Non local analytical and numerical modelling of re-entrant auxetic honeycomb

Auxetic materials, characterized by their negative Poisson's ratio, have been extensively studied for applications in energy absorption and mechanical reinforcement. Re-entrant honeycomb structures, a subtype of auxetic materials, have demonstrated superior mechanical characteristics. However, understanding the mechanical behavior of these structures at the nanoscale remained a significant challenge. To address this gap, the authors explored the influence of size on the deflection behavior of re-entrant auxetic honeycomb structures through non-local continuum mechanics. Their analytical model, incorporating the Euler-Bernoulli beam model and considering four non-dimensional geometrical parameters, was validated through numerical simulations and a comprehensive review of existing literature. The study aimed to provide valuable insights into the design and engineering of re-entrant auxetic honeycomb structures across diverse applications, contributing to the advancement of non-local elasticity theory and deepening the understanding of the mechanical behavior of auxetic structures at the nanoscale. The research laid a foundation for further exploration and optimization of re-entrant honeycomb structures, facilitating their effective utilization in fields such as MEMS/NEMS by leveraging the dimensionless parameters identified in the study.