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Abstract: We study non-convex elastic energy functionals associated to spatiallyperiodic, frame indifferent energy densities with a single non-degenerateenergy well at SOn. Under the assumption that the energy density admits aquadratic Taylor expansion at identity, we prove that the Gamma-limitsassociated to homogenization and linearization commute. Moreover, we show thatthe homogenized energy density, which is determined by a multi-cellhomogenization formula, has a quadratic Taylor expansion with a quadratic termthat is given by the homogenization of the quadratic term associated to thelinearization of the initial energy density.



Author: Stefan Müller, Stefan Neukamm

Source: https://arxiv.org/







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