Plastic yield and collapse mechanism of planar lattice structures

Abstract

Lattice structures possess a huge potential for energy absorbing applications, and the postinitial collapse region should be analyzed with respect to design principles in such cases. This paper presents an analytical method to calculate the ultimate yield surfaces of statically indeterminate planar lattice structures, based on the assessment of static equilibrium of the unit cell before and after initial yielding. The material of the unit cell wall is assumed to be elastic, perfectly plastic. Three statically indeterminate planar lattice structures: the diamond cross cell, the statically-indeterminate square cell (SI-square cell), the new Kagome cell (N-Kagome), are analyzed. The parametric studies reveal the roles of various geometrical parameters on the performance of each structure. The SI-square cell is utilized as an example to demonstrate the evolution of structural yielding, thus providing an insight into the collapse mode of lattice structures. Furthermore, the stress-strain relationships of the SI-square and N-Kagome cells are also calculated, and the effective constitutive relations of both lattices are found to be linearly hardening, which is validated by finite element (FE) simulations.