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Theory and numerics for finite deformation fracture modelling using strong discontinuities
Author(s) -
Fagerström Martin,
Larsson Ragnar
Publication year - 2005
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.1573
Subject(s) - classification of discontinuities , discontinuity (linguistics) , jump , traction (geology) , finite element method , fracture (geology) , extended finite element method , fracture mechanics , representation (politics) , deformation (meteorology) , displacement (psychology) , mathematics , mechanics , mathematical analysis , structural engineering , geology , physics , engineering , law , geotechnical engineering , psychology , quantum mechanics , geomorphology , politics , political science , psychotherapist , oceanography
Abstract A general finite element approach for the modelling of fracture is presented for the geometrically non‐linear case. The kinematical representation is based on a strong discontinuity formulation in line with the concept of partition of unity for finite elements. Thus, the deformation map is defined in terms of one continuous and one discontinuous portion, considered as mutually independent, giving rise to a weak formulation of the equilibrium consisting of two coupled equations. In addition, two different fracture criteria are considered. Firstly, a principle stress criterion in terms of the material Mandel stress in conjunction with a material cohesive zone law, relating the cohesive Mandel traction to a material displacement ‘jump’ associated with the direct discontinuity. Secondly, a criterion of Griffith type is formulated in terms of the material‐crack‐driving force (MCDF) with the crack propagation direction determined by the direction of the force, corresponding to the direction of maximum energy release. Apart from the material modelling, the numerical treatment and aspects of computational implementation of the proposed approach is also thoroughly discussed and the paper is concluded with a few numerical examples illustrating the capabilities of the proposed approach and the connection between the two fracture criteria. Copyright © 2005 John Wiley & Sons, Ltd.