不可压缩的 von Kármán 理论用于薄预应力板

关于变厚度弹性预应变薄膜的Föppl-von Kármán理论

On the Föppl-von Kármán theory for elastic prestrained films with varying thickness

本文利用Γ-收敛将Föppl-von Kármán理论推广至变厚度预应变薄膜，推导极限能量、Euler-Lagrange方程及平衡收敛性，揭示中面变形与生长张量的关联。

Dimension reduction for thin films prestrained by shallow curvature

We are concerned with the dimension reduction analysis for thin three-dimensional elastic films, prestrained via Riemannian metrics with weak curvatures. For the prestrain inducing the incompatible version of the Föppl-von Kármán equations, we find the $Γ$-limits of the rescaled energies, identify the optimal energy scaling laws, and display the equivalent conditions for optimality in terms of both the prestrain components and the curvatures of the related Riemannian metrics. When the stretching-inducing prestrain carries no in-plane modes, we discover similarities with the previously describe…

Convergence of Equilibria for Incompressible Elastic Plates in the von Kármán Regime

We prove convergence of critical points $u^h$ of the nonlinear elastic energies $E^h$ of thin incompressible plates $Ω^h=Ω\times (-h/2, h/2)$, which satisfy the von Kármán scaling: $E^h(u^h)\leq Ch^4$, to critical points of the appropriate limiting (incompressible von Kármán) functional.

Linearized von Kármán theory for incompressible magnetoelastic plates

We study the asymptotic behaviour, in the sense of $Γ$-convergence, of a thin incompressible magnetoelastic plate, as its thickness goes to zero. We focus on the linearized von Kármán regime. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed confguration.

Plates with incompatible prestrain of higher order

We study the effective elastic behaviour of the incompatibly prestrained thin plates, characterized by a Riemann metric $G$ on the reference configuration. We assume that the prestrain is "weak", i.e. it induces scaling of the incompatible elastic energy $E^h$ of order less than $h^2$ in terms of the plate's thickness $h$. We essentially prove two results. First, we establish the $Γ$-limit of the scaled energies $h^{-4}E^h$ and show that it consists of a von Kármán-like energy, given in terms of the first order infinitesimal isometries and of the admissible strains on the surface isometrically…

A Liouville theorem for stationary incompressible fluids of von Mises type

We consider entire solutions $u$ of the equations describing the stationary flow of a generalized Newtonian fluid in 2D concentrating on the question, if a Liouville-type result holds in the sense that the boundedness of $u$ implies its constancy. A positive answer is true for $p$-fluids in the case $p>1$ (including the classical Navier-Stokes system for the choice $p=2$), and recently we established this Liouville property for the Prandtl-Eyring fluid model, for which the dissipative potential has nearly linear growth. Here we finally discuss the case of perfectly plastic fluids whose flow is…