PSI - Issue 71

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ScienceDirect

Procedia Structural Integrity 71 (2025) 453–460

Keywords: Re-entrant honeycomb, Out-of-plane elastic properties, Homogenization, FEM 1. Introduction Honeycomb-inspired structures are widely used for many applications, including aviation, transportation, and other activities, due to its lightweight and better mechanical properties, like stiffness, outstanding energy absorption, and strength (Gibson and Ashby (1997)). A standard hexagonal honeycomb structure exposed to transverse compressions expands horizontally, leading to Poisson's ratio positive in nature. Researchers explored re-entrant honeycombs that consist of negative Poisson's ratio, after Gibson and Ashby (1997) and Lakes (1987) demonstrated large auxetic structures and foams with negative Poisson's ratios. This can be developed by redesigning conventional hexagons to create auxetic re-entrant hexagons by compressing the conventional honeycomb in the transverse direction. When regular honeycombs are bent out of the plane, their form changes into an anticlastic (saddle) shape, limiting their use in sandwich structures with complex out-of-plane geometries (Lakes (1987)). Meanwhile, when bending deformation occurs outside of the plane, structures with re entrant honeycombs exhibit synclastic curvature behaviour, resulting in the creation of dome-shaped surfaces (Alderson (2000)). It was observed that Poisson's ratio is negative, increasing numerous mechanical features such as shear modulus, fatigue strength, sound absorption feature, indentation strength, and variable permeability (Dong et al. Abstract This study employs computational modelling and theoretical analysis to determine the out-of-plane elastic properties of re entrant honeycombs. By extending the strain-energy method using Castigliano's second theorem, a framework was developed to calculate these properties. Finite element (FE) modelling involved selecting a representative cell element (RCE) and applying periodic boundary conditions (PBC) to capture the periodic nature of the structure. The out-of-plane elastic properties derived from FE analysis closely matched with those from the strain-energy approach and were consistent with reference results. This work offers insights for designing periodic structures tailored to achieve specific mechanical properties. © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of SICE 2024 organizers 5 th International Structural Integrity Conference & Exhibition (SICE 2024) Equivalent Out-Of-Plane Elastic Properties of Periodic Re-Entrant Honeycombs – Strain-Energy Approach and FE Modelling A. Kumar a,* , N. Muthu a,b , R. Ganesh Narayanan a a Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati – 781039, Assam, India b Department of Mechanical Engineering, Indian Institute of Technology Palakkad, Palakkad – 678623, Kerala, India

* Corresponding author. E-mail address : avneesh.kumar@iitg.ac.in

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of SICE 2024 organizers 10.1016/j.prostr.2025.08.061