Abstract: Finite element methods are unsuitable for a dispersed system. Particle methods suitable for a dispersed system are limited in their particle shapes of only spheres that require many particles to model a complicated shape especially in 3D. Proposed procedures for a particle method are roughly as follows. 1): Judging the existence of the contact between particles as that between mathematically-smooth closed surfaces representing particle shape and size. 2): Assuming an imaginary contact point and an imaginary contact plane the same as when both closed surfaces are reduced with the same scale to touch at one point. 3): Calculating imaginary contact area and imaginary contact stiffness using the above point and plane. Based on these procedures, particle shapes are not limited but smooth. Therefore, a more complicated shaped problem in a dispersed system can be analyzed with a smaller number of particles. Additionally, combined use with finite elements enlarges usability.

Abstract: Finite element methods are unsuitable for a dispersed system. Particle methods suitable for a dispersed system are limited in the particle shapes only a sphere that requires many particles to model a complicated shape especially in 3D. Proposed procedures for a particle method are roughly as follows. 1): Judging the existence of the contact between particles as that between mathematically-smooth closed surfaces representing particle shape and size. 2): Assuming an imaginary contact point and an imaginary contact plane the same as when both closed surfaces are reduced with the same scale to touch at one point. 3): Calculating imaginary contact area and imaginary contact stiffness etc. using the above point and plane. Based on these procedures, particle shapes are not limited but smooth. Therefore, a more complicated shaped problem in a dispersed system can be analyzed with less number of particles. Additionally, combined use with finite elements is capable.