NONLINEARITIES DURING PATTERN FORMATION IN HOLEY METAMATERIALS

Abstract

The axial loading of a column is a well known cannonical problem first described by Euler and Bernoulli. Recently, buckling in columns with regular arrays of circular voids was studied experimentally for hard materials, indicating a deviation in post-buckling behaviour from that of elastomeric columns. In this study, we extend the theoretical model of holey columns to incorporate the effects of material nonlinearities. We extend the simplified analytical model proposed by Johnson et. al that considers the column to be a collection of rigid sections connected by a network of thin ligaments acting like fixed torsional springs. Notably, in the updated model, the ligaments are modelled as deformable torsional springs that can undergo compressive and shear deformations. The total energy cost of the deformations is minimised numerically to determine the equilibrium state of the system. The response of the ligaments to deformations was modelled using empirical force-displacement curves of a single ligament under compressive, shearing and rotational deformation. We present results obtained from simulations of the column under axial compression, confirming that material nonlinearities can explain the post-buckling behaviour in hard materials, while retaining the assumption of elasticity. Having established that the compressive response of ligaments in holey columns differs significantly from that of individual ligaments, the compressive response was modelled for the entire column instead of extrapolating from single ligaments. We report that for columns with many holes (N ≥ 11), such a model can reflect the behaviour observed in experimental investigations with good precision.

Date of Award	1 Aug 2023
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Finn Box (Supervisor), Christopher Johnson (Supervisor) & Draga Pihler-Puzovic (Supervisor)