TY - JOUR

T1 - Nonlocal operator method for dynamic brittle fracture based on an explicit phase field model

AU - Zhuang, Xiaoying

AU - Ren, Huilong

AU - Rabczuk, Timon

N1 - Funding Information: The authors acknowledge the supports from the the National Basic Research Program of China (973 Program: 2011CB013800 ) and NSFC ( 51474157 ), the Ministry of Science and Technology of China (Grant No. SLDRCE14-B-28 , SLDRCE14-B-31 ). All authors approved the version of the manuscript to be published.

PY - 2021/11

Y1 - 2021/11

N2 - In this work, we present a nonlocal operator method (NOM) for dynamic fracture exploiting an explicit phase field model. The nonlocal strong forms of the phase field and the associated mechanical model are derived as integral forms by variational principle. The equations are decoupled and solved in time by an explicit scheme employing the Verlet-velocity algorithm for the mechanical field and an adaptive sub-step scheme for the phase field model. The sub-step scheme reduces phase field residual adaptively in a few substeps and thus achieves a rate-independent phase field model. The explicit scheme avoids the calculation of the anisotropic stiffness tensor in the implicit phase field model. One advantage of the NOM is its ease in implementation. The method does not require any shape functions and the associated matrices and vectors are obtained automatically after defining the energy of the system. Hence, the approach can be easily extended to more complex coupled problems. Several numerical examples are presented to demonstrate the performance of the current method.

AB - In this work, we present a nonlocal operator method (NOM) for dynamic fracture exploiting an explicit phase field model. The nonlocal strong forms of the phase field and the associated mechanical model are derived as integral forms by variational principle. The equations are decoupled and solved in time by an explicit scheme employing the Verlet-velocity algorithm for the mechanical field and an adaptive sub-step scheme for the phase field model. The sub-step scheme reduces phase field residual adaptively in a few substeps and thus achieves a rate-independent phase field model. The explicit scheme avoids the calculation of the anisotropic stiffness tensor in the implicit phase field model. One advantage of the NOM is its ease in implementation. The method does not require any shape functions and the associated matrices and vectors are obtained automatically after defining the energy of the system. Hence, the approach can be easily extended to more complex coupled problems. Several numerical examples are presented to demonstrate the performance of the current method.

KW - Dual-horizon peridynamics

KW - Explicit phase field

KW - Integral form

KW - Nonlocal operator

KW - Nonlocal strong form

UR - http://www.scopus.com/inward/record.url?scp=85112018980&partnerID=8YFLogxK

U2 - 10.1016/j.euromechsol.2021.104380

DO - 10.1016/j.euromechsol.2021.104380

M3 - Article

AN - SCOPUS:85112018980

VL - 90

JO - European Journal of Mechanics, A/Solids

JF - European Journal of Mechanics, A/Solids

SN - 0997-7538

M1 - 104380

ER -