Consistent Asymptotic Homogenization Method for Lattice Structures Based on the Virtual Power Principle
Date of Award
Master of Science (MS)
Dr. Lonny Thompson, Committee Chair
Dr. Nicole Coutris
Dr. Paul F. Joseph
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.
Bracho, David, "Consistent Asymptotic Homogenization Method for Lattice Structures Based on the Virtual Power Principle" (2016). All Theses. 2546.