Date of Award

12-2016

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering

Committee Member

Dr. Lonny Thompson, Committee Chair

Committee Member

Dr. Nicole Coutris

Committee Member

Dr. Paul F. Joseph

Abstract

The properties of mechanical meta-materials in the form of a periodic lattice have drawnthe attention of researchers in the area of material design. Computational methods for solvingelasticity problems that involve a large number of repeating structures, such as the ones presentin lattice materials, is often impractical since it needs a considerable amount of computationalresources. Homogenization methods aim to facilitate the modeling of lattice materials by definingequivalent effective properties. Various approaches can be found in the literature, but few followa consistent methodology applicable to any lattice geometry. In the present work, the asymptotichomogenization method developed by Caillerie and lated by Dos Reis is examined, which follows aconsistent derivation of effective properties by use of the virtual power principle progressively from abeam, to a cell and finally to the cluster of cells forming the lattice. Because of the scale separationbetween the small scale of the unit cell and the large scale of the lattice domain, the asymptotichomogenization method can be used. It is shown that the virtual power of the continuum resultingfrom this analysis is that of micropolar elasticity. The method is implemented to obtain effectiveproperties for different lattices: a square, triangular, hexagonal (“honeycomb”), “kagome” and asimple chiral lattice topology. Finally, results are compared with effective properties of similarlattices found in other studies.

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