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Silicon-based anodes are an attractive choice for the future of energy storage. However, mechanical stresses generated during lithiation induce a rapid degradation of the anodes. The coupling between mechanical and (electro)chemical phenomena during lithiation is investigated using Molecular Dynamics simulations. First, the diffusion regime of lithium atoms in the silicon is found to depend drastically on the crystalline orientations and on the applied pressure. Above a threshold pressure, a ballistic motion of lithium along certain crystallographic planes is observed. Second, the local complex stress field generated by the lithiation has been computed using a coarse-graining method including thermal effects. It appears to be strongly dependent on the density of lithium in the lithiated layer, on the temperature, and on the crystalline orientation of the free surface. The resulting very high values of the locally induced pressures can be related to the progressive amorphization of the silicon support.