Tunable mechanical bandgaps in elastic metamaterials: Patterning, straining, and spatiotemporal modulation

Metamaterials are novel engineered composites with special microstructural patterns that lead to uncommon macro properties compared to natural material systems. In this work, we first present a novel mechanism for evolving the elastic band gap structure in a bio-inspired composite through tension induced non-planar interfacial deformation. We show that band gaps emerge and may be tuned using externally applied tension forces in three example microstructures. Then we investigate the elastodynamic behavior of a one-dimensional composite system and examine its response within and outside band gaps. We show that total energy will approach a constant in the mean sense for excitation within band gap and will monotonically increase otherwise. This led us to an in-depth investigation of the nature of the transient response of excitations within the band gaps. Further study on the one-dimensional system shows that band gaps may also be generated by coupling two homogeneous systems. We show that coupling introduces resonant gaps which are efficient in attenuating wave propagation. We applied the principle to construct, for the first time, a realization of elastodynamic signal choppers. Next, we show that an alternative pathway for achieving resonance phenomena in materials is through leveraging complex geometry. Wave propagation in domains with curvilinear geometry may be mapped into a dual problem of wave propagation in a domain of varying material properties. By applying the coordinate transformation technique, we show that it is possible to make correlations between curvilinear geometry and variation in impedance. This explains the emergence and evolution of band gaps in curved systems and may reveal regions of amplification and suppression of wave motion without solving the equations of motion. Examples include crest, valley and sinusoidal strips with different steepness are analyzed and indicate the effective material contrast increases with the geometric steepness. The last topic deals with the effect of spatiotemporally modulated elastic substrate on band gap structure. The elastic substrate opens band gap including zero frequency which has broad applications in practice. While the spatial modulation alone opens higher frequency band gaps, the temporal modulation alone can cause instability issue. We show that this instability can be mitigated by increasing damping coefficient. The combination of spatial temporal modulation leads to non-reciprocal wave propagation behavior and we show that fast modulation speed will result in similar instability issue. The topics studied in this work expand our understanding of metamaterial response and open new opportunities for designing materials with extreme properties.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Chen, Qianli

Contributors dc:contributor

• Elbanna, Ahmed E,
• Vakakis , Alexander F.
• Sottos , Nancy R.
• Duarte, Carlos A.
• Matlack, Kathryn

• Metamaterial
• Band Gap

Statement dc:rights

• Copyright 2019 Qianli Chen

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/106420

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/106420