Exploiting nonlinearities through geometric engineering to enhance the auxetic behaviour in re-entrant honeycomb metamaterials

Chetna Srivastava; Lalit Bhola; Vinyas Mahesh; P J Guruprasad; Nik Petrinic; Fabrizio Scarpa; Dineshkumar Harursampath; Sathiskumar A Ponnusami

doi:10.1038/s41598-023-47525-7

Exploiting nonlinearities through geometric engineering to enhance the auxetic behaviour in re-entrant honeycomb metamaterials

Sci Rep. 2023 Nov 27;13(1):20915. doi: 10.1038/s41598-023-47525-7.

Authors

Chetna Srivastava¹, Lalit Bhola², Vinyas Mahesh³, P J Guruprasad², Nik Petrinic⁴, Fabrizio Scarpa⁵, Dineshkumar Harursampath¹, Sathiskumar A Ponnusami⁶

Affiliations

¹ NMCAD Lab, Department of Aerospace Engineering, Indian Institute of Science, Bengaluru, 560012, India.
² Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India.
³ Department of Engineering, City, University of London, Northampton Square, London, EC1V 0HB, UK.
⁴ Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, Oxfordshire, UK.
⁵ Bristol Composites Institute, University of Bristol, Bristol, BS8 1TR, UK.
⁶ Department of Engineering, City, University of London, Northampton Square, London, EC1V 0HB, UK. sathiskumar.ponnusami@city.ac.uk.

Abstract

Classical approaches to enhance auxeticity quite often involve exploring or designing newer architectures. In this work, simple geometrical features at the member level are engineered to exploit non-classical nonlinearities and improve the auxetic behaviour. The structural elements of the auxetic unit cell are here represented by thin strip-like beams, or thin-walled tubular beams. The resulting nonlinear stiffness enhances the auxeticity of the lattices, especially under large deformations. To quantify the influence of the proposed structural features on the resulting Poisson's ratio, we use here variational asymptotic method (VAM) and geometrically exact beam theory. The numerical examples reveal that 2D re-entrant type micro-structures made of thin strips exhibit an improvement in terms of auxetic behaviour under compression. For the auxetic unit cell with thin circular tubes as members, Brazier's effect associated with cross-sectional ovalisation improves the auxetic behaviour under tension; the enhancement is even more significant for the 3D re-entrant geometry. Thin strip-based auxetic unit cells were additively manufactured and tested under compression to verify the numerical observations. The experimentally measured values of the negative Poisson's ratio are in close agreement with the numerical results, revealing a 66% increase due to the nonlinearity. Simulation results showcase these alternative approaches to improve the auxetic behaviour through simple geometric engineering of the lattice ribs.