a b s t r a c tRecent advances in lithium-ion battery electrodes with huge volume changes during intercalation-deintercalation cycles are calling for studies on crack nucleation under diffusion induced stresses. Here we develop a cohesive model of crack nucleation in an initially crack-free strip electrode under galvanostatic intercalation and deintercalation processes. The analysis identifies a critical characteristic dimension below which crack nucleation becomes impossible. The critical size and other predictions of the model are compared to recent experiments on silicon nanowire electrodes. The results suggest nanostructured electrodes are highly promising for applications in high capacity batteries.

a b s t r a c tWe have recently modeled crack nucleation in a 2D strip electrode as localization of a periodic array of cohesive zones subject to diffusion induced stresses in an initially crack-free thin strip under galvanostatic solute insertion and extraction. Here we generalize this model to crack nucleation in a cylindrical electrode under axisymmetric diffusion induced stresses, focusing on the effect of the cylindrical geometry on the crack nucleation condition. Similar to our previous findings for the 2D strip geometry, the present analysis identifies a critical electrode size, typically in the nanometer range, to avoid crack nucleation.

Spatially overlapping plates in tiled configurations represent designs that are observed widely in nature (e.g., fish and snake scales) and man-made systems (e.g., shingled roofs) alike. This imbricate architecture offers fault-tolerant, multifunctional capabilities, in layouts that can provide mechanical flexibility even with full, 100% areal coverages of rigid plates. Here, the realization of such designs in microsystems technologies is presented, using a manufacturing approach that exploits strategies for deterministic materials assembly based on advanced forms of transfer printing. The architectures include heterogeneous combinations of silicon, photonic, and plasmonic scales, in imbricate layouts, anchored at their centers or edges to underlying substrates, ranging from elastomer sheets to silicon wafers. Analytical and computational mechanics modeling reveal distributions of stress and strain induced by deformation, and provide some useful design rules and scaling laws.