Hinged-3D metamaterials with giant and strain-independent Poisson’s ratios

Current designs of artificial metamaterials with giant Poisson’s ratios proposed microlattices that secrete the transverse displacement nonlinearly varies with the longitudinal displacement, and the Poisson’s ratio depends on the applied strain (i.e., tailorable Poisson’s ratio). Whereas metamaterials with tailorable Poisson’s ratios would find many important applications, the design of a metamaterial with a giant Poisson’s ratio that is constant over all the material deformation range has been a major challenge. Here, we develop a new class of bimaterial-3D-metamaterials with giant and strain-independent Poisson’s ratios (i.e., Poisson’s ratio is constant over the entire deformation range). The unit cell is 3D assembled of hinged-struts. Specially designed spherical hinges were utilized to give constant Poisson’s ratios. This new class of metamaterials has been demonstrated by means of experimental and numerical mechanics. 15 material samples were 3D printed by Stereolithography (SLA) and tested. We revealed a robust anisotropy dependence of the Poisson’s ratio. A giant negative Poisson’s ratio of −16 was obtained utilizing a highly anisotropic unit cell of dissimilar materials and stiffnesses. Materials with giant and strain-independent Poisson’s ratios provide a new class of artificial metamaterials, which would be used to optimize the performance of many existing devices, e.g., strain amplifiers and gauges.

designed with an external opening of 1.25 mm diameter to avoid a separation of the strut while it is loaded. A neck of 1.1 mm diameter and 2.4 mm length was shaped between the strut body and 3 its spherical end to permit the strut's rotation during the unit cell deformation. The dimensions of the spherical hinge and the strut were carefully chosen such that the struts can be easily assembled to the spherical hinges with no separation of stretched struts during the unit cell deformation (see Fig. S1).

S2: Stereolithography 3D Printing
The struts and spherical hinges were 3D printed by Stereolithography (SLA) printing technique available at 3D-layers©. Fig. S2 shows the 3D printing process of the spherical hinges and struts. The process started with a computer aided design (CAD) of the parts to be printed using SolidWorks. Then, parts were assembled and checked for interference using SolidWorks' interference check tool. Afterwards, the CAD parts were exported into STL files. The dimensions of the parts to be printed and their printability were verified using a 3D builder tool ( Fig. S2(a)). A photoreactive polymer resin (FLGPGR04) was used (Fig.S2(c)). Bottom-up building technique with 205 layers was applied to build the spherical hinges while 65 layers was applied to build up the struts. A solid base with pin-shaped two supports was built first from the same resin material to allow the building of the spherical hinge since it is not possible to start building a spherical geometry from a point ( Fig.S2(b)). In addition, the strut was supported horizontally with 6 supports such that two supports were used underneath the spherical ends and the other four were distributed over the struts body to avoid bending while printing ( Fig.S2(b)). The temperature of the resin was kept constant at 30°C and the processing time for a single strut was 30 min while for one spherical hinge was 60 min. After printing, the parts were submerged in isopropyl alcohol (IPA) to remove any contaminants of uncured resin. Then, the base and supports were removed of the parts. Afterwards, parts were subjected to ultraviolet light for 30 min (Fig.S2(c)). Finally, the spherical cap-ends of the strut were polished using a series of sandpapers up to 4000 grit size.

S3: Finite Element Modeling (Our Developed Numerical Model)
A computational package of a 3D-truss finite element model was built to investigate the microstructural topology effects on the Poisson's ratio and to extract the results presented in Fig.   3. Three main parameters affect the Poisson's ratio, e.g. / , / , and 2 / 1 . We found that investigating the influence of each one of these parameters using a commercial software, e.g. ANSYS, is time consuming. Therefore, we built our own 3D-truss model of the designed metamaterial, which can effectively give results in a short time.
A discretization procedure was utilized where nodes and their coordinates were defined over , , and -directions as shown in Fig. S3. Then, elements were setup between these nodes where elements' numbers were assigned, and nodes were specified for each element. In addition, the cross sectional area and Young's modulus were defined for each element. These data were automatically generated using the discretization procedure and saved in excel files. The outputs of the discretization approach were used to form the element stiffness matrix of all elements, and then the global element stiffness matrix. Boundary conditions were then defined such that a distributed load was applied acting on a surface whose normal is −axis, and the opposite surface was free to move only along y and −axes (Fig. S3). The other surfaces were free surfaces allowed to move in , , and -directions.

S4: Numerical Simulations using ANSYS
3D-truss elements were used to build our proposed metamaterial model using ANSYS commercial software to simulate the predicted Poisson's ratio of a single cell and a structure made of the proposed metamaterial. The model was built to using LINK180 elements with circular cross section and a predefined diameter of 1 mm. Two materials were defined using elastic material model in the library of the software. For all the tested materials (except sample 15), a material with a low Young's modulus of 2 = 0.001 GPa was assigned for links located in the −plane Simulations were performed to determine the Poisson's ratios of the 15 material samples.
The Poisson's ratio as determined by ANSYS are compared to the ones determined by our developed finite element model (Section S3) in Table S1. All of these results are also compared to the experimentally determined ones (Table S1). Table S1 shows an excellent match between the results of ANSYS and our proposed finite element model. This demonstrates the effectiveness of our developed numerical model and the validity of the results presented in Fig. 3. In addition, an excellent match between the numerical results and the experimental measurements of the Poisson's ratio is very clear in Table S1. This demonstrates the effectiveness of our designed spherical hinges, which gave a free rotation with a nearly-zero friction between the struts and hinges.