Experimentally informed modeling of nonlinear wave propagation and phononic behavior in prescribed delaminations

Smith, Elizabeth

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https://hdl.handle.net/2142/130173 Copy

Description

Title

Experimentally informed modeling of nonlinear wave propagation and phononic behavior in prescribed delaminations

Author(s)

Smith, Elizabeth

Issue Date

2025-07-14

Director of Research (if dissertation) or Advisor (if thesis)

Matlack, Kathryn H

Doctoral Committee Chair(s)

Matlack, Kathryn H

Committee Member(s)

• Vakakis, Alexander F
• Tawfick, Samel
• Elbanna, Ahmed

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• nonlinear dynamics
• nonlinear phononic materials
• hysteresis
• wave propagation

Abstract

Phononic materials are constructed of periodically arranged features that can be engineered to manipulate mechanical waves with wavelengths on the order of the periodicity. They exhibit wave propagation phenomena such as frequency-dependent band gaps. Recently, their study has extended to the nonlinear regime, with the goal of augmenting phononic systems with nonlinear dynamic behavior. A variety of nonlinear sources have been incorporated in phononic materials, including contact nonlinearity, bistable elements, and material nonlinearity, to study phenomena such as energy transfer between frequencies and amplitude-dependent band gaps. Delaminated materials, with partial bonding at the interface of two materials or layers, exhibit nonlinear responses including asymmetric stiffness and hysteretic nonlinearity. Understanding the dynamic behavior of delaminations is of great interest to the non-destructive evaluation community as delaminations exist across a range of materials including rocks, composites, and additively manufactured materials. The dynamic response of delaminations throughout their transition between closed to open states is complex and strongly nonlinear. The nonlinear dynamic behavior in materials containing delaminations has been well documented, including amplitude dependent resonance, harmonic generation, and slow dynamics. However, the relationship between the nonlinear mechanism and nonlinear response remains an open research question. Therefore, this dissertation proposes a modeling approach to 1) generate a deeper understanding of the nonlinear mechanism and dynamic response of delaminated materials and 2) engineer delaminations as a physical nonlinear mechanism to control nonlinear wave propagation in nonlinear phononic materials. To develop an experimentally informed model, the quasi-static and transient behavior of a delamination between a stiff and soft materials is experimentally characterized. Results show asymmetric stiffness and hysteresis, as well as displacement offset in a propagating wave that is amplitude dependent. The experimentally observed asymmetric stiffness and hysteresis are modeled as a coupling element between linear elastic waveguides. Extensive parametric numerical studies of longitudinal wave propagation through a single discrete coupling elucidate the distinct influences of bilinear asymmetry and the shape of the hysteresis curve on the nonlinear response. The impedance mis-match between linear elastic layers and the coupling mimics scattering induced by a delamination in an open state, without using a full-scale contact model. The bilinear asymmetry generates nonlinear responses including offset in the displacement profile, harmonic generation, and distinct frequency dependent transmission of tensile and compressive waves. The relationship between the shape of a hysteresis curve and the amplitude and frequency dependent harmonic generation, power loss, and power transmission is determined using the Bouc-Wen model. These reduced order models capture the predominant behavior of the complex mechanisms, including amplitude dependence and displacement offset, while greatly reducing computational power required by full scale models. The reduced order model is used to study the nonlinear wave propagation in periodic arrays of asymmetric bilinear couplings and linear elastic layers. Finite element studies reveal distinct band gap behavior of tensile and compressive components of the wave as well as cumulative displacement offset in the layers. This work generates a deeper understanding of the nonlinear mechanisms and dynamic response of delaminations. The modeling approach bridges the gap between the nonlinear mechanism of a contact and its dynamic behavior and uses this understanding to engineer nonlinear phononic materials. The research paves the way to create new engineering materials with prescribed delaminations to control the wave propagation of elastic waves and develop materials for applications such as energy conversion and passive mechanical sensing.

Graduation Semester

2025-08

Type of Resource

Thesis

Handle URL

https://hdl.handle.net/2142/130173

Copyright and License Information

Copyright 2025 Elizabeth Smith

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