A stochastic multiscale asymptotic homogenization approach to 3D printed biodegradable resin TPMS bio-inspired structures

Abstract

Gyroid (G), Primitive (P), and IWP porous structures, belonging to the category of complex triply periodic minimal surface (TPMS) architectures, have diverse applications across various scientific and technological fields. These intricately designed structures, inspired by biological architectures, are increasingly gaining attention in 3D printing because they fulfill the biological and mechanical requirements necessary for natural reconstruction. This paper promotes a novel computational framework for TPMS structures using a stochastic multiscale homogenization (SMH) method, which not only effectively predicts the homogenized engineering constants, microscopic strains, and damage propagation, but also accounts for their natural uncertainties. For computing a nonlinear problem on a standard desktop computer, the preconditioned element-by-element scaled conjugate gradient (EBE-SCG) method has been used to solve these stochastic models, particularly for intricate TPMS structures. To demonstrate the effectiveness of the present approach, the behaviors of the three above TPMS types with different layer levels, ranging from one to three within the same cell size, are automatically designed, formulated, and analyzed using an in-house Fortran code. This is a first attempt to demonstrate that the simulated stochastic homogenization predictions closely align with the experimental compressive Young’s modulus and damage behaviors of 3D-printed TPMS specimens made from a biodegradable resin, polyamide (PLA), using a vat photopolymerization printing process. The relative errors in the mean values, ranging from 2.45 to 11.25%, are attributed to uncertainties in the printed models involving small uncertainties. Notably, the stochastic approach effectively captures both the uncertainty and the probabilistic nature of the mechanical properties, with measured values falling within the predicted distributions. Moreover, this research framework enables more efficient design and fabrication of TPMS-based bio-inspired structures with potential applications in mechanical, civil, aerospace, engineering, etc., especially biomedical engineering.