论文标题
具有许多平行裂缝的培养基的有效弹性
Effective elasticity of a medium with many parallel fractures
论文作者
论文摘要
我们考虑了获得破裂培养基的有效弹性特性的另一种方法。同样，对于流行的线性滑移模型，我们假设平坦的平行断裂和长波长。但是，我们不会将骨折视为位移不连续性的弱平面。与经典模型相反，我们通过嵌入背景介质中的薄层表示断裂。换句话说，我们遵循Schoenberg-douma矩阵形式，用于平均靠背，但我们放宽了它们对层的无限弱和边缘厚度的假设，以使其与线性滑动平面不符。为了表示断裂的特性，我们需要第四阶弹性张量和厚度参数。有效的张量变得更加复杂，但可以更准确地描述更高的平行裂纹浓度。除了有效弹性张量的推导外，我们还执行数值实验，其中我们将方法的性能与高度断裂介质的背景下的线性滑移模型进行了比较。如果填充裂纹占据有效培养基的百分之一以上，我们的模型就会相关。
We consider an alternative way of obtaining the effective elastic properties of a cracked medium. Similarly, to the popular linear-slip model, we assume flat, parallel fractures, and long wavelengths. However, we do not treat fractures as weakness planes of displacement discontinuity. In contrast to the classical models, we represent fractures by a thin layer embedded in the background medium. In other words, we follow the Schoenberg-Douma matrix formalism for Backus averaging, but we relax their assumptions of infinite weakness and marginal thickness of a layer so that it does not correspond to the linear-slip plane. To represent the properties of a fracture, we need a fourth order elasticity tensor and a thickness parameter. The effective tensor becomes more complicated, but it may describe a higher concentration of parallel cracks more accurately. Apart from the derivations of the effective elasticity tensors, we perform numerical experiments in which we compare the performance of our approach with a linear-slip model in the context of highly fractured media. Our model becomes pertinent if filled-in cracks occupy more than one percent of the effective medium.
