Multi-scale computational homogenization–localization for propagating discontinuities using X-FEM

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Uittreksel

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.
TaalEngels
Pagina's496-527
TijdschriftInternational Journal for Numerical Methods in Engineering
Volume102
Nummer van het tijdschrift3-4
DOI's
StatusGepubliceerd - 2015

Vingerafdruk

Homogenization
Discontinuity
Finite element method
Cohesive Crack
Strain Localization
Cracks
Damage
Traction (friction)
Propagation
Unloading
Extended Finite Element Method
Macros
Kinematics
Microstructure
Continuum
Adjacent
Numerical Examples

Citeer dit

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title = "Multi-scale computational homogenization–localization for propagating discontinuities using X-FEM",
abstract = "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.",
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Multi-scale computational homogenization–localization for propagating discontinuities using X-FEM. / Bosco, E.; Kouznetsova, V.G.; Geers, M.G.D.

In: International Journal for Numerical Methods in Engineering, Vol. 102, Nr. 3-4, 2015, blz. 496-527.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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AB - 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.

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