Load specific phase-field based structural optimization and experimental validation of sheet-based gyroid structures

In the following, a detailed investigation of two phase-field based variants for optimizing unidirectionally loaded gyroid unit cells is presented. The optimization is conducted within the linear-elastic range, aiming to maximize the stiffness of the structure while preserving its periodicity. In the first approach, a gyroid unit cell with an initial porosity of approximately 75% is volumetrically reduced by 5%. This volume reduction in the less stressed regions results in a topological modification of the structure. In the second approach, a gyroid unit cell with an initial porosity of approximately 80% is also volumetrically reduced by 5%. Subsequently, the volume is increased by 5% through a phase-field based shape optimization process, resulting in a final porosity of 80%. Both modified structures are compared to a reference structure-an unmodified gyroid structure with a porosity of 80%. The results indicate that the modified structures exhibit an approximately 32% higher effective Young’s modulus. Furthermore, a correlation between the simulation results and experimental data is established.