We investigate failure of particulate materials with constituents having rotational degrees of freedom and producing moment stresses. We show that micro tensile stresses in the inter-particle links bent due to particle relative rotations are the dominant stresses mode. Analysis and discrete element modelling show that rolling of compound particles (grouping of two spherical particles) produces apparent negative stiffness. We also identify a new, momentarily emerging, negative stiffness during the formation of crack or bond breakage. This, transitional negative stiffness, increases the Poisson's ratio to the critical values corresponding to elastic instability, which forms a mechanism of strain localisation.