The mechanics of films undergoing volume expansion on curved substrates plays a key role in a variety of technologies including biomedical implants, thermal and environmental barrier coatings, and electrochemical energy storage systems. Silicon anodes for lithium-ion batteries are an especially challenging case because they can undergo volume variations up to 300% that results in cracking, delamination, and thus significant loss in performance. In this study, we use finite element analysis to model the volume expansion during lithiation for silicon coated on spinodal, inverse opal, gyroid, and Schwartz primitive nickel backbones and compare the distributions of maximum principal stress, strain energy density, and von Mises stress, which we use as indicators for propensity for cracking, delamination, and yielding, in order to explore the effect of backbone morphology on mechanical degradation during expansion. We show that, when compared to the inverse opal, the spinodal morphology reduces and uniformly distributes the maximum principal stress and strain energy density in the silicon layer, and delays the onset of expansion-induced yielding at all silicon layer thicknesses, which we ascribe to the unique interfacial curvature distribution of spinodal structures. This work highlights the importance of morphology on coatings undergoing volume variations and unveils the particular promise of spinodally derived materials for the design of next generation lithium-ion battery electrodes.