论文标题
在结构化变形的背景下进行周期性均质化
Periodic homogenization in the context of structured deformations
论文作者
论文摘要
在周期性均质化的背景下，获得了一阶结构变形的能量。这种能量原则上是通过放松整体类型的初始能量，这些能量具有散装和界面项的贡献，被证明在放松的散装和界面能量密度方面具有不可或缺的代表。这些能量密度反过来是通过适当平均，越来越大的立方体定义的渐近细胞公式获得的，初始能量的批量和表面贡献。整体表示定理是本文的主要结果，是通过在结构化变形的背景下与平均均化理论的平均过程中的典型背景下混合爆破技术获得的。
An energy for first-order structured deformations in the context of periodic homogenization is obtained. This energy, defined in principle by relaxation of an initial energy of integral type featuring contributions of bulk and interfacial terms, is proved to possess an integral representation in terms of relaxed bulk and interfacial energy densities. These energy densities, in turn, are obtained via asymptotic cell formulae defined by suitably averaging, over larger and larger cubes, the bulk and surface contributions of the initial energy. The integral representation theorem, the main result of this paper, is obtained by mixing blow-up techniques, typical in the context of structured deformations, with the averaging process proper of the theory of homogenization.
