Metal hydride hydrogen storage technology is considered a potential alternative energy and energy storage solution in promoting global economic decarbonization. However, the heat transfer coefficient between hydrogen storage materials and reactors is relatively low, which cannot meet the heat transfer and hydrogen storage requirements of the metal hydride tank. This study employs a triply periodic minimal surface (TPMS) based hydrogen storage reactor and design of experiments (DOE) to reveal the relationship between various parameters and their characteristics. The multi-physics coupling of fluid flow, heat transfer, chemical reactions, and stress in a metal hydride hydrogen storage reactor is also combined to promote the synergistic improvement of heat transfer and hydrogen storage efficiency. Numerical simulation results demonstrate that the hydrogen absorption volume fraction of tank equipped with TPMS is 0.926, which is significantly higher than that of conventional finned one. The absorption of hydrogen leads to volume expansion, resulting in a 30.61 % increase in expansion stress. Furthermore, the optimal hydrogen absorption volume fraction occurs at a temperature of 273.15 K, a pressure of 3.49 MPa, and a velocity of 5 m/s.