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

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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.