论文标题
通过浅曲率预言的薄膜的尺寸降低
Dimension reduction for thin films prestrained by shallow curvature
论文作者
论文摘要
我们关注的是较薄的三维弹性膜的降低分析，该薄膜通过曲线较弱的黎曼指标（Riemannian Metrics）预言。 对于诱导föppl-vonKármán方程不相容的版本的Prestrain，我们发现了重新固定能量的$γ$ - 限制，确定最佳的能量扩展定律，并以同等的条件在Prestrain组件和相关Riemannian Metrics Metrics Metrics的曲率方面显示出最佳条件。当拉伸诱导的prestrain不带平面模式时，我们发现与先前描述的浅壳模型的相似之处。 在较高的Prestrain方案中，我们通过构建变形来证明新的能量上限是通过凸集成获得的Monge-Ampere方程的高度扰动的Hölder-Hölder规范溶液的Kirchhoff-Love扩展。
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 described shallow shell models. In higher prestrain regimes, we prove new energy upper bounds by constructing deformations as the Kirchhoff-Love extensions of the highly perturbative, Hölder-regular solutions to the Monge-Ampere equation obtained by means of convex integration.
