Research Papers

Continuum Models for the Plastic Deformation of Octet-Truss Lattice Materials Under Multiaxial Loading

[+] Author and Article Information
Jong Wan Hu

Assistant Professor
Department of Civil and Environmental
University of Incheon,
Incheon 406-840,Republic of Korea

Taehyo Park

Department of Civil and Environmental
Hanyang University,
Seoul 133-791,Republic of Korea

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the Journal of Engineering Materials and Technology. Manuscript received May 28, 2012; final manuscript received November 30, 2012; published online March 25, 2013. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 135(2), 021004 (Mar 25, 2013) (11 pages) Paper No: MATS-12-1114; doi: 10.1115/1.4023772 History: Received May 28, 2012; Revised November 30, 2012

The continuum models that take plastic material behavior into consideration are derived to analyze periodic octet-truss lattice materials under multiaxial loading. The main focus of this study is to investigate the basic topology of unit cell structures having the cubic symmetry and to formulate the analytical models for predicting pressure load-dependent stress surfaces accurately. The discrete lattice materials are converted into equivalent model continua that are obtained by physically homogenizing the property of the unit cell structures. The effective continuum models contain information on the mechanical characteristics of internal truss members with respect to axial stiffness, internal stress variable, structural packing, and material density at the microscale level. With the hardening material model introduced in the homogenization process, the plastic flow acting on the microscopic truss members gives rise to extend the elastic domain of the analytical stress function derived from homogenize constitutive equations at the macroscale level. Analytical stress predictions show excellent agreements with the results obtained from finite element (FE) analyses.

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Fig. 1

Basic topology for the tetrahedral unit cell element

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Fig. 3

Octet-truss unit cell structure with the cubic symmetry

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Fig. 2

Octet-truss lattice material fabricated by packing unit cell structures

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Fig. 4

Decomposition of the homogenization procedure

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Fig. 5

Truss-lattice materials under either uniaxial loading or multiaxial loading

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Fig. 6

General failure criteria according to stress-strain models

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Fig. 7

Stress-strain relationships at the microscale level

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Fig. 8

Performance levels of microscale stress

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Fig. 9

FE modeling for the unit cell structure and deformation shape under uniaxial loading

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Fig. 10

Plastic surface at the axial-axial (ii-jj) space for the octet-truss unit cell elements

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Fig. 11

Plastic surface at the axial-shear (ii-ij) space for the octet-truss unit cell elements

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Fig. 12

Force equivalence between FE test and analytical prediction for the octet unit cell under uniaxial loading



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