Is it wise to keep laminating
Is it wise to keep laminating
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继续层压是否明智
DOI：
10.1051/cocv:2004015
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
V. Nesi
中科院分区：
文献类型：
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作者：
M. Briane;V. Nesi
我们研究了电导率方程的修正矩阵Pe。我们证明了如果Pe弱收敛到恒等式，则对任意层合板，Pe≥几乎在每一点都为0。在Briane等人的工作中，如果尺寸大于2，那么对于一般的微几何来说，这一简单的性质被证明是错误的。(拱门。定量配给。机甲。(出席者)在两个维度上，作为Alessandrini和Nesi(拱门)工作的必然结果，它适用于任何微观几何。定量配给。机甲。肛门。158(2001)155-171)。我们利用层合板的这一性质来证明，在任何维度上，当相数目大于2时，在某些区域中，层合板不能达到经典的Hashin-Shtrikman边界。此外，我们还建立了有效导电率的新的界，它对于包括正交层合板在内的一类微几何中的三个各向同性相的混合物是渐近最优的，我们称之为准正交。数学学科分类。35B27，74Q15。
We study the corrector matrix P e to the conductivity equations. We show that if P e con- verges weakly to the identity, then for any laminate detP e ≥ 0 at almost every point. This simple property is shown to be false for generic microgeometries if the dimension is greater than two in the work Briane et al. (Arch. Ration. Mech. Anal., to appear). In two dimensions it holds true for any microgeometry as a corollary of the work in Alessandrini and Nesi (Arch. Ration. Mech. Anal. 158 (2001) 155-171). We use this property of laminates to prove that, in any dimension, the classi- cal Hashin-Shtrikman bounds are not attained by laminates, in certain regimes, when the number of phases is greater than two. In addition we establish new bounds for the effective conductivity, which are asymptotically optimal for mixtures of three isotropic phases among a certain class of microgeometries, including orthogonal laminates, which we then call quasiorthogonal. Mathematics Subject Classification. 35B27, 74Q15.