mechanism that leads to a negative Poisson’s ratio in the double-T sample is mostly due to rotation of the single base cells and not connected with the material by itself validating all the assumption and observation made along the paper. An interesting application would be focusing on in-plane modes at higher frequencies to demonstrate the auxetic behaviour in a more critical dynamical stage and for different stiffness and geometry that was not possible during this investigation since this investigation was limited by the maximum frequency, of about 10,000 Hz, allowed by the piezoactuators the amplifier and the controller. 42.5 Conclusions Three different thin low porosity metal negative Poisson’s ratio structures were tested numerically and experimentally with speckle interferometry to assess their auxetic behavior and their eigenmodes. Different interferometers sensitive to the in-plane displacements were used during this investigation to obtain the displacement maps along the whole surface of the samples and the results were compared with the numerical calculation of the modal analysis performed with the finite element software Abaqus/Standard and an excellent agreement was found. Torsional, flexural and in-plane modes were observed and the experimental natural frequencies were found to be very close to the ones provided experimentally, thus obtaining a very good prediction of the real resonance frequencies of the structures. The results validate the numerical approaches used to predict the overall response opening a way to design more complex and advanced auxetic structures. This investigation validates the utilization of this type of meta-structure using ductile materials, and demonstrates that by varying the pore’s geometry and the stiffness, it’s possible to modify the dynamical behavior of the samples tuning the auxetic properties in function of the requirement of the design. In addition, the findings of this study provide a basis for future researches to address some of the problems related to using ductile materials to create more advanced metallic auxetic structures, such as optimizing the geometry, the fabrication processes and minimize the stress concentration for different scenarios. References 1. Evans, K.E., Alderson, A.: Auxetic materials: functional materials and structures from lateral thinking. Adv. Mater. 12(9), 617–628 (2000) 2. Alderson, A., Alderson, K.L.: Auxetic materials. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 221(4), 565–575 (2007) 3. Lakes, R.: Advances in negative Poisson’s ratio materials. Adv. Mater. 5, 293–296 (1993) 4. Prawoto, Y.: Seeing auxetic materials from the mechanics point of view: a structural review on the negative Poisson’s ratio. Comput. Mater. Sci. 58, 140–153 (2012) 5. Sanami, M., Ravirala, N., Alderson, K., Alderson, A.: Auxetic materials for sports applications. Procedia Eng. 72, 453–458 (2014) 6. Bertoldi, K., Reis, P.M., Willshaw, S., Mullin, T.: Negative Poisson’s ratio behaviour induced by an elastic instability. Adv. Mater. 22, 361–366 (2010) 7. Lehmann, M.: Statistical theory of two-wave speckle interferometry and its application to the optimization of deformation measurements. PhD Thesis, Ecole Polytechnique Federal de Lausanne (1998) 8. Taylor, M., Francesconi, L., Gerendas, M., Shanian, A., Carson, C., Bertoldi, K.: Low porosity metallic periodic structures with negative Poisson’s ratio. Adv. Mater. 26(15), 2365–2370 (2014) 9. Jacquot, P.: Speckle interferometry: a review of the principal methods in use for experimental mechanics applications. Strain44, 57–69 (2008) 10. Baldi, A., Jacquot, P.: Data analysis of speckle interferometry measurements for residual stress determination in composite specimen. In: Proceedings of ICEM12—12th International Conference on Experimental Mechanics (2012) 11. Hariharan, P., Oreb, B.F., Eiju, T.: Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm. Appl. Optics 26(13), 2504–2506 (1987) 12. Tiziani, H.J., Klenk, J.: Vibration analysis by speckle techniques in real time. Appl. Optics 20(8), 1467–1470 (1981) 13. Romero, G., Alvarez, L., Alanis, E., Nallim, L., Grossi, R.: Study of a vibrating plate: comparison between experimental (ESPI) and analytical results. Opt. Lasers Eng. 40, 81–90 (2003) 42 Numerical and Experimental Eigenmode Analysis of Low Porosity Auxetic Structures 341
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