Multiscale Simulation of Nanoindentation Using the Generalized Interpolation Material Point (GIMP) Method, Dislocation Dynamics (DD) and Molecular Dynamics (MD)

A multiscale simulation technique coupling three scales, namely, the molecular dynamics (MD) at the atomistic scale, the discrete dislocations at the meso scale and the generalized interpolation material point (GIMP) method at the continuum scale is presented. Discrete dislocations are first coupled with GIMP using the principle of superposition (van der Giessen and Needleman (1995)). A detection band seeded in the MD region is used to pass the dislocations to and from the MD simulations (Shilkrot, Miller and Curtin (2004)). A common domain decomposition scheme for each of the three scales was implemented for parallel processing. Simulations of indentation were performed on the (111) plane of Cu at 0 ̊ K using a cylindrical indenter. The effects of indenter radius and indentation speed on the indentation load-depth curve and nucleation of dislocations were investigated. For simulations at finite temperatures, spatially averaged velocities were used to reduce atom vibrations in the transition region to achieve seamless coupling. Simulations were also performed at different temperatures using a wedge indenter. keyword: Multiscale Simulation, GIMP, MD, Discrete Dislocations, Nanoindentation, Coupling, Mesoplasticity

[1]  N. Ghoniem,et al.  Dislocation dynamics. I. A proposed methodology for deformation micromechanics. , 1990, Physical review. B, Condensed matter.

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

[3]  van der Erik Giessen,et al.  Discrete dislocation plasticity: a simple planar model , 1995 .

[4]  Satya N. Atluri,et al.  A Tangent Stiffness MLPG Method for Atom/Continuum Multiscale Simulation , 2005 .

[5]  A. N. Gulluoglu,et al.  Simulation of dislocation microstructures in two dimensions. II. Dynamic and relaxed structures , 1993 .

[6]  G. Pawley,et al.  Role of the secondary slip system in a computer simulation model of the plastic behaviour of single crystals , 1993 .

[7]  L. P. Kubin,et al.  The modelling of dislocation patterns , 1992 .

[8]  Jin Ma,et al.  Structured mesh refinement in generalized interpolation material point (GIMP) method for simulation of dynamic problems , 2006 .

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

[10]  A. N. Gulluoglu,et al.  Simulation of dislocation microstructures in two dimensions. I. Relaxed structures , 1992 .

[11]  S. Bardenhagen,et al.  The Generalized Interpolation Material Point Method , 2004 .

[12]  Satya N. Atluri,et al.  Multiscale Simulation Based on The Meshless Local Petrov-Galerkin (MLPG) Method , 2004 .

[13]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[14]  E. Kaxiras,et al.  Atomistic simulations of solid-phase epitaxial growth in silicon , 2000 .

[15]  Howard L. Schreyer,et al.  Axisymmetric form of the material point method with applications to upsetting and Taylor impact problems , 1996 .

[16]  Hussein M. Zbib,et al.  On plastic deformation and the dynamics of 3D dislocations , 1998 .

[17]  W. Dahl,et al.  Investigation of the formation of dislocation cell structures and the strain hardening of metals by computer simulation , 1993 .

[18]  Ranga Komanduri,et al.  Multiscale Simulations Using Generalized Interpolation Material Point (GIMP) Method And SAMRAI Parallel Processing , 2005 .

[19]  Richard D. Hornung,et al.  Multiscale simulation using Generalized Interpolation Material Point (GIMP) method and Molecular Dynamics (MD) , 2006 .

[20]  R Komanduri,et al.  Ab initio potential-energy surfaces for complex, multichannel systems using modified novelty sampling and feedforward neural networks. , 2005, The Journal of chemical physics.

[21]  H. Fischmeister,et al.  Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model , 1991 .

[22]  J. C. Hamilton,et al.  Dislocation nucleation and defect structure during surface indentation , 1998 .

[23]  D. Sulsky Erratum: Application of a particle-in-cell method to solid mechanics , 1995 .

[24]  E. Nembach,et al.  Dynamic dislocation effects in precipitation hardened materials , 1993 .

[25]  S. Atluri,et al.  Computational Nano-mechanics and Multi-scale Simulation , 2004 .

[26]  R. Komanduri,et al.  Multiscale simulation from atomistic to continuum – coupling molecular dynamics (MD) with the material point method (MPM) , 2006 .

[27]  V. Tewary,et al.  Integrated Green's Function Molecular Dynamics Method for Multiscale Modeling of Nanostructures: Application to Au Nanoisland in Cu , 2004 .

[28]  G. Gladwell Contact Problems in the Classical Theory of Elasticity , 1980 .

[29]  William A. Curtin,et al.  Coupled Atomistic/Discrete Dislocation Simulations of Nanoindentation at Finite Temperature , 2005 .

[30]  Hussein M. Zbib,et al.  A multiscale model of plasticity , 2002 .

[31]  Gregory A. Voth,et al.  Simple reversible molecular dynamics algorithms for Nosé-Hoover chain dynamics , 1997 .

[32]  William A. Curtin,et al.  A coupled atomistics and discrete dislocation plasticity simulation of nanoindentation into single crystal thin films , 2004 .

[33]  T. Hasebe Multiscale Crystal Plasticity Modeling based on Field Theory , 2006 .

[34]  Satya N. Atluri,et al.  Atomic-level Stress Calculation and Continuum-Molecular System Equivalence , 2004 .

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

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

[37]  R. Komanduri,et al.  Combined numerical simulation and nanoindentation for determining mechanical properties of single crystal copper at mesoscale , 2005 .

[38]  M. Cross,et al.  A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate , 1998 .

[39]  J. Bogdanoff,et al.  On the Theory of Dislocations , 1950 .