Session: 16-01-01: Government Agency Student Poster Competition

Paper Number: 150909

150909 - Strain Induced Localized to Bulk Mode Transition in Hexagonal Elastic Meta-Structures 

We predict the existence of in-plane localized modes without requiring frequency bandgap in a Hexagon
- Re-entrant - Hexagon (HRH) lattice based structure and the switchabilty of the localized modes to bulk
modes by applying boundary strain. Most existing approaches to achieve localized modes in elastic media
require frequency bandgaps which is hard to achieve. Also, the simultaneous presence of transverse and
longitudinal waves and their hybridization in elastic media results in high number of dispersion branches at
a particular frequency. For these reasons, it is desirable to get rid of the requirement of bandgap for elastic
wave energy localization and guiding.

Here we achieve elastic wave confinement and its release by applying an external strain. We first analyze
in-plane waves in a structure comprising of two identical hexagonal spring mass lattice connected by a layer
of re-entrant lattice based spring mass system. The masses interact with other masses in the lattice via
axial and rotational springs. The mode shapes of this structure show the existence of two distinct type
of localized modes: leaky resonances and decaying modes in the re-entrant part, whose frequency lies in
frequency passband of both the hexagon and re-entrant lattices. Then, based on the spring mass system of
HRH lattice, we modeled a 3D HRH structure made of hyper-elastic TPU. The reason for choosing TPU is
that the shape of the structure can be changed easily by applying boundary strain. To analyze the in-plane
waves in 3D HRH structure, we developed a nonlinear 3D finite element solver with using a compressible
Neo-Hookean model for TPU. Finite element analysis predicts the existence of analogous localized modes as
that found in case of the spring mass system.

Next, we determined the deformed configuration of the HRH structure for the boundary strain and
understand the behavior of the localized modes in the deformed configuration. We used Newton-Raphson
solver applying the total displacement in incremental steps. After determining the deformed configuration,
we analyze the mode shapes of the deformed structure and observe that when the re-entrant part changes
its shape to hexagon, the localized mode turned to a bulk mode and span the whole structure. Finally, we
conduct a transient analysis for the 3D structure, where we excite the re-entrant part at the localized mode
frequency and pull the lattice from both sides. Our analysis shows a localized mode at the re-entrant part
before pulling. As we pull the lattice, the localized wave starts to leak energy and turns to a bulk mode
when the re-entrant part is turned to hexagon. Such switching of a localized mode to bulk mode is useful to
storing and releasing wave energy at will, for potential application in wave-based sensors and actuators.

Presenting Author: Adib Rahman Texas A&M University

Presenting Author Biography: Adib Rahman completed his BSc in Mechanical Engineering from Bangladesh University of Engineering and Technology (BUET) in 2019. After that, in the spring 2021, he joined the PhD program at department of Mechanical and Nuclear Engineering in Kansas State University. His research focus is computational mechanics and elastic metamaterial. In fall 2024, he transferred to Texas A&M University and continued his research there under the supervision of Dr. Raj Kumar Pal.

Authors:

Adib Rahman Texas A&M University
Tyler Hogenkamp Kansas State University
Raj Kumar Pal Texas A&M University