Amin Joodaky PhD Dissertation.pdf (5.29 MB)

# MECHANICS AND DESIGN OF POLYMERIC METAMATERIAL STRUCTURES FOR SHOCK ABSORPTION APPLICATIONS

thesis
posted on 12.08.2020, 20:04 authored by Amin JoodakyAmin Joodaky
This body of work examines analytical and numerical models to simulate the response of structures in shock absorption applications. Specifically, the work examines the prediction of cushion curves of polymer foams, and a topological examination of a $\chi$ shape unit cell found in architected mechanical elastomeric metamaterials. The $\chi$ unit cell exhibits the same effective stress-strain relationship as a closed cell polymer foam. Polymer foams are commonly used in the protective packaging of fragile products. Cushion curves are used within the packaging industry to characterize a foam's impact performance. These curves are two-dimensional representations of the deceleration of an impacting mass versus static stress. The main drawback with cushion curves is that they are currently generated from an exhaustive set of experimental test data. This work examines modeling the shock response using a continuous rod approximation with a given impact velocity in order to generate cushion curves without the need of extensive testing. In examining the $\chi$ unit cell, this work focuses on the effects of topological changes on constitutive behavior and shock absorbing performance. Particular emphasis is placed on developing models to predict the onset of regions of quasi-zero-modulus (QZM), the length of the QZM region and the cushion curve produced by impacting the unit cell. The unit cell's topology is reduced to examining a characteristic angle, defining the internal geometry with the cell, and examining the effects of changing this angle.
However, the characteristic angle cannot be increased without tradeoffs; the cell's effective constitutive behavior evolves from long regions to shortened regions of quasi-zero modulus. Finally, this work shows that the basic $\chi$ unit cell can be tessellated to produce a nearly equivalent force deflection relationship in two directions. The analysis and results in this work can be viewed as new framework in analyzing programmable elastomeric metamaterials that exhibit this type of nonlinear behavior for shock absorption.

## Degree Type

Doctor of Philosophy

## Department

Mechanical Engineering

West Lafayette

James M Gibert

Patricia Davies

Anil K Bajaj

Tyler Tallman