Abstract The behavior of two dimensional (2D) materials constructed as three-dimensional (3D) structures is studied to bring such materials one step closer to the real life application. Lattices structures of gyroid triply periodic minimal surface (TPMS) were fabricated out of two-dimensional (2D) materials, namely, molybdenum disulfide (MoS2), and reduced graphene oxide (rGO), forming for the first time free-standing MoS2 (FSM) lattice and free-standing hetero-structural lattice of MoS2 and rGO (FSH) out of TPMS. These 2D materials were also integrated with polydimethylsiloxane (PDMS) elastomer forming FSM/PDMS and FSH/PDMS composites. Mechanical characterization, including compression and cyclic tests, were conducted on FSM, FSH, and composites. 
Additionally, electromechanical characterization was conducted to evaluate the sensing potential of these structures. It is worth noting that the elastic modulus of the 10 unit-cells with either FSM or FSH was higher than the other lattices of the same type. Overall, FSH tends to have a higher modulus at 1504.4 kPa in the 10 unit-cells, this modulus is even higher at 3 MPa when PDMS is added to the FSH lattice. FSM or FSH lattices follow the layer-by-layer failure mechanism as a result of the brittle fracture. Samples with PDMS are more stable towards such cyclic tests without noticeable failures or a decrease in elastic modulus. Finally, the 10 unit-cell lattices of FSH/PDMS composite have the highest conductivity at 2.5 mA, and a comparable sensitivity at 0.365 kPa-1 over the range of 0 to 100 kPa.