A multiscale molecular dynamics / extended finite element method for dynamic fracture

P. Aubertin, J. Rethore, R. Borst, de

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Abstract

A multiscale method is presented which couples a molecular dynamics approach for describing fracture at the crack tip with an extended finite element method for discretizing the remainder of the domain. After recalling the basic equations of molecular dynamics and continuum mechanics the discretization is discussed for the continuum subdomain where the partition-of-unity property of finite element shape functions is used, since in this fashion the crack in the wake of its tip is naturally modelled as a traction-free discontinuity. Next, the zonal coupling method between the atomistic and continuum models is described, including an assessment of the energy transfer between both domains for a one-dimensional problem. It is discussed how the stress has been computed in the atomistic subdomain, and a two-dimensional computation is presented of dynamic fracture using the coupled model. The result shows multiple branching, which is reminiscent of recent results from simulations on dynamic fracture using cohesive-zone models.
Original languageEnglish
Title of host publicationComputer Methods in Mechanics Lectures of the CMM 2009
EditorsM. Kuczma, K. Wilmanski
Place of PublicationBerlin
PublisherSpringer
Pages211-237
ISBN (Print)978-3-642-05240-8
DOIs
Publication statusPublished - 2010

Publication series

NameAdvanced structured materials
ISSN (Print)1869-8433

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finite element method
molecular dynamics
continuums
continuum mechanics
shape functions
traction
crack tips
wakes
unity
partitions
discontinuity
cracks
energy transfer
simulation

Cite this

Aubertin, P., Rethore, J., & Borst, de, R. (2010). A multiscale molecular dynamics / extended finite element method for dynamic fracture. In M. Kuczma, & K. Wilmanski (Eds.), Computer Methods in Mechanics Lectures of the CMM 2009 (pp. 211-237). (Advanced structured materials). Berlin: Springer. https://doi.org/10.1007/978-3-642-05241-5_12
Aubertin, P. ; Rethore, J. ; Borst, de, R. / A multiscale molecular dynamics / extended finite element method for dynamic fracture. Computer Methods in Mechanics Lectures of the CMM 2009. editor / M. Kuczma ; K. Wilmanski. Berlin : Springer, 2010. pp. 211-237 (Advanced structured materials).
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Aubertin, P, Rethore, J & Borst, de, R 2010, A multiscale molecular dynamics / extended finite element method for dynamic fracture. in M Kuczma & K Wilmanski (eds), Computer Methods in Mechanics Lectures of the CMM 2009. Advanced structured materials, Springer, Berlin, pp. 211-237. https://doi.org/10.1007/978-3-642-05241-5_12

A multiscale molecular dynamics / extended finite element method for dynamic fracture. / Aubertin, P.; Rethore, J.; Borst, de, R.

Computer Methods in Mechanics Lectures of the CMM 2009. ed. / M. Kuczma; K. Wilmanski. Berlin : Springer, 2010. p. 211-237 (Advanced structured materials).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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AB - A multiscale method is presented which couples a molecular dynamics approach for describing fracture at the crack tip with an extended finite element method for discretizing the remainder of the domain. After recalling the basic equations of molecular dynamics and continuum mechanics the discretization is discussed for the continuum subdomain where the partition-of-unity property of finite element shape functions is used, since in this fashion the crack in the wake of its tip is naturally modelled as a traction-free discontinuity. Next, the zonal coupling method between the atomistic and continuum models is described, including an assessment of the energy transfer between both domains for a one-dimensional problem. It is discussed how the stress has been computed in the atomistic subdomain, and a two-dimensional computation is presented of dynamic fracture using the coupled model. The result shows multiple branching, which is reminiscent of recent results from simulations on dynamic fracture using cohesive-zone models.

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Aubertin P, Rethore J, Borst, de R. A multiscale molecular dynamics / extended finite element method for dynamic fracture. In Kuczma M, Wilmanski K, editors, Computer Methods in Mechanics Lectures of the CMM 2009. Berlin: Springer. 2010. p. 211-237. (Advanced structured materials). https://doi.org/10.1007/978-3-642-05241-5_12