rspa.royalsocietypublishing.org Research Article submitted to journal Subject Areas: xxxxx, xxxxx, xxxx Keywords: xxxx, xxxx, xxxx Author for correspondence: D. Rayneau-Kirkhope e-mail: daniel.rayneau-kirkhope@aalto.fi Analytic analysis of auxetic metamaterials through analogy with rigid link systems Daniel Rayneau-Kirkhope 1,2 , Chengzhao Zhang 2,3 , Louis Theran 2,4 , Marcelo A. Dias 2,5 1 Department of Applied Physics, Aalto University, FI-02150 Espoo, Finland 2 Aalto Science Institute, Aalto University, FI-02150 Espoo, Finland 3 Department of Mathematics, Massachusetts Institute of Technology, USA 4 School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland, UK 5 Department of Engineering, Aarhus University, Inge Lehmanns Gade 10, 8000 Aarhus C, Denmark In recent years many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic instability. Such metamaterials switch from conventional behaviour to an auxetic response for loads greater than some threshold value. This paper develops a novel methodology in the analysis of auxetic metamaterials which exhibit elastic instability through analogy with rigid link lattice systems. The results of our analytic approach are confirmed by finite element simulations for both the onset of elastic instability and post-buckling behaviour including Poisson’s ratio. The method gives insight into the relationships between mechanisms within lattices and their mechanical behaviour; as such, it has the potential to allow existing knowledge of rigid link lattices with auxetic paths to be used in the design of future buckling induced auxetic metamaterials. 1. Introduction The response of a structure to an external mechanical stimulus is often a direct consequence of the structure’s geometry; thus it is reasonable to expect that with c The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/ by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Analytic analysis of auxetic metamaterials through analogy with rigid link systems
Jun 24, 2023
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