Hierarchical analysis and multiscale modelling of cellular structures: From meta materials to bone structure

Oftadeh, Ramin. 
 Northeastern University ProQuest Dissertations Publishing,  2016. 10116198.

Abstract (summary)

Materials with structural hierarchy over nanometer to millimeter length scales are found throughout Kingdoms Plantae and Animalia. The idea of using structural hierarchy in engineering structures and materials goes back at least to Eiffel’s Garabit Viaduct and then Tower. Incorporating hierarchy into honeycomb lattice structures has been the focus of a number of studies and has significance with regard to the application of honeycombs in impact energy absorption and structural protection, thermal isolation and as the structural core of sandwich panels. Here we explore the mechanical properties of two kind of cellular structures: hierarchical honeycombs and trabecular bone.

Hexagonal honeycomb structures are known for their high strength and low weight. We construct a new class of fractal-appearing cellular metamaterials by replacing each three-edge vertex of a base hexagonal network with a smaller hexagon and iterating this process. The mechanical properties of the structure after different orders of the iteration are optimized. We find that the optimal structure (with highest in-plane stiffness for a given weight ratio) is self-similar but requires higher order hierarchy as the density vanishes. These results offer insights into how incorporating hierarchy in the material structure can create low-density metamaterials with desired properties and function.

The second aim of this study was to explore the hierarchical arrangement of structural properties in cortical and trabecular bone and to determine a mathematical model that accurately predicts the tissue’s mechanical properties as a function of these indices. By using a variety of analytical techniques, we were able to characterize the structural and compositional properties of cortical and trabecular bones, as well as to determine the suitable mathematical model to predict the tissue’s mechanical properties using a continuum micromechanics approach. Our hierarchical analysis demonstrated that the differences between cortical and trabecular bone reside mainly at the micro- and ultrastructural levels. By gaining a better appreciation of the similarities and differences between the two bone types, we would be able to provide a better assessment and understanding of their individual roles, as well as their contribution to bone health overall.

Keywords: structural hierarchy; anisotropy; honeycombs; cellular structures; cortical and trabecular bone; hierarchical analysis; continuum micromechanics; bone mechanical properties; bone composition and structure

Indexing (details)

Mechanical engineering;
0346: Mechanics
0548: Mechanical engineering
0648: Biomechanics
Identifier / keyword
Biological sciences; Applied sciences; Bone composition; Bone structure; Cellular structures; Cortical bone; Structural hierarchy; Trabecular bone
Hierarchical analysis and multiscale modelling of cellular structures: From meta materials to bone structure
Oftadeh, Ramin
Number of pages
Degree date
School code
DAI-B 77/11(E), Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
Vaziri, Ashkan; Nazarian, Ara
Committee member
Nazarian, Ara; Neyeb Hashemi, Hamid; Vaziri, Ashkan
Northeastern University
Mechanical and Industrial Engineering
University location
United States -- Massachusetts
Source type
Dissertation or Thesis
Document type
Dissertation/thesis number
ProQuest document ID
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL