SONG Lai-zhong, LI Yao-hui. Numerical Simulation of the Geometric Models for Particle-Reinforced Composite Materials[J]. Applied Mathematics and Mechanics, 2015, 36(2): 220-232. doi: 10.3879/j.issn.1000-0887.2015.02.011
Citation: SONG Lai-zhong, LI Yao-hui. Numerical Simulation of the Geometric Models for Particle-Reinforced Composite Materials[J]. Applied Mathematics and Mechanics, 2015, 36(2): 220-232. doi: 10.3879/j.issn.1000-0887.2015.02.011

Numerical Simulation of the Geometric Models for Particle-Reinforced Composite Materials

doi: 10.3879/j.issn.1000-0887.2015.02.011
Funds:  The National Natural Science Foundation of China(General Program)(11171181)
  • Received Date: 2014-08-12
  • Rev Recd Date: 2014-11-10
  • Publish Date: 2015-02-15
  • To simulate the meso-level structures of multiphase particle-reinforced composite materials, such as concrete and soil-rock mixture, the corresponding reinforcing particles were assumed as convex polyhedrons. Firstly, the method was developed for obtaining an arbitrary polyhedron as well as its parametric equation through transformation of a randomly chosen octahedron. Secondly, the conditions for determining whether a spatial point is in the interior or exterior of a given convex polyhedron were presented. Moreover, the procedure for calculating the distance between a spatial point and a convex polyhedron or the distance between 2 polyhedrons was established, based on which the algorithm to generate a region with abundant randomly distributed convex polyhedrons was proposed. In order to increase the content of the polyhedrons in the region to be simulated, the descent algorithm was presented. The numerical results show that, for the 2-graded distribution, the content of the generated polyhedrons in the simulated region reaches 35% (volume ratio), with higher content realizable through combination of this method and those previously published. The work provides an effective way to build realistic meso-level geometric models for particle-reinforced composite materials.
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