Analyzing out-of-plane deformations caused by varying Poisson ratio distributions in a metamaterial

Master thesis (2023)

Authors

A.M.J. van Soest Mechanical Engineering

Contributors

W.W.P.J. van de Sande Mechatronic Systems Design - Mechanical, Maritime and Materials Engineering (supervisor 1)
F.G.J. Broeren Precision and Microsystems Engineering (supervisor 1)
J.L. Herder Precision and Microsystems Engineering (supervisor 2)
Faculty
Mechanical Engineering
Copyright: © 2023 Anna van Soest
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Published Date

25-08-2023

Language

English

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Faculty

Mechanical Engineering

Abstract

Auxetic metamaterials offer various novel abilities, one of the abilities is to deform into a dome-shape under out-of-plane deformation. Contrary to a material with a positive Poisson's ratio, which deforms into a saddle-shape. A dome-shape is named synclastic deformation and a saddle-shape is named anticlastic deformation. Under out-of-plane deformation, the magnitude and sign of the Poisson's ratio influence the curvature of the material, and hence the final shape. Starting from a flat plane, manipulation of the Poisson's ratio can create various unusual shapes, such as an egg or a wave-shape. A desired shape might require a uniform Poisson's ratio or a varying Poisson's ratio distribution. Most of the current estimations on the relation between an auxetic material and the deformation shape are performed experimentally. This paper presents an analytical approach which shows the influence of a varying Poisson's ratio on the out-of-plane deformation of a material under pure bending conditions. Four Poisson's ratio distributions are applied which follow the formulas: S-curve, parabolic and cosine in one and two directions. The same model is build in the FEM software COMSOL which serves as the reference model. Comparison of the COMSOL model shows a Mean Absolute Percentage Error between 0.30% and 11.93% for the analytical model. Remarkably, the accuracy of the analytical model is high if a Poisson's ratio distribution varies in one direction, resulting in a Mean Absolute Percentage Error lower than one percent point. A limitation of the analytical model is that the Mean Absolute Percentage Error increases to 0.69% till 11.93% when the Poisson's ratio varies in two directions. The presented analytical approach provides a first step in determining a varying Poisson's ratio distribution that can deform into any desired shape. The resulting shapes are synclastic and combinations of synclastic and anticlastic.