A deformation gradient tensor and strain tensors for atomistic simulations

A kinematical algorithm is proposed for the construction of strain tensors from atomistic simulation data. Local strain tensors such as the Almansi and Green strain tensors suitable for use in large deformation molecular dynamics/statics simulations are computed directly from a discrete form of the deformation gradient. The discrete, incremental form of the deformation gradient emerges from a weighted least squares minimization that includes a length scale relating the distance from the atom in question with a particular radius. This region defines the nonlocal domain of the strain at that atom. The local atomic strain tensors are then computed using continuum definitions in terms of the deformation gradient. The results of molecular dynamics simulations are presented that compare the Almansi and Green strain tensors under inhomogeneous deformation and indicate that the small-strain approximation should not be used to determine large atomic strains.

[1]  R. Ogden.  Non-Linear Elastic Deformations , 1984 .

[2]  Murray S. Daw,et al.  The embedded-atom method: a review of theory and applications , 1993 .

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

[4]  C. Catlow,et al.  Computational studies of layered silicates , 2003 .

[5]  J. C. Hamilton,et al.  Surface step effects on nanoindentation. , 2001, Physical review letters.

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

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

[8]  Mark F. Horstemeyer,et al.  A multiscale analysis of fixed-end simple shear using molecular dynamics, crystal plasticity, and a macroscopic internal state variable theory , 2003 .

[9]  David P. Dobkin,et al.  The quickhull algorithm for convex hulls , 1996, TOMS.

[10]  M. Falk.  Molecular-dynamics study of ductile and brittle fracture in model noncrystalline solids , 1998, cond-mat/9803058.

[11]  Steven J. Plimpton,et al.  LENGTH SCALE AND TIME SCALE EFFECTS ON THE PLASTIC FLOW OF FCC METALS , 2001 .

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

[13]  A. Argon,et al.  The Atomic Strain Tensor , 1991 .

[14]  Olivier Devillers,et al.  Fully Dynamic Delaunay Triangulation in Logarithmic Expected Time Per Operation , 1992, Comput. Geom..

[15]  D. Ward,et al.  Mechanical behavior of aluminum-silicon nanocomposites : A molecular dynamics study , 2006 .