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Homogenization of the incremental response of grids made up of preloadedelastic rods leads to homogeneous effective continua which may suffermacroscopic instability, occurring at the same time in both the grid and theeffective continuum. This instability corresponds to the loss of ellipticity inthe effective material and the formation of localized responses as, forinstance, shear bands. Using lattice models of elastic rods, loss ofellipticity has always been found to occur for stress states involvingcompression of the rods, as usually these structural elements buckle only undercompression. In this way, the locus of material stability for the effectivesolid is unbounded in tension, i.e. the material is always stable for a tensileprestress. A rigorous application of homogenization theory is proposed to showthat the inclusion of sliders (constraints imposing axial and rotationalcontinuity, but allowing shear jumps) in the grid of rods leads to loss ofellipticity in tension, so that the locus for material instability becomesbounded. This result explains (i.) how to design elastic materials passible oflocalization of deformation and shear banding for all radial stress paths;(ii.) how for all these paths a material may fail by developing strainlocalization and without involving cracking.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

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