scholarly journals Prise en compte de discontinuités en espace et en temps par la méthode des éléments finis étendus

2007 ◽  
pp. 827-843
Author(s):  
Julien Réthoré ◽  
Anthony Gravouil ◽  
Alain Combescure
Keyword(s):  
Extended Finite Element Method ◽  
Continuity Condition ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Shape Functions ◽  
Extended Finite Element ◽  
Weak Formulation ◽  
Growth Simulation ◽  
Crack Growth Simulation ◽  
Éléments Finis

This paper is aimed at presenting an application of the extended finite element method to the time variable in the framework of dynamic crack propagation. We take advantage of the partition of the unity properties of finite elements and use an enriched basis of shape functions in space as well as time. To solve the problem in time, we use a weak formulation including a continuity condition for the velocity. It allows to model mechanical problems with space and time discontinuities. Applications to dynamic crack growth simulation are presented.

scholarly journals A molecular dynamics/extended finite element method for dynamic crack propagation

2008 ◽  
Vol 30 (4) ◽  
Author(s):  
Pascal Aubertin ◽  
Julien Réthoré ◽  
René De Borst
Keyword(s):  
Finite Element Method ◽  
Molecular Dynamics ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Coupled Model ◽  
Partition Of Unity ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Extended Finite Element ◽  
Element Method

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.

On the Growth, the Arrest and the Restart of a Crack during a Dynamic Brittle Fracture Experiment

2008 ◽  
Vol 385-387 ◽  
pp. 245-248 ◽  
Author(s):  
David Grégoire ◽  
Hubert Maigre ◽  
Alain Combescure
Keyword(s):  
Finite Element Method ◽  
Brittle Fracture ◽  
Mixed Mode ◽  
Extended Finite Element Method ◽  
Crack Arrest ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Mixed Mode Loading ◽  
Extended Finite Element ◽  
Dynamic Brittle Fracture

Our purpose is to propose a methodology for assessing dynamic crack propagation laws under mixed-mode loading. Dynamic brittle fracture experiments are performed on polymethylmethacrylate (PMMA) in which mode combination changes and crack arrest phases occur. Then, these experiments are numerically reproduced by using the eXtended Finite Element Method (X-FEM) in order to validate the algorithms and the criteria assumed.

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