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Magnetar flares generate Alfv\'en waves bouncing in the closed magnetospherewith energy up to $\sim 10^{46}$ erg. We show that on a 10-ms timescale thewaves are transmitted into the star and form a compressed packet of high energydensity. This packet strongly shears the stellar crust and initiates a plasticflow, heating the crust and melting it hundreds of meters below the surface. Afraction of the deposited plastic heat is eventually conducted to the stellarsurface, contributing to the surface afterglow months to years after the flare.A large fraction of heat is lost to neutrino emission or conducted into thecore of the neutron star.

Plastic damping of Alfv\'en waves in magnetar flares and delayed afterglow emission