论文标题
基于均化理论的多孔培养基裂缝模型
A porous media fracture model based on homogenization theory
论文作者
论文摘要
提出了一种新型的正规裂缝模型，用于多孔介质中的裂纹繁殖。我们的模型是通过均化理论和形式的渐近扩展获得的。我们从定期穿孔的结构域中构成的正则化准静态断裂模型开始，该模型通过定期扩展带有孔的重新尺寸的单元细胞获得。这种设置使我们能够为主要（位移）和次级变量以及能量关系平衡写两个分离的最小条件。然后，当单位细胞的重新缩放参数消失时，我们应用通常的渐近扩展匹配来推断极限关系。通过引入细胞问题溶液和均质张量，我们可以将获得的关系重塑为多孔培养基中裂纹传播的新型模型。所提出的模型可以解释为用于多孔介质的正则准静态断裂模型。该模型产生了两个分离的（均质）最小条件，用于主要和次要变量，并平衡均质能量关系。
A novel regularized fracture model for crack propagation in porous media is proposed. Our model is obtained through homogenization theory and formal asymptotic expansions. We start with a regularized quasi-static fracture model posed in a periodically perforated domain obtained by periodic extension of a re-scaled unit cell with a hole. This setup allows us to write two separated minimality conditions for the primary (displacement) and secondary variables plus a balance of energy relation. Then we apply the usual asymptotic expansion matching to deduce limit relations when the re-scaling parameter of the unit cells vanishes. By introducing cell problems solutions and a homogenized tensor we can recast the obtained relations into a novel model for crack propagation in porous media. The proposed model can be interpreted as a regularized quasi-static fracture model for porous media. This model yields two separated (homogenized) minimality conditions for the primary and secondary variables and a balance of homogenized energy relation.
