Bilayer Plates: Model Reduction, Γ‐Convergent Finite Element Approximation, and Discrete Gradient Flow

The bending of bilayer plates is a mechanism that allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed herein, consists of a nonlinear fourth‐order problem with a pointwise isometry constraint. A discretization based on Kirchhoff quadrilaterals is devised and its Γ‐convergence is proved. An iterative method that decreases the energy is proposed, and its convergence to stationary configurations is investigated. Its performance, as well as reduced model capabilities, are explored via several insightful numerical experiments involving large (geometrically nonlinear) deformations.© 2015 Wiley Periodicals, Inc.

• Publication year

  2015

• Venue

  Communications on Pure and Applied Mathematics

• Publication date

  2015-06-10

• Fields of study

  Mathematics, Materials Science, Physics, Engineering

• Identifiers
  DOI 10.1002/cpa.21626arXiv 1506.03335
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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