Shape optimization of porous structures by phase-field modeling with strain energy density reduction

Abstract

Triply periodic minimal surfaces (TPMS) are cell structures defined by mathematical formulas. Due to their special structure and properties, such as a high surface-to-volume ratio and good mechanical properties, these structures are used in a wide range of applications, e.g., for implants or heat exchangers. Given the diverse applicability of these structures, both scientific and industrial interest resides in the tailored shape optimization, where structural integrity is preserved on the one hand, while stiffness is selectively enhanced on the other.Therefore, in the following investigation, three TPMS unit cells are shape-optimized under mechanical loading, in the linear-elastic regime, by minimizing the strain energy density, using the phase-field method. The novelty lies in the shape optimization of TPMS structures with respect to the effective stiffness under mechanical load which is addressed with a phase-field method. It is shown that with the present optimization approach, an increase in the effective Young’s modulus of up to 55% can be achieved for specific TPMS structures.