Research On Geometric Modeling And Simulation For Semi-regular Porous Structures

Porous models widely exist in nature including bones, plant stems and so on. These models, formed via a nature evolution process for millions of year, exhibit exceptional physical properties at light weight, and have wide industrial application prospects. The fast development of addictive manufacturing (3D printing), also makes accurate manufacturing of such complex model possible.We propose here a concept of novel semi-regular porous models, which have similar microstructure geometries, and also follow a certain distributions at macro scale. These nice properties provide possibility to optimize their geometric modeling and property simulation. This research studies the geometric modeling and control, fast simulation for semi-order porous models, and also implemented a prototyping system for it. It hopes to compensate the limitations of conventional modeling and simulation approaches, and contributes to the researches and applications in related fields.The main contributions of this paper include:1、A bi-scale porous structure modeling method is first proposed that both can control the microstructures’ geometry and their overall distributions, realizing the geometric coupling between the micro- and macro- scales. The macrostructure of porous unit is controlled by the distribution of hexahedron mesh units, and the geometrical design and control of the microstructure is determinate by a porous unit modeling method. It is the first systematic study on this topic.2、Three different microstructure modeling approaches are proposed to meet different design requirements:polygon surface mesh, triple periodic minimal surface (implicit surface) and parametric surface defined by super-formulas. The mapping relationship between standard hexahedron unit and general hexahedron units is also obtained via an interpolation approach, and the deformation of macro structure is controlled by radial basis function interpolation when the outer shape is deformed under use specification.3、Based on the fact that the microstructures have similar geometries, a homogenization simulation method is introduced here for rapid simulation of porous structures, and avoids the expensive computation using traditional FEM.4、A modeling and simulation prototyping system for the semi-regular porous structures is implemented, providing functions of geometric modeling, editing and simulations. Built on the system, we also test relationship between micro-structure and macro-property. The system lays a good foundation for future researches on this topic.