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A generalized phase field multiscale finite element method for brittle fracture
Author(s) -
Triantafyllou Savvas P.,
Kakouris Emmanouil G.
Publication year - 2020
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.6293
Subject(s) - microscale chemistry , finite element method , extended finite element method , benchmark (surveying) , displacement field , mixed finite element method , fracture (geology) , field (mathematics) , displacement (psychology) , phase (matter) , mathematics , mathematical analysis , structural engineering , physics , engineering , geology , geotechnical engineering , psychology , mathematics education , geodesy , quantum mechanics , pure mathematics , psychotherapist
SUMMARY A generalized multiscale finite element method is introduced to address the computationally taxing problem of elastic fracture across scales. Crack propagation is accounted for at the microscale utilizing phase field theory. Both the displacement‐based equilibrium equations and phase field state equations at the microscale are mapped on a coarser scale. The latter is defined by a set of multinode coarse elements, where solution of the governing equations is performed. Mapping is achieved by employing a set of numerically derived multiscale shape functions. A set of representative benchmark tests is used to verify the proposed procedure and assess its performance in terms of accuracy and efficiency compared with the standard phase field finite element implementation.