Tensile material instabilities in elastic beam lattices lead to a bounded stability domain

Abstract

Homogenization of the incremental response of grids made up of preloaded elastic rods leads to homogeneous effective continua which may suffer macroscopic instability, occurring at the same time in both the grid and the effective continuum. This instability corresponds to the loss of ellipticity in the effective material and the formation of localized responses as, for instance, shear bands. Using lattice models of elastic rods, loss of ellipticity has always been found to occur for stress states involving compression of the rods, as usually these structural elements only buckle under compression. In this way, the locus of material stability for the effective solid is unbounded in tension, i.e. the material is always stable for a tensile prestress. A rigorous application of homogenization theory is proposed to show that the inclusion of sliders (constraints imposing axial and rotational continuity, but allowing shear jumps) in the grid of rods leads to loss of ellipticity in tension, so that the locus for material instability becomes bounded. This result explains (i.) how to design elastic materials passible of localization of deformation and shear banding for all radial stress paths; (ii.) how for all these paths a material may fail by developing strain localization and without involving cracking.

Topology Morphing in Lattice Structures Through Tensile Buckling

“…The elastica of such a structure, derived using analytical expressions, are in good agreement with the experimental observations [23]. Ongoing work has paid considerable attention to utilizing sliding elements and the tensile buckling phenomenon as constituents in the design of structures that are mainly subjected to tensile loads [24][25][26][27][28][29][30]. Employing tensile buckling in (meta-)material/structural design paves a new way to control the elastic characteristics at large deformations where plastic or catastrophic failure of the constituent materials would normally have occurred.…”