This note is about a novel, thermodynamically consistent formulation for small strains continuum electro-chemo-mechanics applied to all solid state batteries, which are claimed to be the next-generation battery system in view of their safety accompanied by high energy densities. The response of a cell, made of a lithium metal foil, a solid electrolyte, and a porous LiCoO2 cathode, has been investigated in terms of quantities of interest such as the electric potential, the lithium concentrations profiles, displacements, and stresses. The plating and stripping of the lithium has been considered together with the volumetric evolution of the porous cathode. Together they contribute to the outbreak of mechanical stresses, which may influence the life cycle of a battery.
