Data-driven enhanced phase field models for highly accurate prediction of Mode I and Mode II fracture

By coupling the elastic and crack surface energy in the total potential function, phase field methods favor a natural track of crack initiation and propagation within the continuum mechanics framework. However, in turn, it raises a critical issue in determining the coupling factor-energy degradation function. This work aims to tackle the problems induced by assigning a degradation function empirically, including the inaccurate reproduction of critical loads and unphysical stiffness reduction prior to fracture. Inspired by the concepts of data-driven computational mechanics, we propose a data-driven phase field scheme to enhance the numerical reproduction of physically consistent fracture responses. This method collaborates a datasets generator, a classifier, a physical-constrained learning algorithm, and the phase field solver in an extensible modular framework, allowing searching for the optimized damage constitutive relation in a carefully designed degradation function space with flexible form. In the case studies, mode I and mode II fracture characteristics of linear elastic and hyperelastic materials are well predicted by the data-driven phase field algorithm, which learns and derives the results from simple scalar datasets, controlling the average error lower than 10%. When introducing the input dataset noise, the model still shows robustness. The results demonstrate the model's interpretability, thermodynamical consistency, and accuracy.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

By coupling elastic and crack surface energy, phase field methods can track crack initiation and propagation within the continuum mechanics framework. This study proposes a data-driven phase field scheme to enhance the numerical reproduction of physically consistent fracture responses.