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.
Recommended Citation
Bracho, David, "Consistent Asymptotic Homogenization Method for Lattice Structures Based on the Virtual Power Principle" (2016). All Theses. 2546.
https://open.clemson.edu/all_theses/2546