Fractal Geometries Design for Three-dimensional Printing: Analysis of Performance and Vibration Response for Product Design

Additive Manufacturing (AM) has enhanced the development of complex designs and geometries that are difficult or impossible to achieve with conventional manufacturing methods. Therefore, research focused on the analysis of the functional properties related to the behavior conferred by the filling material and the internal structure became especially relevant. In this sense, fractal geometry is one of the most established theories to characterize complex geometries based on repetitive self-similar patterns that allow complex shapes to be described and relate them to mechanical, rheological and morphological properties. The design of fractal microstructures promises the development of advanced materials with improved mechanical properties and multiple functions related to vibration absorption, weight reduction, among others. In relation to the compatibility of elastic materials with three-dimensional printing processes, the study of fractal geometries in terms of geometric design and its correlation with improved mechanical behavior is established as an objective. Several TPU-based fractal samples were designed and tested using compression processes to characterize the behavior of elastic fractal geometries as a function of fractal dimension. Specifically, Sierpinski pyramids-based specimens were designed to explore the influence of fractal dimensions and iterations on the elasticity of the samples. Additionally, a case study was carried out to by using Finite Element Method (FEA) in order to analyze the stress distribution and vibrational behavior based on fractal order. The results demonstrated a notable variation in compression behavior and vibrational behavior depending on the fractal order, highlighting the potential of fractal geometries to enhance mechanical performance in AM applications. Keywords: Fractal Geometries, Product Design, Three-Dimensional Printing, Performance, Thermoplastic Polyurethane.