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. Finally, a two-dimensional computation is presented of dynamic fracture using the coupled model. | Vietnam Journal of Mechanics, VAST, Vol. 30, No. 4 (2008), pp. 205 – 217 Special Issue of the 30th Anniversary A MOLECULAR DYNAMICS / EXTENDED FINITE ELEMENT METHOD FOR DYNAMIC CRACK PROPAGATION Pascal Aubertin1 , Julien Réthoré1 , and René de Borst2 de Lyon, CNRS INSA-Lyon, LaMCoS UMR 5259, France 2 Eindhoven University of Technology, Eindhoven, Netherlands 1 Université 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. Finally, a two-dimensional computation is presented of dynamic fracture using the coupled model. Keywords. multiscale methods, molecular dynamics, extended finite element method, fracture, crack propagation 1. INTRODUCTION Modern research into fracture commences with the seminal work of Griffith [1]. Later, Irwin [2] and Rice [3] established the relation between the stress intensity factors and the energy release rate, and gave linear elastic fracture mechanics a firm basis. However, linear elastic fracture mechanics only applies to crack-like flaws in an otherwise linear elastic solid and when the singularity associated with that flaw is characterized by a nonvanishing energy release rate. The fracture and any dissipative processes must also be confined to a small region in the vicinity of the crack tip. When the region in which the separation and dissipative process take
