Experimental Evaluation of Phase-Field-based Load-Specific Shape Optimization of Nature-Inspired Porous Structures

Triply periodic minimal surface (TPMS) structures excel in various research fields, ranging from bone support structures to heat exchangers. By implementing measures for shape alteration, the mechanical properties of the structure can be improved under certain load conditions. While interface-based methods such as the phase-field method have established themselves as powerful simulation techniques for the analysis of microstructure evolution and morphologically complex dynamic processes, they are not yet very well known and widely used for the application of shape optimization in mechanically loaded complex structures. In this study, an experimental procedure to validate shape-optimized samples is presented and applied to validate three computationally derived optimal candidates for sheet-based TPMS structures (Diamond, Gyroid, and Primitive) proposed by applying a mathematical model for shape optimization formulated in terms of the phase-field approach combined with linear elastic continuum mechanics and subject to the constraints of volume conservation. The present experimental study aims to validate recently obtained theoretical research results predict three different TPMS structures were shape-optimized under mechanical stress, using the phase-field method. In the following, the previous theoretical study is validated experimentally. The validation procedure creates a rare intersection between shape optimization phase-field simulations and experimental samples. The measurements show that the shape-optimized structures have a higher average stiffness, which leads to a shift in the plastic deformation range and thus confirms the computationally determined shape optimization.