Numerical analysis of the influence of triply periodic minimal surface structures morphometry on the mechanical response

Abstract

Background and objective: Design of bone scaffolds requires a combination of material and geometry to fulfil requirements of mechanical properties, porosity and pore size. Triply Periodic Minimal Surface (TPMS) structures have gained attention due to their similarities to cancellous bone. In this work, we aim at exploring relationships between morphometry and mechanical properties for TPMS configurations.

Methods: Eight TPMS structures are defined considering six porosity levels and their morphometry is characterized. The stiffness matrix of each structure is assessed and related to morphometry through a statistical analysis.

Results: An orthotropic mechanical behavior has been derived from the numerical homogenization. Properties decay exponentially for decreasing volume fraction. Through volume fraction variation, TPMS mechanical properties can be selected to match bone properties in a range of 0.2% to 70% of the bulk material properties.

Conclusions: The comparison between cancellous bone and TPMS morphometry, considering a unit cell size of 1.5 mm, reveals that the configurations analyzed in this work match the requirements of volume fraction, mean thickness and pore size. However, the TPMS studied in this work differ from cancellous bone anisotropy. The results in this paper provide a framework to select the proper TPMS configuration and its geometry for patient-specific applications.

Keywords: Finite element method; Homogenization; Morphometric characterization; Triply periodic minimal surface structures.