Data driven approach to fatigue crack growth modeling

疲劳是力学中的一个关键现象，是大多数结构失效的原因。然而，该问题的固有复杂性使得预测模型的开发成为一项艰巨的任务，并且使从实验结果出发的材料疲劳本构行为的识别变得非常复杂。因此，尽管这个问题具有相关性，但仍然缺乏一个被广泛接受的具有真正预测能力的模型。本项目的目的是开发一种数据驱动的疲劳裂纹扩展建模方法。采用数据驱动技术可以直接将一组实验或数值性质的离散数据嵌入到问题的解决方案中。这样做的优点是克服了校准分析疲劳本构关系的必要性。申请人最近提出的疲劳裂纹扩展的变分相场方法将被采用作为参考力学模型。然后，利用机器学习和数据挖掘技术，提出一种基于数值本构行为识别的数据驱动程序。为此，将使用一种涉及材料行为数据在有限扩展的材料空间的子簇内插值的技术。这种方法允许确定一组组合系数来参数化材料的数值（疲劳）本构流形。该程序将首先研究一维问题，并基于数值生成的材料数据集。然后，它将扩展到二维和实验数据集的使用。最初采用数值数据可以精确地估计程序的准确性，因为参考解是可用的，即采用可用本构关系的数值模拟结果。该方法的能力将通过模拟用于表征疲劳行为的标准试验来研究，例如紧致拉伸或三点弯曲试验。这里，将采用不同于训练数值流形检测相位的加载和边界条件。

Fatigue is a key phenomenon in mechanics, and is responsible for most structural failures. However, the inherent complexity of the problem makes the development of predictive models a non-trivial task and it greatly complicates the identification of the material fatigue constitutive behavior starting from experimental results. Hence, despite the relevance of the problem, a widely accepted model with truly predictive capabilities is still lacking.Aim of the present project is to develop a data driven approach to fatigue crack growth modeling. The adoption of data driven techniques allows to directly embed into the solution of the problem a discrete set of data of experimental or numerical nature. This has the advantage of overcoming the necessity of calibrating analytical fatigue constitutive material relationships. A recent variational phase-field approach to fatigue crack growth proposed by the applicant will be adopted as a reference mechanical model. Then, taking advantage of machine learning and data mining techniques, a data driven procedure will be proposed based on the identification of the numerical constitutive behavior. To this end, a technique involving the interpolation of the material behavior data within sub-clusters of the material space with limited extension will be used. This approach allows to determine a set of combination coefficients that parameterize the numerical (fatigue) constitutive manifold of the material.The procedure will be first studied for a 1D problem and based on a numerically generated material data set. Then, it will be extended to 2-3D and to the employment of experimental data sets. The initial adoption of numerical data allows to precisely estimate the accuracy of the procedure since a reference solution is available, i.e. the results of the numerical simulations adopting available constitutive relationships. The capability of the method will be investigated by simulating standard tests used to characterize the fatigue behavior, such as the compact tension or three-point-bending tests. Here, loading and boundary conditions different that those used to train the numerical manifold detection phase will be adopted.