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

Homogenization of the incremental response of grids made up of 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 these structural elements buckle only under compression.