Abstract
A method is presented for simulating dynamic crack propagation using a coupled molecular dynamics/extended finite element method. Molecular dynamics is used at the crack tip while the extended finite element method naturally models the crack in the wake of the tip as a traction-free discontinuity. After recalling the basic molecular dynamics equations, the discretization of the continuum and the traction-free discontinuity via the extended finite element method, and the zonal coupling method between both domains, two-dimensional computations of dynamic fracture are presented, including a discussion on how to move and/or expand the zone in which molecular dynamics is used upon crack propagation.
Highlights
Quantum mechanics is probably the most appropriate theory to describe fracture from a physics point of view, but the difficulties to relate quantum mechanics to continuum mechanics, e.g. via Density Functional Theory [1, 2] presently seem insurmountable
A disadvantage of the approach is that it is computationally demanding. For this reason multi-scale approaches have been introduced, in fracture [6], as well as in plasticity [7], in which only a part of the body is analysed using molecular dynamics, while the remaining part of the body is modelled using continuum mechanics and discretized using a finite element method. This contribution furthers along this line and combines molecular dynamics for modelling the fracture process at the crack tip with an extended finite element method, where the partition-of-unity property of the polynomial shape functions is
A numerical approach has been proposed for combining a molecular dynamics method and a finite element method that exploits the partition-of-unity property of finite element shape
Summary
A method is presented for simulating dynamic crack propagation using a coupled molecular dynamics / extended finite element method. Molecular dynamics is used at the crack tip while the extended finite element method naturally models the crack in the wake of the tip as a traction-free discontinuity. After recalling the basic molecular dynamics equations, the discretization of the continuum and the traction-free discontinuity via the extended finite element method, and the zonal coupling method between both domains, two-dimensional computations of dynamic fracture are presented, including a discussion how to move and/or expand the zone in which molecular dynamics is used upon crack propagation.
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