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Multi‐scale computational homogenization–localization for propagating discontinuities using X‐FEM
Author(s) -
Bosco E.,
Kouznetsova V. G.,
Geers M. G. D.
Publication year - 2015
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.4838
Subject(s) - microscale chemistry , homogenization (climate) , classification of discontinuities , discontinuity (linguistics) , finite element method , mechanics , cohesive zone model , materials science , structural engineering , physics , mathematical analysis , mathematics , engineering , biodiversity , ecology , mathematics education , biology
Summary The aim of this paper is to propose a continuous–discontinuous computational homogenization–localization framework to upscale microscale localization toward the onset and propagation of a cohesive discontinuity at the macroscale. The major novelty of this contribution is the development of a fully coupled micro–macro solution strategy, where the solution procedure for the macroscopic domain is based on the extended finite element method. The proposed approach departs from classical computational homogenization, which allows to derive the effective stress–strain response before the onset of localization. Upon strain localization, the microscale is characterized by a strain localization band where damage grows and by two adjacent unloading bulk regions at each side of the localization zone. The microscale localization band is lumped into a macroscopic cohesive crack, accommodated through discontinuity enriched macroscale kinematics. The governing response of the continuum with a discontinuity is obtained numerically based on proper scale transition relations in terms of the traction–separation law and the stress–strain description of the continuous surrounding material at both sides of the discontinuity. The potential of the method is demonstrated with a numerical example, which illustrates the onset and propagation of a macroscale cohesive crack emerging from microstructural damage within the underlying microstructure. Copyright © 2015 John Wiley & Sons, Ltd.