Constitutive Models for Uniaxially-Post-Buckled Square Lattices

Abstract:

The objective of this paper is to analyse the mechanical stress-strain response of an ini-tially uniaxially-post-buckled periodic structure. This requires selecting a representative volume ele-ment (RVE) that contains all the micro-structural features and responds as the infinite medium when subjected to uniform load and boundary conditions. Selection is done by analysing the stress-strain response for macro-cells of increasing size as well as identifying dominant length scales with a 2D-FFT. For a uniaxially–post buckled square lattice, the RVE is found to be a Y3x3 (3x3 unit cells for the undeformed configuration). A study for the post-buckled behaviour of the pre-stressed RVE, with in-ternal components modelled as long slender beams, beyond elastic buckling is presented. Incremental constitutive models are then formulated analytically and numerically for loads above the critical load.

• Periodical: Advanced Materials Research (Volume 1016)
• Pages: 105-110
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.1016.105
• Online since: August 2014
• Authors: Edgar A. Flores Parra*, Alessandro Spadoni
• Keywords: Incremental Response, Macro-Cell Analysis, Micromechanics, Post-Buckled Lattices

References

[1] Lorna J Gibson and Michael F Ashby. Cellular solids: structure and properties. Cambridge university press, (1999).

[2] Rajesh S Kumar and David L McDowell. Generalized continuum modeling of 2-d periodic cellular solids. International Journal of Solids and Structures, 41(26): 7399-7422, (2004).

DOI: 10.1016/j.ijsolstr.2004.06.038

[3] N Ohno, D Okumura, and T Niikawa. Long-wave buckling of elastic square honey- combs subject to in-plane biaxial compression. International journal of mechanical sciences, 46(11): 1697-1713, (2004).

DOI: 10.1016/j.ijmecsci.2004.09.011

[4] Nicolas Triantafyllidis and William C Schnaidt. Comparison of microscopic and macroscopic instabilities in a class of two-dimensional periodic composites. Journal of the Mechanics and Physics of Solids, 41(9): 1533-1565, (1993).

DOI: 10.1016/0022-5096(93)90039-i

[5] Andrea Vigliotti, Vikram S Deshpande, and Damiano Pasini. Non linear constitutive models for lattice materials. Journal of the Mechanics and Physics of Solids, (2013).

DOI: 10.1016/j.jmps.2013.10.015

[6] Scott D Papka and Stelios Kyriakides. In-plane compressive response and crushing of honey- comb. Journal of the Mechanics and Physics of Solids, 42(10): 1499-1532, (1994).

DOI: 10.1016/0022-5096(94)90085-x

[7] C Felippa. Nonlinear finite element methods (asen 6107), (2012).

[8] Gerhard A Holzapfel. Nonlinear solid mechanics: a continuum approach for engineering. (2000).

[9] Augusto Beléndez Vázquez, Antonio Hernández Prados, Sergi Gallego Rico, Manuel Or-tuño Sánchez, Cristian Neipp López, Tarsicio Beléndez Vázquez, et al. Post-buckling of a can- tilever column: a more accurate linear analysis of a classical nonlinear problem. (2007).

DOI: 10.7227/ijmee.35.4.4

[10] Johannes Tesse Bastiaan Overvelde, Sicong Shan, and Katia Bertoldi. Compaction through buckling in 2d periodic, soft and porous structures: effect of pore shape. Advanced Materials, 24(17): 2337-2342, (2012).

DOI: 10.1002/adma.201104395

[11] Zdeněk P Bažant and Luigi Cedolin. Stability of structures: elastic, inelastic, fracture and damage theories. World Scientific, (2010).

DOI: 10.1142/7828