Derivation of the homogenized von K´arm´an plate theory from 3d elasticity
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
We rigorously derive a homogenized von-Karman plate theory as a G-limit from nonlinear three-dimensional elasticity by combining homogenization and dimension reduction. Our starting point is an energy functional that describes a nonlinear elastic, threedimensional plate with spatially periodic material properties. The functional features two small length scales: the period e of the elastic composite material, and the thickness h of the slender plate. We study the behavior as e and h simultaneously converge to zero in the von-Karman scaling regime. The obtained limit is a homogenized von-Karman plate model. Its effective material properties are determined by a relaxation formula that exposes a non-trivial coupling of the behavior of the out-of-plane displacement with the oscillatory behavior in the in-plane directions. In particular, the homogenized coefficients depend on the relative scaling between h and epsilon, and different values arise for h << epsilon, epsilon similar to h and epsilon << h.
Details
Original language | English |
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Pages (from-to) | 2701-2748 |
Number of pages | 48 |
Journal | Mathematical Models and Methods in Applied Sciences |
Volume | 23 |
Issue number | 14 |
Publication status | Published - Dec 2013 |
Peer-reviewed | Yes |
Externally published | Yes |
External IDs
Scopus | 84885639972 |
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Keywords
Keywords
- Elasticity, dimension reduction, homogenization, von-Karman plate theory, two-scale convergence, DOUBLE-POROSITY MODEL, INTEGRAL FUNCTIONALS, 2-SCALE CONVERGENCE, GAMMA-CONVERGENCE, FLOW