# The Effect of Non-Uniform Material Distribution on the Bending Strength and Energy Absorption of TPMS Structures

## TL;DR

This study examines how uneven material distribution affects the strength and energy absorption of TPMS structures, finding that Primitive structures perform best under bending loads.

## Contribution

The study reveals that targeted material inhomogeneity can enhance deformation stability and energy efficiency in TPMS structures.

## Key findings

- Primitive structures with 45% volume fraction showed highest strength (σf = 28.35 MPa; Fmax = 756 N).
- Gyroid structures with 45% volume fraction absorbed more energy (34.58 J) than those with 55%.
- Primitive structures proved most resistant to uneven material distribution and offered optimal strength-toughness balance.

## Abstract

Optimizing the mechanical response of structures with triple periodic minimal surfaces (TPMS) is key to their use in lightweight applications focused on energy absorption. This study evaluated the influence of cell geometry and uneven material distribution on the bending behavior of Primitive, Gyroid, and Diamond structures. Nylon 12 CF samples were produced using an additive method (FDM) with volume fractions of 35%, 40%, 45%, and 55%. The mechanical response was quantified using a three-point bending test according to ISO 178, from which the maximum force (Fmax), flexural strength (σf), absorbed energy (Eabs), and ductility index (µd) were determined. The Primitive structure achieved the highest strength at a volume fraction of 45% (σf = 28.35 MPa; Fmax = 756 N). The Primitive structure also demonstrated the highest toughness with a ductility index of up to µd = 8.62 at 55%. The study identified a significant deformation phenomenon in the Gyroid structure, where the sample with a volume fraction of 45% showed higher absorbed energy (34.58 J) than the sample with a higher fraction of 55% (26.81 J). This finding suggests that targeted material inhomogeneity (gradient) can, under specific conditions, lead to stabilization of the deformation mechanism through progressive collapse, thereby increasing energy efficiency. The Primitive structure proved to be the most resistant to uneven material distribution and, with a volume fraction of 45–55%, offers an optimal compromise between high strength and toughness, making it most suitable for the design of gradient structures subjected to bending loads.