Quantification of fabrication-related uncertainties in TPMS lattices with image processing and surrogate modeling

This paper addresses the quantification of fabrication-related uncertainties in Polydimethylsiloxane (PDMS) Triply Periodic Minimal Surface (TPMS) lattice structures using image processing techniques and surrogate modeling. The aim is to develop a Finite Element (FE) model that captures the uncertainties originating from thermal and mechanical fluctuations during the 3-D printing process, enabling the assessment of homogenized mechanical properties crucial for various engineering applications. The fabrication process often introduces deviations in TPMS lattices such as defects and surface distortions. To quantify these variations, micro-computed tomography (micro-CT) imaging is employed, providing cross-sectional images of the PDMS lattice morphology produced using 3D printed sacrificial molds. Image processing algorithms are then applied to parametrically quantify deviations, laying the groundwork for subsequent analysis. Next, the image-based data is incorporated into a sophisticated FE model, allowing for a realistic representation of the TPMS structure’s mechanical behavior. To validate the prediction accuracy of the FE model, its results for stress and strain fields are compared to the experimental data. Remarkably, a close match is observed between the experimental data and the FE model predictions, affirming the effectiveness of our approach in capturing the intricate interplay of fabrication-related uncertainties. This agreement not only validates the accuracy of the FE model but also underscores the significance of our image-processing methodology in quantifying fabrication-related uncertainties. Furthermore, we develop a neural network (NN)-based surrogate model to predict the homogenized mechanical properties as a function of the parametric representation of the TPMS lattice structure obtained through image processing. This surrogate model improves the computing times required for the determination of mechanical properties and thus allows for the efficient creation of sufficient statistical data needed for assessing the propagation of the uncertainty on properties. Accordingly, the surrogate model representation is utilized to predict the effects of uncertainty on the homogenized mechanical properties as a function of the variations in the geometric parameters of the TPMS lattices resulting from the fabrication-related uncertainty. In conclusion, presented study contributes to a deeper understanding of lattice behavior under real-world fabrication conditions, advancing the design and application of TPMS lattices in various engineering fields. The study’s findings are expected to enhance the reliability and performance of TPMS lattice structures in applications such as lightweight structural components and biomedical scaffolds.