On the Commutability of Homogenization and Linearization in Finite Elasticity
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Contributors
Abstract
We consider a family of non-convex integral functionals 1/h(2) integral(Omega) W(x/epsilon, Id +h del g(x)) dx, g is an element of W-1,W-p (Omega; R-n) where W is a Carath,odory function periodic in its first variable, and non-degenerate in its second. We prove under suitable conditions that the I"-limits corresponding to linearization (h -> 0) and homogenization (epsilon -> 0) commute, provided W is minimal at the identity and admits a quadratic Taylor expansion at the identity. Moreover, we show that the homogenized integrand, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the second variation of W.
Details
Original language | English |
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Pages (from-to) | 465-500 |
Number of pages | 36 |
Journal | Archive for rational mechanics and analysis |
Volume | 201 |
Issue number | 2 |
Publication status | Published - Aug 2011 |
Peer-reviewed | Yes |
Externally published | Yes |
External IDs
Scopus | 79960580409 |
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Keywords
Keywords
- DERIVATION, LIMIT