This study introduces a new synthesis algorithm for triply periodic minimal surfaces based on determining the equilibrium configuration of elastic membranes constrained at their boundaries. Beyond the methodology itself and its computational efficiency, the scientific relevance of this work lies in the 66 surfaces with these characteristics that it enabled to generate. Leveraging their continuous and highly regular geometry, these surfaces were used to define novel shell-based lattices, the mechanical behavior of which was investigated numerically and experimentally through both static and dynamic analyses. The computational models demonstrated high predictive accuracy, with numerical results deviating by less than 10% from the experimental data. Across the new geometries, the surface-area-to-volume ratio ranged from 1.8 to 4.8cm−1. At infill coefficients of 10%, 20%, and 30%, the structures exhibited a wide range of stiffness and anisotropic behaviors, with equivalent elastic modulus spanning from 0.02% to 25% that of the base material and Zener indices from 4.67×10−2 to 11.8. Ultimately, the study revealed a clear influence of cell geometry on stress concentration and modal response.
Casucci et al. (Tue,) studied this question.