scholarly journals 3D Hierarchical Lattice Ferroelectric Metamaterials

2020 ◽  
Author(s):  
Jiahao Shi ◽  
Hamid Akbarzadeh
Keyword(s):  
Hierarchical Lattice

scholarly journals A random hierarchical lattice: the series-parallel graph and its properties

2004 ◽  
Vol 36 (03) ◽  
pp. 824-838 ◽  
Author(s):  
B. M. Hambly ◽  
Jonathan Jordan
Keyword(s):  
Phase Transition ◽  
Random Graphs ◽  
Effective Resistance ◽  
First Passage Percolation ◽  
Hierarchical Lattice ◽  
First Passage ◽  
In Series ◽  
Parallel Graph

We consider a sequence of random graphs constructed by a hierarchical procedure. The construction replaces existing edges by pairs of edges in series or parallel with probability p. We investigate the effective resistance across the graphs, first-passage percolation on the graphs and the Cheeger constants of the graphs as the number of edges tends to infinity. In each case we find a phase transition at

Design of composite lattice materials combined with fabrication approaches

2018 ◽  
Vol 53 (3) ◽  
pp. 393-404 ◽  
Author(s):  
Jun Xu ◽  
Yaobo Wu ◽  
Xiang Gao ◽  
Huaping Wu ◽  
Steven Nutt ◽  
...  
Keyword(s):  
Shear Strength ◽  
Mechanical Performance ◽  
Analytical Models ◽  
Core Material ◽  
Foam Core ◽  
Hierarchical Lattice ◽  
Bottom Up ◽  
Lattice Materials ◽  
Assembly Technique ◽  
Composite Lattice

Lattice materials can be designed through their microstructure while concurrently considering fabrication feasibility. Here, we propose two types of composite lattice materials with enhanced resistance to buckling: (a) hollow lattice materials fabricated by a newly developed bottom-up assembly technique and the previously developed thermal expansion molding technique and (b) hierarchical lattice materials with foam core sandwich trusses fabricated by interlocking assembly process. The mechanical performance of sandwich structures featuring the two types of lattice cores was tested and analyzed theoretically. For hollow lattice core material, samples from two different fabrication processes were compared and both failed by nodal rupture or debonding. In contrast, hierarchical lattice structures failed by shear buckling without interfacial failure in the sandwich struts. Calculations using established analytical models indicated that the shear strength of hollow lattice cores could be optimized by judicious selection of the thickness of patterned plates. Likewise, the shear strength of hierarchical foam core truss cores could be maximized (with minimal weight) through design of truss geometry. The bottom-up assembly technique could provide a feasible way for mass production of lattice cores, but the design about how to assembly is critical. Hierarchical lattice cores with foam sandwich trusses should be a suitable choice for future lightweight material application.

scholarly journals Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 678
Author(s):  
Zijun Wu ◽  
Renbin Xiao
Keyword(s):  
Topology Optimization ◽  
High Efficiency ◽  
Spline Interpolation ◽  
Optimization Method ◽  
Optimality Criteria ◽  
Lattice Structures ◽  
Hierarchical Lattice ◽  
B Spline ◽  
Design Variables ◽  
Optimality Criteria Method

This work presents a topology optimization method for symmetric hierarchical lattice structures with substructuring. In this method, we define two types of symmetric lattice substructures, each of which contains many finite elements. By controlling the materials distribution of these elements, the configuration of substructure can be changed. And then each substructure is condensed into a super-element. A surrogate model based on a series of super-elements can be built using the cubic B-spline interpolation. Here, the relative density of substructure is set as the design variable. The optimality criteria method is used for the updating of design variables on two scales. In the process of topology optimization, the symmetry of microstructure is determined by self-defined microstructure configuration, while the symmetry of macro structure is determined by boundary conditions. In this proposed method, because of the educing number of degree of freedoms on macrostructure, the proposed method has high efficiency in optimization. Numerical examples show that both the size and the number of substructures have essential influences on macro structure, indicating the effectiveness of the presented method.

scholarly journals Synchronization of Phase Oscillators on the Hierarchical Lattice

2018 ◽  
Vol 174 (1) ◽  
pp. 188-218 ◽  
Author(s):  
D. Garlaschelli ◽  
F. den Hollander ◽  
J. M. Meylahn ◽  
B. Zeegers
Keyword(s):  
Phase Oscillators ◽  
Hierarchical Lattice

scholarly journals Frustrated Ising Model on a Diamond Hierarchical Lattice

2009 ◽  
Vol 78 (7) ◽  
pp. 074004 ◽  
Author(s):  
Hiroyuki Kobayashi ◽  
Yoshiyuki Fukumoto ◽  
Akihide Oguchi
Keyword(s):  
Ising Model ◽  
Hierarchical Lattice ◽  
Diamond Hierarchical Lattice

scholarly journals On the extendedness of eigenstates in a hierarchical lattice: A critical view

2011 ◽  
Vol 151 (24) ◽  
pp. 1894-1898 ◽  
Author(s):  
Biplab Pal ◽  
Arunava Chakrabarti ◽  
Nitai Bhattacharya
Keyword(s):  
Hierarchical Lattice ◽  
Critical View

scholarly journals A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures

2016 ◽  
Vol 90 ◽  
pp. 179-202 ◽  
Author(s):  
Qiang Ma ◽  
Huanyu Cheng ◽  
Kyung-In Jang ◽  
Haiwen Luan ◽  
Keh-Chih Hwang ◽  
...  
Keyword(s):  
Nonlinear Mechanics ◽  
Hierarchical Lattice ◽  
Mechanics Model ◽  
Lattice Materials
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