Theoretical and numerical analysis for a phase-field model describing the crack growth phenomenon

在本计画中，我们首先研究断裂韧度随空间变化的非均匀介质中的裂纹扩展。通过使用基于两种不同的表面能泛函的两个相场模型，这是所谓的AT 1和AT 2模型，我们进行了模拟的裂纹扩展，并表明J积分反映了有效的非均匀韧性。然后，我们制定反问题来估计空间依赖的断裂韧性从裂纹路径。我们的方法，这是基于数据的预处理和回归，成功地估计的位置和更强硬的区域的大小。我们还表明，我们的方法适用于不同的几何形状的不均匀性。

In this project, we first study the crack propagation in an inhomogeneous media in which fracture toughness varies in space. By using the two phase-field models based on two different surface energy functionals, which are so called AT1 and AT2 models, we perform simulations of the crack propagation and show that the J-integral reflects the effective inhomogeneous toughness. We then formulate inverse problems to estimate space-dependent fracture toughness from the crack path. Our method which is based on data pre-processing and regression, successfully estimates the positions and magnitude of tougher regions. We also demonstrate that our method works for different geometry of inhomogeneity.