Mechanical behaviour of aperiodic monotile minimal surface metamaterials

• Aperiodic monotile minimal surfaces generated using the boundary method • Mechanical properties quantified across randomised aperiodic configurations • Gaussian process models predict modulus, anisotropy, and their variances • Distinct stiffness trends arise from facet alignment in different topologies • Increasing RVE size reduces mechanical variability toward statistical homogeneity The recent discovery of the first aperiodic monotile has sparked widespread interest in its geometric and physical implications, leading to the identification of families of related tiles. Inspired by these developments, this study presents novel minimal surface shell structures enclosed within aperiodic monotiles and the mechanical response of these lightweight metamaterials is subsequently investigated. While previous works have largely examined the geometric uniqueness of planar aperiodic monotiles, this work presents minimal surfaces that tile aperiodically. Finite element analysis is employed to quantify the anisotropic stiffness characteristics of aperiodic monotile minimal surfaces across different orientations and local configurations. Statistical variations in the mechanical response are evaluated to capture the inherent sensitivity to the aperiodic arrangement. A Gaussian process regression model is then trained to estimate the effective mechanical properties and associated uncertainty across the design space, enabling rapid evaluation without full-scale simulation. The results demonstrate that aperiodic monotile minimal surfaces can achieve in-plane stiffness isotropy. This study establishes a framework for the design and optimisation of aperiodic minimal surface metamaterials, bridging geometric aperiodicity and mechanical functionality.