Homogenization and equivalent in-plane properties of two-dimensional periodic lattices

By Stefano Gonella, Massimo Ruzzene. 2008

204 citations recorded by the source corpus.

Abstract The equivalent in-plane properties for hexagonal and re-entrant (auxetic) lattices are investigated through the analysis of partial differential equations associated with their homogenized continuum models. The adopted homogenization technique interprets the discrete lattice equations according to a finite differences formalism, and it is applied in conjunction with the finite element description of the lattice unit cell. It therefore allows handling of structures with different levels of complexity and internal geometry within a general and compact framework, which can be easily implemented. The estimation of the mechanical properties is carried out through a comparison between the derived differential equations and appropriate elasticity models. Equivalent Young’s moduli, Poisson’s ratios and relative density are estimated and compared with analytical formulae available in the literature. In-plane wave propagation characteristics of honeycombs are also investigated to evaluate phase velocity variation in terms of frequency and direction of propagation. Comparisons are performed with the values obtained through the application of Bloch theorem for two-dimensional periodic structures, to show the accuracy of the technique and highlight limitations introduced by the long wavelength approximation associated with the homogenization technique.

Subfields: Biomedical Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/ef9a370a425a11fe2198e984e12f7a6346802b60

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In Biomedical Engineering

In Mechanical Engineering

Citations in the corpus

Mechanical properties of 3D re-entrant honeycomb auxetic structures realized via additive manufacturing (2015, background): “Furthermore, when boundary effects could be minimized, analytical modeling also possesses an advantage over the homogenization methods due to the closed-form expressions (Gonella and Ruzzene, 2008; Spadoni and Ruzzene, 2012).”
Equivalent models of corrugated panels (2012, background): “, 2011), topology optimisation (Allaire, 2001; Bendsoe and Kikuchi, 1998) and waves propagation in periodic media (Ruzzene and Baz, 2000; Andrianov et al., 2008; Gonella and Ruzzene, 2008).”
Strain gradient and generalized continua obtained by homogenizing frame lattices (2018, result): “This result differs from the ones given in [54], [53] or [44] where very similar discrete systems are studied.”
Stiffness and strength of tridimensional periodic lattices (2012, background): “Gonella and Ruzzene [16] studied the in-plane properties of hexagonal and auxetic lattices and derived the parameters of the equivalent continuum by comparing the coefficients of the in-plane wave equations of a discrete lattice to those of an equivalent continuum model.”