We present a Melan-type theorem applying to cyclically loaded media in which plastic flow and diffusion of guest atoms are coupled, such as electrode materials in lithium-ion batteries. The presented theorem ensures that elastic shakedown occurs (i.e. that the plastic strain stabilizes to a time-independent limit), independently of the initial state. Building on that theorem, a general two-step procedure is presented for designing any given structure against elastic shakedown. As an illustration, that procedure is applied to the model problem of a spherical electrode particle under time-harmonic lithiation.
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