# Analysis of the Mechanical Behavior of Tree-like Fractal Structures in SLM-Manufactured Components

## TL;DR

This paper studies tree-like fractal structures in 3D-printed parts to understand how their shape affects mechanical performance, especially in absorbing impacts.

## Contribution

The study introduces a new method using polynomial regression to predict mechanical behavior based on fractal geometry in SLM-manufactured components.

## Key findings

- Tree-like fractal structures deform uniformly and predictably during flexure tests.
- A polynomial regression model accurately predicts mechanical response with low error.
- These structures show potential for impact absorption applications due to their deformation behavior.

## Abstract

Tree-like fractals as internal structures are a novel alternative to conventional lattice structures for mechanical components produced via Selective Laser Melting (SLM). This study explores the mechanical behavior of tree-like fractals, targeting flexure tests on SLM test samples manufactured using two distinct fractal configurations. The main objective is to develop numerical models that can predict the effect of the branching angle on the stress-strain curves, for both fractal configurations, from experimental flexure tests. A polynomial regression model is proposed to predict mechanical response variations based on fractal geometry, and the prediction model provides acceptable errors, less than the natural variance of multiple experiments. Furthermore, the tree-like fractal samples showed an interesting behavior on the flexure test, where the fractals deformed uniformly and in a predictable pattern, enabling mechanical advantages in impact absorption applications.