Variational models for prestrained plates with Monge-Ampère constraint

Abstract

We derive a new model for pre-strained thin films, which consists of minimizing a biharmonic energy of deformations $v\in W^{2,2}$ satisfying the Monge-Ampère constraint $\det {\nabla }^{2}v=f$. We further discuss multiplicity properties of the minimizers of this model, in some special cases.

arXiv comment27 pages

References in corpus (5)

• Elastic theory of unconstrained non-Euclidean plates
• The von Karman equations for plates with residual strain
• The Monge-Ampere constrained elastic theories of shallow shells
• Plates with incompatible prestrain of higher order
• A remark on constrained von Karman theories

Cited by in corpus (5)

• Plates with incompatible prestrain of higher order
• Dimension reduction for thin films prestrained by shallow curvature
• LDG approximation of large deformations of prestrained plates
• The linearized Kirchhoff theory for plates with incompatible prestrain
• Dimension reduction for thin films with transversally varying prestrain: the oscillatory and the non-oscillatory case