Phase field fracture modeling for chemically strengthened glass and Machine Learning for Reaction-- diffusion equations

Abstract

Chemically Strengthening (CS) of glass through artificial process like ion-exchange has emerged as a leading technique to improve the fracture toughness of glass. In this study a novel finding with regards to fracture resistance has been presented. The stress intensity factor of CS glass with varying initial flaw depths have been measured using experimental, analytical and numerical simulations. The main focus in this thesis is modeling CS glass using finite element simulations with phase field fracture modeling. Through thorough investigation of the numerical, analytical and experimental results it has been observed that the fracture toughness of CS glass varies with factors like intial crack depth and the degree of chemical strengthening. A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the solution of a partial differential equation (PDE) and its spatio-temporal input. However, for strongly non-linear and higher order partial differential equations PINN's accuracy reduces significantly. To resolve this problem, we propose a novel PINN scheme that solves the PDE sequentially over successive time segments using a single neural network. The key idea is to re-train the same neural network for solving the PDE over successive time segments while satisfying the already obtained solution for all previous time segments. Thus it is named as backward compatible PINN (bc-PINN). To illustrate the advantages of bc-PINN, we have used the Cahn Hilliard and Allen Cahn equations, which are widely used to describe phase separation and reaction diffusion systems. Our results show significant improvement in accuracy over the PINN method while using a smaller number of collocation points. Additionally, we have shown that using the phase space technique for a higher order PDE could further improve the accuracy and efficiency of the bc-PINN scheme.