## 3 Results and Discussion
### Mechanical and Piezoresistive Characterization  
The effect of porosity and geometry on the mechanical behavior of the TPU/GE porous structures was investigated by compression tests. Figure 6a shows the stress-strain curves for all investigated samples. An initial toe region caused by a take-up of slack and alignment of the specimen followed by a linear region can be observed. Elastic modulus was calculated from the linear region of the curves for all the geometries considered (Figure 6b). In particular, the samples were tested at small strain values (<10%), in order to ensure that all samples were in their elastic deformation region. D and G architecture structures show, in the deformation range which has been investigated, a linear increase of stress with increasing strain, while the S geometry structures exhibit a progressive strengthening during compression, which results in higher stress values in comparison to the corresponding D and G structures. This outcome is ascribed to the different morphology of pores present in the systems obtained by starting from S unit cells with respect to D and G systems. In fact, the structures with S geometry result in having less pores with bigger dimensions [33; 34; 35]. This implies that at a given porosity value, the average thickness of the trabeculae in the S structure is bigger, so the mechanical stress required to get a defined deformation is larger (as compared to other structures with same porosity). The porous structures exhibit a dramatic enhancement of the elastic compression modulus (more than 2 orders of magnitude in the case of D and G structures) when the porosity decreases from 80% to 40%. Moreover, unit cells (i.e., S, D, or G) also affected the mechanical performance of the porous structures, with the S structures being significantly stiffer than the corresponding G and D-based structures. Figure 5: (**a**) DSC and (**b**) TGA curves of SLS fabricated TPU and TPU/GE nanocomposite. All SLS fabricated structures, except for TPU/GE D80, which gave no reliable results, were tested as concerning their electrical conductivity. Indeed, in the presence of graphene, the insulating polymer matrix became conductive, due to the formation of a segregated percolated graphene network at the boundary of the TPU particles. While neat TPU displayed a conductivity value of \(10^{-13}\) S/m, all the porous structures exhibited values ranging from 7 \(\times\)\(10^{-5}\) (TPU/GE S80) to 9 \(\times\)\(10^{-4}\) S/m (TPU/GE G80). These conductivities are comparable with those reported in literature for graphene/TPU foams fabricated by thermal induced phase separation [41, 42], indicating the formation of a stable graphene conductive network in all samples. The piezoresistive behavior of the porous TPU/GE porous structures was studied by submitting the samples to compression cycles with strain up to 8%. Figure 7 shows the results characterizing the piezoresistive behavior of the D, G, and S-based structures with 40% porosity. All samples showed a negative piezoresistive behavior that is the electrical resistance decreasing with increasing strain. Figure 6: (**a**) Compression stress-strain curves, and (**b**) compression elastic modulus of the SLS fabricated TPU/GE porous structures. Figure 7: Piezoresistive behavior of (**a**) TPU/GE D40, (**b**) TPU/GE G40, and (**c**) TPU/GE S40 under cyclic compression. (**d**) Resistance ratio and gauge factor of TPU/GE porous structures at 8% compression strain. This outcome arises from the compactness of TPU particles and the enhancement of the GE nanoplatelet contact upon compression, which leads to the formation of more conductive pathways [46]. Electrical conductivity strongly depends on the percentage of porosity but also on internal architectures of the 3D structures, both at low (i.e., zero deformation corresponding to the case of constant preload applied to the samples) and high deformation (i.e., 8% deformation in compression). In detail, the conductivity at zero deformation decreases as the percentage of porosity increases.