To have a better protection, strong toughness and good flexibility, all lives and plants must have skins, similarly, all books should have covers. In this paper, we follow in the footsteps of Poincloux et al. [Phy.Rev.Lett. 126, 218004 (2021)] and extend their centerline-based theory from books without covers to hardcover books with internal friction. Our investigations show that the hardcover are more essential than the core layers in terms of bending response as well as energy absorption. The central goal of studying the covered book is not only to predict the bending deformation of the books, but also as a representative case to help finding some clue on the universal behaviours of multilayered architectures with internal friction.
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