Interpenetration of matter in plate theories obtained as Gamma-limits
Interpenetration of matter in plate theories obtained as Gamma-limits
复制标题
作为伽马极限获得的板块理论中物质的相互渗透
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Eris Runa
中科院分区：
文献类型：
--
作者：
H. Olbermann;Eris Runa
我们认为在板理论的推导中潜在的病理学是Friesecke James和Muller的三维非线性弹性的伽玛极限（Comm. Pure Appl. Math.，55：1461-1506和Arch.定量。机械肛门，180：183-236），其包括收敛到不可逆极限的可逆映射的恢复序列。Muller和Spector（Arch. Ration.机械肛门131：1-66）在不同的背景下。结合度理论、Lipschitz函数对Sobolev函数的逼近和几何刚性，我们证明了在板理论的推导中潜在的病态情况为恢复序列元素的图的自相交提供了充分条件，从而排除了病态.
We consider a potential pathology in the derivation of plate theories as Gamma-limits of 3-dimensional nonlinear elasticity by Friesecke James and Muller (Comm. Pure Appl. Math., 55:1461-1506 and Arch. Ration. Mech. Anal., 180:183-236), which consists in recovery sequences of invertible maps that converge to a non-invertible limit. These pathologies have been noted by Muller and Spector (Arch. Ration. Mech. Anal. 131:1-66) in a different context. Using a combination of degree theory, the approximation of Sobolev functions by Lipschitz functions and geometric rigidity we show that the potentially pathological situation in the derivation of plate theories provides sufficient conditions for the self-intersection of the graph of the recovery sequence element, and thus the pathology is excluded.