Effective property evaluation and analysis of three-dimensional periodic lattices and composites through Bloch-wave homogenization

Ganesh U. Patil, Kathryn Matlack

Research output: Contribution to journalArticle

Abstract

Periodic lattices offer enhanced mechanical and dynamic properties per unit mass, and the ability to engineer the material response by optimizing the unit cell. Characterizing the effective properties of these lattice materials through experiments can be a time consuming and costly process, so analytical and numerical methods are crucial. Specifically, the Bloch-wave homogenization approach allows one to characterize the effective static properties of the lattice while simultaneously analyzing wave propagation properties such as band gaps, propagating modes, and wave directionality. While this analysis has been used for some time, a thorough study of this approach on three-dimensional (3D) lattice materials with different symmetries and geometries is presented here. Bloch-wave homogenization is applied to extract the effective stiffness tensor of 3D periodic lattices and confirmed with elastostatic homogenization, both within a finite element framework. Multiple periodic lattices with cubic, transversely isotropic, and tetragonal symmetry, including an auxetic geometry, over a wide range of relative densities are analyzed. Further, this approach is used to analyze 3D periodic composite structures, and a way to tailor their overall anisotropy is demonstrated. This work can serve as the basis for nondestructive evaluation of metamaterials properties using ultrasonic velocity measurements.

Original languageEnglish (US)
Pages (from-to)1259-1269
Number of pages11
JournalJournal of the Acoustical Society of America
Volume145
Issue number3
DOIs
StatePublished - Mar 1 2019

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homogenizing
composite materials
evaluation
elastostatics
composite structures
symmetry
geometry
velocity measurement
dynamic characteristics
engineers
Three-dimensional
Waves
Evaluation
Homogenization
wave propagation
stiffness
ultrasonics
mechanical properties
tensors
anisotropy

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics

Cite this

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abstract = "Periodic lattices offer enhanced mechanical and dynamic properties per unit mass, and the ability to engineer the material response by optimizing the unit cell. Characterizing the effective properties of these lattice materials through experiments can be a time consuming and costly process, so analytical and numerical methods are crucial. Specifically, the Bloch-wave homogenization approach allows one to characterize the effective static properties of the lattice while simultaneously analyzing wave propagation properties such as band gaps, propagating modes, and wave directionality. While this analysis has been used for some time, a thorough study of this approach on three-dimensional (3D) lattice materials with different symmetries and geometries is presented here. Bloch-wave homogenization is applied to extract the effective stiffness tensor of 3D periodic lattices and confirmed with elastostatic homogenization, both within a finite element framework. Multiple periodic lattices with cubic, transversely isotropic, and tetragonal symmetry, including an auxetic geometry, over a wide range of relative densities are analyzed. Further, this approach is used to analyze 3D periodic composite structures, and a way to tailor their overall anisotropy is demonstrated. This work can serve as the basis for nondestructive evaluation of metamaterials properties using ultrasonic velocity measurements.",
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N2 - Periodic lattices offer enhanced mechanical and dynamic properties per unit mass, and the ability to engineer the material response by optimizing the unit cell. Characterizing the effective properties of these lattice materials through experiments can be a time consuming and costly process, so analytical and numerical methods are crucial. Specifically, the Bloch-wave homogenization approach allows one to characterize the effective static properties of the lattice while simultaneously analyzing wave propagation properties such as band gaps, propagating modes, and wave directionality. While this analysis has been used for some time, a thorough study of this approach on three-dimensional (3D) lattice materials with different symmetries and geometries is presented here. Bloch-wave homogenization is applied to extract the effective stiffness tensor of 3D periodic lattices and confirmed with elastostatic homogenization, both within a finite element framework. Multiple periodic lattices with cubic, transversely isotropic, and tetragonal symmetry, including an auxetic geometry, over a wide range of relative densities are analyzed. Further, this approach is used to analyze 3D periodic composite structures, and a way to tailor their overall anisotropy is demonstrated. This work can serve as the basis for nondestructive evaluation of metamaterials properties using ultrasonic velocity measurements.

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