We present the mechanics of folding surface-layer wrinkles on a soft substrate, i.e. inter-touching of neighbouring wrinkle surfaces without forming a cusp. Upon laterally compressing a stiff layer attached on a finite-elastic substrate, certain material nonlinearities trigger a number of bifurcation processes to form multi-mode wrinkle clusters. Some of these clusters eventually develop into folded wrinkles. The first bifurcation of the multi-mode wrinkles is investigated by a perturbation analysis of the surface-layer buckling on a pre-stretched neo-Hookean substrate. The post-buckling equilibrium configurations of the wrinkles are then trailed experimentally and computationally until the wrinkles are folded. The folding process is observed at various stages of wrinkling, by sectioning 20–80 nm thick gold films deposited on a polydimethylsiloxane substrate at a stretch ratio of 2.1. Comparison between the experimental observation and the finite-element analysis shows that the Ogden model deformation of the substrate coupled with asymmetric bending of the film predicts the folding process closely. In contrast, if the bending stiffness of the film is symmetric or the substrate follows the neo-Hookean behaviour, then the wrinkles are hardly folded. The wrinkle folding is applicable to construction of long parallel nano/micro-channels and control of exposing functional surface areas.
Abstract Mechanical degradation and resultant capacity fade in high-capacity electrode materials critically hinder their use in high-performance rechargeable batteries. Despite tremendous efforts devoted to the study of the electro–chemo–mechanical behaviours of high-capacity electrode materials, their fracture properties and mechanisms remain largely unknown. Here we report a nanomechanical study on the damage tolerance of electrochemically lithiated silicon. Our in situ transmission electron microscopy experiments reveal a striking contrast of brittle fracture in pristine silicon versus ductile tensile deformation in fully lithiated silicon. Quantitative fracture toughness measurements by nanoindentation show a rapid brittle-to-ductile transition of fracture as the lithium-to-silicon molar ratio is increased to above 1.5. Molecular dynamics simulations elucidate the mechanistic underpinnings of the brittle-to-ductile transition governed by atomic bonding and lithiation-induced toughening. Our results reveal the high damage tolerance in amorphous lithium-rich silicon alloys and have important implications for the development of durable rechargeable batteries.
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