## 2 Materials and Methods
### Mechanical Properties  
To investigate the effect of iron powder on the energy absorption behavior of re-entrant polymer structures, a quasi-static compression test was implemented, Table 5. As illustrated in Figure 10, like typical metamaterials, all compression stress-strain curves have three stages, including the linear elastic region, plateau stress region, and densification stage. Figure 8: DSC graph of neat PLA and PLA/iron composite samples. Figure 9: Rheology results of samples, complex viscosity vs. angular frequency. For neat PLA re-entrant structures, as demonstrated in Figure 10a, the stress exhibited a rapid increase until reaching 2.8 MPa, after which it sharply decreased towards zero. Subsequently, the stress underwent fluctuations until a strain of 0.4, at which point the entire structure collapsed. This observed trend resulted from the successive collapse of cells within the structures. Overall, the neat PLA structures exhibited a brittle fracture pattern, indicative of poor energy absorption behavior. However, a significant alteration in deformation behavior was observed for structures containing 5% iron powders. While exhibiting relatively similar behavior to neat PLA in the linear elastic region, with an initial stress peak of 2.8 MPa and a compressive modulus of 82.2 MPa, these structures displayed a distinct pattern thereafter. The stress underwent a smooth decline to approximately 1 MPa, followed by fluctuation ranging from 1 to 2.3 MPa until reaching a strain of 0.37, signifying the transition into the densification region. In contrast to neat PLA, the structures with 5% iron powder exhibited a more consistent deformation characterized by reduced layer breakage and cell wall detachment. Moving to the PLA/10% Fe structures, an even more pronounced enhancement in deformation behavior was observed by adding more iron to PLA. The compressive modulus increased to 91.36 MPa, accompanied by an initial stress peak of approximately 3 MPa. After this, the stress exhibited a gradual decrease to around 1.5 MPa, followed by a resurgence to a second peak at 2.5 MPa. The structures experienced their maximum stress in the plateau stage, reaching 3.57 MPa at a strain of 0.36. Upon reaching a strain of 0.4, the structures entered the densification stage, leading to the compaction of all cells. Notably, the structures with a higher iron filler loading of 10% Fe exhibited a consistent and uniform deformation behavior, with no evidence of layer breakage or cell wall detachment, even under high compressive strains. This improvement in compressive properties with added iron particles can be attributed to several key factors. Firstly, the presence of iron particles introduces a reinforcing effect within the polymer matrix. This strengthening effect, stemming from the metal particulate phase, enhances both the compressive modulus and overall strength of the composite. Specifically, the composites containing 5% and 10% Fe showed a higher compressive modulus and strength compared to neat PLA, as the metal particles increased the rigidity of the structure. Additionally, the iron particles contributed to stress redistribution throughout the structure, especially at critical areas like nodes where stress concentrations are high. This redistribution reduces localized strain and delays the onset of fracture, thereby improving the structural integrity and durability of the composites under compression [35]. Secondly, iron particles in the PLA matrix acted as stress concentrators [30], leading to a significant improvement in the energy absorption capacity of the PLA/iron composites. The SEM images further validated this effect by representing that the particles are embedded uniformly in polymer matrix (Figure 6). This phenomenon can be also attributed to the reduced residual shear stress. The printing process can result in residual shear stresses caused by thermal expansion, typically concentrated at the intersections of struts, making them preferred sites for crack initiation.