The linearized Kirchhoff theory for plates with incompatible prestrain

Abstract

In this paper, we derive a linearized Kirchhoff model from three dimensional nonlinear elastic energy of plates with incompatible prestrain as its thickness $h$ tends to zero and its elastic energy scales like $h^{\beta }$ with $2<\beta <4.$ The incompatible prestrain is given as a Riemannian metric $G(x^{\prime })$ in the three dimensional thin plate which only depends on mid-plate of the thin plates. The problem is studied rigorously by using a variational approach and establishing the $\Gamma -$ limit of the non-Euclidean version of the nonlinear elasticity functional when the gauss curvature of the mid-plate $(\Omega ,g=G_{2\times 2})$ is always positive, negative or zero.

arXiv commentarXiv admin note: text overlap with arXiv:1503.08845, arXiv:1910.00404 by other authors

References in corpus (5)

• Elastic theory of unconstrained non-Euclidean plates
• Variational models for prestrained plates with Monge-Ampère constraint
• The Monge-Ampere constrained elastic theories of shallow shells
• Space of Infinitesimal Isometries and Bending of Shells
• Linear Strain Tensors and Optimal Exponential of thickness in Korn's Inequalities for Hyperbolic Shells