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The problem governing the transient deformation of an elastic cantilever beam with viscoelastic coating, subjected to a time-dependent coating eigenstrain, is mathematically formulated. An analytical solution for an exponential eigenstrain history, exact within the context of beam theory, is obtained in terms of the coating and base layer thicknesses, the elastic modulus of the base material, the initial coating modulus, the coating relaxation percentage ͑0%-100%͒, and the time constants of thedoi:10.1063/1.3148291 fatcat:prn3wrdcmvcn7i6ulduuhzmipy