论文标题
随机穿孔域中自由透视功能的随机均质化
Stochastic homogenisation of free-discontinuity functionals in random perforated domains
论文作者
论文摘要
在本文中，我们研究了一个随机自由透视能量的渐近行为$ e_ \ varepsilon $定义在随机穿孔域上定义的，因为$ \ varepsilon $占零。功能$ e_ \ varepsilon $模拟与可以发展裂纹的多孔随机材料相关的能量。为了获得具有有界能量的位移序列的紧凑性，我们需要克服缺乏功能的等值性。在假设随机穿孔不能彼此太近的假设下，我们通过扩展结果做到这一点。然后以两个步骤获得极限能量。作为第一步，我们将自由透视功能的随机收敛性的一般结果应用于$ e_ \ varepsilon $的修改后的强制版本。然后，通过仔细的极限程序确定有效的体积和表面能密度。
In this paper we study the asymptotic behaviour of a family of random free-discontinuity energies $E_\varepsilon$ defined on a randomly perforated domain, as $\varepsilon$ goes to zero. The functionals $E_\varepsilon$ model the energy associated to displacements of porous random materials that can develop cracks. To gain compactness for sequences of displacements with bounded energies, we need to overcome the lack of equi-coerciveness of the functionals. We do so by means of an extension result, under the assumption that the random perforations cannot come too close to one another. The limit energy is then obtained in two steps. As a first step we apply a general result of stochastic convergence of free-discontinuity functionals to a modified, coercive version of $E_\varepsilon$. Then the effective volume and surface energy densities are identified by means of a careful limit procedure.
