Forecasting phase-field variables of brittle fracture problems using ARIMA and LSTM

Abstract

In this thesis, we divide the content into five chapters. Chapter 1 is the introduction of the thesis. Chapter 2 summarizes the fundamental theories to establish a mathematical model for brittle fractures, provides numerical methods for solving the model in commercial software, and gives a brief understanding of the process of forecasting by machine learning. In more detail, section 2.1 and section 2.2 present knowledge about Griffith’s theory and phase-field method in brittle fracture problems. Section 2.3 explains the formulas used to create the user-defined element in Abaqus so that the phase-field method can be applied in commercial software. Section 2.4 and section 2.5 introduce the processes of two ML methods: ARIMA and LSTM. Chapter 3 focuses on presenting the phase-field results on Abaqus. The reliability of the UEL element is verified in Section 3.1 by comparing the simulation result with the analytical result. Sections 3.2, 3.3, 3.4, and 3.5 simulate the cracking behaviors of specimens in various loading cases and verify their accuracy by comparing them with reference works. The specimen in Section 3.2 adjusted the size of meshes to create several results. All of these results are not presented in this thesis because the accuracy did not improve too much while the cost of calculation increased greatly.