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An asynchronous variational integrator for the phase field approach to dynamic fracture
Author(s) -
Niu Zongwu,
ZiaeiRad Vahid,
Wu Zongyuan,
Shen Yongxing
Publication year - 2022
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.7127
Subject(s) - integrator , displacement field , phase field models , phase (matter) , field (mathematics) , computer science , fracture mechanics , topology (electrical circuits) , finite element method , mathematics , mathematical analysis , structural engineering , engineering , physics , computer network , bandwidth (computing) , quantum mechanics , combinatorics , pure mathematics
The phase field approach is widely used to model fracture behaviors due to the absence of the need to track the crack topology and the ability to predict crack nucleation and branching. In this work, the asynchronous variational integrator (AVI) is adapted for the phase field approach of dynamic brittle fracture. The AVI is derived from Hamilton's principle and allows each element in the mesh to have its own local time step that may be different from others'. While the displacement field is explicitly updated, the phase field is implicitly solved, with upper and lower bounds strictly and conveniently enforced. In particular, two important variants of the phase field approach, the AT1 and AT2 models, are equally easily implemented. Several benchmark problems are used to study the performances of both the AT1 and AT2 models, and the results show that the AVI for the phase field approach significantly speeds up the computational efficiency and successfully captures the complicated dynamic fracture behavior.