Mechanical behavior of functionally graded cellular materials around a circular hole.

摘要

The mechanical behavior of cellular materials under uniaxial tension with a circular hole has been investigated. Two dimensional Voronoi meshes have been employed to simulate common commercially available cellular materials like Duocel and Alporas. A combination of Matlab and Abaqus, a finite element package, have been utilized to numerically generate the meshes and simulate them under uniaxial tension. Force boundary conditions were used and all meshes were considered linear elastic.;The inspiration for this study comes from nutrient forimina found in cellular bone. These are circular and elliptical holes that allow veins to pass into the interior of the bone. Unlike what is seen from engineering materials like metal, fracture never initiates from these holes. This implies that there is no stress intensification happening around these forimina. The mechanical cause for this lack of stress riser has been investigated by other authors and is the core goal of this study.;Circular holes were found to cause an increase in axial stress in the cell sidewalls around the hole by a factor up to about 1.5. Varying the hole size showed a trend of lower stress intensification when reducing the hole size. This is opposite the effect of hole size on homogeneous continuum plates where the stress intensification increases to some maximum as the circular hole is reduced. Microstructural gradation in the form of linear and radial variation was studied as a method of reducing the intensification of stress of the cell side walls. Intuitively it was found that increasing material in the vicinity of the hole reduces the stresses experienced by the cell side walls in that area. Finally cell sidewall strut thickness distribution was iteratively optimized by giving more material to higher stressed sidewalls and removing material from lower stress ones. The result of this scheme showed a significant reduction of overall stress in the entire model.