论文标题
在二维中的几何非线性弹性夹杂物的最小能量
Minimal Energy for Geometrically Nonlinear Elastic Inclusions in Two Dimensions
论文作者
论文摘要
我们关注的是等等问题的变体，在我们的环境中，这是在弹性上的几何非线性两孔问题中产生的。更确切地说，我们研究了固定体积的弹性包含能量的最佳尺度，该固定体积由表面和（各向异性）弹性贡献确定。遵循\ cite {cs}和\ cite {knuepferkohn-2011}的想法，我们通过调用两孔刚度参数和覆盖结果来得出较低的缩放。上限是从众所周知的晶状体弹性包含的结构中。
We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion of a fixed volume for which the energy is determined by a surface and an (anisotropic) elastic contribution. Following ideas from \cite{CS} and \cite{KnuepferKohn-2011}, we derive the lower scaling bound by invoking a two-well rigidity argument and a covering result. The upper bound follows from a well-known construction for a lens-shaped elastic inclusion.
