Mechanical Response and Data-Driven Design of Sheet-Based TPMS and Re-Entrant Auxetic Lattices

This study presents a unified finite element and surrogate-assisted computational framework for comparative analysis and design exploration of sheet-based triply periodic minimal surface (TPMS) and Re-entrant auxetic lattice architectures. Four TPMS topologies, including Gyroid, Schwarz Primitive, Diamond, and Neovius, together with a Re-entrant lattice, were modelled using a consistent sheet-based geometric representation and evaluated under finite-specimen uniaxial compression conditions using linear-elastic finite element analysis (FEA). Relative density was calculated from the actual solid volume of generated geometries rather than prescribed as an independent design variable, enabling thickness-controlled comparison among different lattice families. The results demonstrated that topology, relative density, and loading orientation significantly influence the apparent elastic response of the investigated architectures. The Re-entrant lattice exhibited negative directional Poisson’s-ratio responses for selected orientations, whereas TPMS architectures showed different stiffness and deformation characteristics depending on topology and loading direction. These observations represent configuration-dependent numerical trends within the adopted framework and are not interpreted as universal topology ranking. A surrogate-assisted framework based on Gaussian Process Regression (GPR) was developed for finite element response approximation, inverse wall-thickness identification, and topology–orientation screening. Symbolic Regression (SR) was additionally applied to selected Gyroid Poisson’s-ratio responses to obtain interpretable analytical representations of specific numerical trends. The developed surrogate models accurately reproduced the finite element response curves within the investigated topology, orientation, and thickness domains; however, the obtained performance represents interpolation accuracy within the generated numerical design space rather than unrestricted prediction capability. The proposed framework provides an efficient computational strategy for reducing repeated finite element evaluations and supporting multi-property exploration of architected lattice materials. The results are limited to the investigated architectures, idealized homogeneous isotropic material assumptions, linear-elastic small-strain behaviour, finite-specimen boundary conditions, and numerical geometry representations, highlighting the need for further experimental validation and nonlinear analyses for manufactured lattice components.