
• quasi-quadric shape
• spherical harmonics
• curvature
• contact

Additional information

Notes on contributors

Urtė Radvilaitė

Urtė RADVILAITĖ. PhD student at the Department of Strength of Materials and Engineering Mechanics, Vilnius Gediminas Technical University, Lithuania. Research interests: spherical harmonics, granular materials, mathematical modelling.

Álvaro Ramírez-Gómez

Álvaro RAMÍREZ-GÓMEZ. Assoc. Prof. Dr Department of Mechanical, Chemical and Industrial Design Engineering, Technical University of Madrid, Spain. Research interests: Discrete element method, particle shape models, particle flow experiments, modelling of silo.

Arūnas Jaras

Arūnas JARAS. Assoc. Prof. Dr Department of Strength of Materials and Engineering Mechanics, Vilnius Gediminas Technical University, Lithuania. Research interests: Finite element analysis, investigation of buildings of cultural heritage.

Rimantas Kačianauskas

Rimantas KAČIANAUSKAS. Prof. Dr Habil. Institute of Mechanics, Vilnius Gediminas Technical University, Lithuania. Research interests: Computational mechanics, modelling of structures and materials, fracture mechanics, coupled problems, finite element method, discrete element method.

Dainius Rusakevičius

Dainius RUSAKEVIČIUS. Assoc. Prof. Dr Department of Strength of Materials and Engineering Mechanics, Vilnius Gediminas Technical University, Lithuania. Research interests: Computational mechanics, finite element method, optimization methods.