Homogenization Methods of Lattice Materials

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Jo, B. Homogenization Methods of Lattice Materials. Encyclopedia. Available online: https://encyclopedia.pub/entry/23651 (accessed on 19 May 2024).

Jo B. Homogenization Methods of Lattice Materials. Encyclopedia. Available at: https://encyclopedia.pub/entry/23651. Accessed May 19, 2024.

Jo, Bruce. "Homogenization Methods of Lattice Materials" Encyclopedia, https://encyclopedia.pub/entry/23651 (accessed May 19, 2024).

Jo, B. (2022, June 01). Homogenization Methods of Lattice Materials. In Encyclopedia. https://encyclopedia.pub/entry/23651

Jo, Bruce. "Homogenization Methods of Lattice Materials." Encyclopedia. Web. 01 June, 2022.

Peer Reviewed

Homogenization Methods of Lattice Materials

This is a peer-reviewed entry published in Encyclopedia Journal, full entry can be found at 10.3390/encyclopedia2020072

The existing methods for analyzing the behaviors of lattice materials require high computational power. The homogenization method is the alternative way to overcome this issue. Homogenization is an analysis to understand the behavior of an area of lattice material from a small portion for rapid analysis and precise approximation. This paper provides a summary of some representative methodologies in homogenization.

homogenization method lattice materials periodic cellular materials multi-scale mechanics

The homogenization approach is based on the idea that the properties of a heterogeneous medium can be determined by analyzing a small portion of it ^[1]. In other words, Representative Volume Element (RVE) is a sample for the entire area. It needs to be underlined that the RVE includes the micro-structural property of effective materials and expands to the global domain, where uniformly applied strain or stress exists with a boundary condition ^[1]^[2]^[3], which does not require extensive and full-scale simulations. Meanwhile, this strategy is only applicable when the homogeneities are dual orders of magnitude that are below the effective medium’s characteristic length ^[1]^[2]^[3].

The idea of lattice material homogenization is represented where the RVE is a square unit cell. A body Ω with a periodic lattice with a t at the traction boundary

Γ_{t}

, a displacement d at the displacement boundary

Γ_{d}

, and a body force f is inserted by a homogenized body

\bar{Ω}

. The mechanical properties of RVE are to be determined by the macroscopic behavior of Ω and

\bar{Ω}

are equivalent ^[1].

References

Phani, A.S.; Hussein, M.I. Dynamics of Lattice Materials; Wiley Online Library: Hoboken, NJ, USA, 2017.
Yan, J.; Cheng, G.; Liu, S.; Liu, L. Comparison of prediction on effective elastic property and shape optimization of truss material with periodic microstructure. Int. J. Mech. Sci. 2006, 48, 400–413.
Xia, Z.; Zhou, C.; Yong, Q.; Wang, X. On selection of repeated unit cell model and application of unified periodic boundary conditions in micro-mechanical analysis of composites. Int. J. Solids Struct. 2006, 43, 266–278.

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Subjects: Crystallography

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Bruce Jo

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Online Date: 01 Jun 2022

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