Extension of the Voronoi Diagram Algorithm to Orthotropic Space for Material Structural Design

Area of Science:

• Materials Science
• Mechanical Engineering
• Computational Design

Background:

• Additive manufacturing enables the creation of complex microarchitectures, influencing material weight and mechanical properties.
• Reconstructing complex microarchitectures presents geometric challenges.
• Voronoi cells offer a potential solution for geometry reconstruction in material design.

Purpose of the Study:

• To present an extension of the Voronoi diagram algorithm for material structural design in orthotropic space.
• To investigate the impact of varying microarchitecture parameters on structural properties.
• To analyze the stress-strain state of optimized porous structures.

Main Methods:

• Extension of the Voronoi diagram algorithm to orthotropic space.
• Utilizing inputs such as porosity, ellipticity, and ellipticity direction fields.
• Application to a beam model with fixed ends and center kinematic loading.
• Analysis of structures with 50, 75, and 100 clusters.

Main Results:

• Achieved porosity in smoothed structures ranged from 21.5% to 22.8%.
• Stiffness remained consistent between initial and smoothed structures.
• Local stress factors emerged in smoothed structures with 75 and 100 clusters.
• Maximum von Mises stress decreased by 20% under kinematic loading and increased by 20% at end faces.

Conclusions:

• The extended Voronoi algorithm facilitates the design of complex porous structures with tunable properties.
• While stiffness is maintained, localized stress concentrations require careful consideration in design.
• The method shows potential for optimizing structural performance in additive manufacturing applications.