Microscale modeling of kinking nonlinear elastic solids

Recently we identified and classified a class of solids as kinking nonlinear elastic (KNE) because they deform by the formation of kink bands. KNE solids represent a large family that include, among others, layered ternary carbides and nitrides, layered oxides and semiconductors, zinc, cadmium, graphite, ice, and the layered silicates, such as mica, present in nonlinear mesoscopic elastic solids. Herein we present a microscale model that accounts for the mechanical response of KNE solids to compressive stresses and apply it to two very different solids: Ti3SiC2 and graphite. Building on the Frank and Stroh model put forth in the 1950's for the formation of kink bands, we developed a comprehensive theory that accounts for the contributions of incipient kink bands (IKBs) and dislocations pile-ups produced by normal glide processes to the nonlinear strains and stored strain energies. The theory provides estimates for the densities of IKBs, the dislocation densities, both from the IKBs and dislocation pileups, as well as the energy dissipated by the motion of the dislocations.