The bridging scale for two-dimensional atomistic/continuum coupling

In this paper, we present all necessary generalisations to extend the bridging scale, a finite-temperature multiple scale method which couples molecular dynamics (MD) and finite element (FE) simulations, to two dimensions. The crucial development is a numerical treatment of the boundary condition acting upon the reduced atomistic system, as such boundary conditions are analytically intractable beyond simple one-dimension systems. The approach presented in this paper offers distinct advantages compared to previous works, specifically the compact size of the resulting time history kernel, and the fact that the time history kernel can be calculated using an automated numerical procedure for arbitrary multi-dimensional lattice structures and interatomic potentials. We demonstrate the truly two-way nature of the coupled FE and reduced MD equations of motion via two example problems, wave propagation and dynamic crack propagation. Finally, we compare both problems to benchmark full MD simulations to validate the accuracy and efficiency of the proposed method.

[1]  Gregory J. Wagner,et al.  Hierarchical enrichment for bridging scales and mesh-free boundary conditions , 2001 .

[2]  D. L. Dorofeev,et al.  On static analysis of finite repetitive structures by discrete Fourier transform , 2002 .

[3]  A. Voter,et al.  Extending the Time Scale in Atomistic Simulation of Materials Annual Re-views in Materials Research , 2002 .

[4]  Dong Qian,et al.  A Virtual Atom Cluster Approach to the Mechanics of Nanostructures , 2004 .

[5]  R. A. Uras,et al.  Enrichment of the Finite Element Method With the Reproducing Kernel Particle Method , 1995 .

[6]  Harold S. Park,et al.  An introduction and tutorial on multiple-scale analysis in solids , 2004 .

[7]  Eduard G. Karpov,et al.  Initial tension in randomly disordered periodic lattices , 2003 .

[8]  William A. Curtin,et al.  Multiscale plasticity modeling: coupled atomistics and discrete dislocation mechanics , 2004 .

[9]  Eduard G. Karpov,et al.  Molecular dynamics boundary conditions for regular crystal lattices , 2004 .

[10]  W. Cai,et al.  Minimizing boundary reflections in coupled-domain simulations. , 2000, Physical review letters.

[11]  Noam Bernstein,et al.  Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture , 1998 .

[12]  J. D. Doll,et al.  Generalized Langevin equation approach for atom/solid-surface scattering: General formulation for classical scattering off harmonic solids , 1976 .

[13]  Gregory J. Wagner,et al.  Coupling of atomistic and continuum simulations using a bridging scale decomposition , 2003 .

[14]  Robert E. Rudd,et al.  COARSE-GRAINED MOLECULAR DYNAMICS AND THE ATOMIC LIMIT OF FINITE ELEMENTS , 1998 .

[15]  Gregory J. Wagner,et al.  A multiscale projection method for the analysis of carbon nanotubes , 2004 .

[16]  M. Baskes,et al.  Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals , 1984 .

[17]  M. Ortiz,et al.  Quasicontinuum analysis of defects in solids , 1996 .

[18]  Ronald E. Miller,et al.  Atomistic/continuum coupling in computational materials science , 2003 .

[19]  E Weinan,et al.  A dynamic atomistic-continuum method for the simulation of crystalline materials , 2001 .

[20]  Lucy T. Zhang,et al.  A Parallelized Meshfree Method with Boundary Enrichment for Large-Scale CFD , 2002 .

[21]  T. Belytschko,et al.  A bridging domain method for coupling continua with molecular dynamics , 2004 .

[22]  Hiroshi Kadowaki,et al.  Bridging multi-scale method for localization problems , 2004 .

[23]  Harold S. Park,et al.  A temperature equation for coupled atomistic/continuum simulations , 2004 .

[24]  Harold S. Park,et al.  An introduction to computational nanomechanics and materials , 2004 .