Porous structure modeling with computers

Abstract

Porous structures are a particular type of solids, where a large number of pores exist in the geometric domain of interest. Research on porous structures have received increasingly keen interest in recent years and this is largely because of many unique and superior properties that porous structures possess. They can undertake special tasks which general solid materials are not competent to do.

In recent twenty years numerous representations are put forward for porous structure modeling. But the challenges in practical porous structure design still exist and the structure heterogeneity brings many difficulties. This thesis is motivated to propose new porous structure modeling strategies which are more accurate, flexible and easy for porous structure description.

An approach of porous structure modeling based on quadtree/octree and NURBS is proposed first. Quadtree and octree are tools for modeling domain partition. The pore size and pore distribution are controlled by the flexibility of quadtree and octree enumeration technique. Derived polygon and polyhedron are then introduced to assist the generation of NURBS curves and surfaces. These NURBS curves and surfaces form the boundaries of the porous structures.

However there are limitations of the above method. The accurate control of porosity is not easily achieved in 3D porous structure modeling and seemingly adopting quadtree/octree for the modeling domain partition is also less than satisfactory. Hence a new representation for porous structures based on Centroidal Voronoi tessellation (CVT) and pore-network is put forward. CVT is utilized for modeling domain partition because the CVT cells are approximate hexagons which is widely existent in plants, animals and other cellular structures in nature. The density distribution function used in CVT generation also helps to build functionally graded porous structures. Pore-network, which is a mature and commonly used model in the research of multiphase flow in porous media, is subsequently introduced to build the porous structures. This modeling approach results in porous structures that could mimic the geometry and performance of structures in nature.

To evaluate the object’s properties, finite element analysis (FEA) is conducted on the porous structure models represented by the two methods. The mechanics properties of the two types of models are analyzed. The stress-strain curve of each sample is plotted and the effective Young’s modulus is calculated. Comparison of these two types of models is also done. Besides, the contributions of the thesis and suggestions for future research are also discussed.