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Constitutive Models for Uniaxially-Post-Buckled Square Lattices

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.