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A new application of M ‐ and L ‐integrals for the numerical loading analysis of two interacting cracks
Author(s) -
Judt Paul O.,
Ricoeur Andreas
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201500012
Subject(s) - stress intensity factor , fracture mechanics , boundary (topology) , boundary element method , numerical analysis , fracture (geology) , path (computing) , j integral , mathematics , mathematical analysis , boundary value problem , structural engineering , materials science , computer science , finite element method , composite material , engineering , programming language
A new application of the path‐independent M‐ and L‐integrals in linear elastic fracture mechanics is presented for the accurate calculation of loading quantities related to two‐cracks problems in engineering structures. Path‐independent integrals are used to avoid special requirements concerning crack tip meshing and contour size. The numerical calculation of M‐ and L‐integrals is performed along the external boundary of the model. This global contour includes both crack tips and thus the resulting values represent the sum of loading quantities related to each crack tip. A separation technique is necessary to calculate local values of the J‐integral and stress intensity factors. Numerical examples of crack propagation simulations are presented and the resulting crack paths are verified and compared with those from conventional methods.