While the high capacity of silicon makes it an attractive negative electrode for Li-ion batteries, the associated large volume change results in fracture and capacity fade. Composite electrodes incorporating silicon have additional complexity, as active material is attached to surrounding material which must likewise experience significant volume change. In this paper, a finite-deformation model is used to explore, for the first time, mechanical interactions between a silicon particle undergoing lithium insertion, and attached binder material. Simulations employ an axisymmetric model system in which solutions vary in two spatial directions and shear stresses develop at interfaces between materials. The mechanical response of the amorphous active material is dependent on lithium concentration, and an equation of state incorporating reported volume expansion data is used. Simulations explore the influence of active material size and binder stiffness, and suggest delamination as an additional mode of material damage. Computed strain energies and von Mises equivalent stresses are in physically-relevant ranges, comparable to reported yield stresses and adhesion energies, and predicted trends are largely consistent with reported experimental results. It is hoped that insights from this work will support the design of more robust silicon composite electrodes.