Continuum Definitions for Stress in Atomistic simulation

This report is a collection of documents written by the group members of the Engineering Sciences Research Foundation (ESRF), Laboratory Directed Research and Development (LDRD) project titled ''A Robust, Coupled Approach to Atomistic-Continuum Simulation''. An essential requirement of this project is to develop definitions for continuum quantities that can be evaluated locally within an atomistic region. We are developing physical measures of stress, deformation and temperature that are calculable in an atomistic simulation and have well-defined meanings when evaluated in the continuum limit. During the course of FY02, we reviewed many articles presenting the use of definitions of stress in atomistic simulation. The key articles were identified and summarized via internal documents.

[1]  R. Clausius,et al.  XVI. On a mechanical theorem applicable to heat , 1870 .

[2]  J. Kirkwood,et al.  The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics , 1950 .

[3]  Wing Kam Liu,et al.  Mesh-free simulations of shear banding in large deformation , 2000 .

[4]  Wing Kam Liu,et al.  Moving Least Square Reproducing Kernel Method (III): Wavelet Packet Its Applications , 1997 .

[5]  Ted Belytschko,et al.  Multiple scale meshfree methods for damage fracture and localization , 1999 .

[6]  Albert-László Barabási,et al.  Molecular-dynamics investigation of the surface stress distribution in a Ge/Si quantum dot superlattice , 1999 .

[7]  Robert J. Swenson,et al.  Comments on virial theorems for bounded systems , 1983 .

[8]  Martin,et al.  Quantum-mechanical theory of stress and force. , 1985, Physical review. B, Condensed matter.

[9]  Gregory J. Wagner,et al.  Application of essential boundary conditions in mesh-free methods: a corrected collocation method , 2000 .

[10]  S. Li,et al.  Synchronized reproducing kernel interpolant via multiple wavelet expansion , 1998 .

[11]  T. Belytschko,et al.  Element-free Galerkin method: Convergence of the continuous and discontinuous shape functions , 1997 .

[12]  Ted Belytschko,et al.  Explicit Reproducing Kernel Particle Methods for large deformation problems , 1998 .

[13]  Charles B. Kafadar,et al.  Micropolar media—I the classical theory , 1971 .

[14]  T. Belytschko,et al.  Element-free galerkin methods for static and dynamic fracture , 1995 .

[15]  T. Belytschko,et al.  THE NATURAL ELEMENT METHOD IN SOLID MECHANICS , 1998 .

[16]  T. Belytschko,et al.  Nodal integration of the element-free Galerkin method , 1996 .

[17]  Li,et al.  Moving least-square reproducing kernel methods (I) Methodology and convergence , 1997 .

[18]  Wing Kam Liu,et al.  Numerical simulations of strain localization in inelastic solids using mesh‐free methods , 2000 .

[19]  Ted Belytschko,et al.  Numerical integration of the Galerkin weak form in meshfree methods , 1999 .

[20]  J. Q. Broughton,et al.  Concurrent coupling of length scales: Methodology and application , 1999 .

[21]  S. Atluri,et al.  A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach , 1998 .

[22]  W. H. Weinberg,et al.  Theoretical study of the energetics, strain fields, and semicoherent interface structures in layer-by-layer semiconductor heteroepitaxy , 1999 .

[23]  Sidney Yip,et al.  Atomic‐level stress in an inhomogeneous system , 1991 .

[24]  Mark F. Horstemeyer,et al.  Atomistic Finite Deformation Simulations: A Discussion on Length Scale Effects in Relation to Mechanical Stresses , 1999 .

[25]  Ted Belytschko,et al.  A coupled finite element-element-free Galerkin method , 1995 .

[26]  Ted Belytschko,et al.  Advances in multiple scale kernel particle methods , 1996 .

[27]  J. Henderson,et al.  Statistical mechanics of inhomogeneous fluids , 1982, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[28]  Su Hao,et al.  Computer implementation of damage models by finite element and meshfree methods , 2000 .

[29]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[30]  Wing Kam Liu,et al.  Wavelet and multiple scale reproducing kernel methods , 1995 .

[31]  Ted Belytschko,et al.  THE ELEMENT FREE GALERKIN METHOD FOR DYNAMIC PROPAGATION OF ARBITRARY 3-D CRACKS , 1999 .

[32]  Wing Kam Liu,et al.  Multiple‐scale reproducing kernel particle methods for large deformation problems , 1998 .

[33]  T. Belytschko,et al.  Fracture and crack growth by element free Galerkin methods , 1994 .

[34]  P. Lancaster,et al.  Surfaces generated by moving least squares methods , 1981 .

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

[36]  Ted Belytschko,et al.  Multi-scale methods , 2000 .

[37]  Mark A Fleming,et al.  Smoothing and accelerated computations in the element free Galerkin method , 1996 .

[38]  Ju Li,et al.  Mechanistic aspects and atomic-level consequences of elastic instabilities in homogeneous crystals , 2001 .

[39]  R. Hardy,et al.  Formulas for determining local properties in molecular‐dynamics simulations: Shock waves , 1982 .

[40]  J. Kirkwood,et al.  The Statistical Mechanical Theory of Surface Tension , 1949 .

[41]  O. C. Zienkiewicz,et al.  A new cloud-based hp finite element method , 1998 .

[42]  B. Nayroles,et al.  Generalizing the finite element method: Diffuse approximation and diffuse elements , 1992 .

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

[44]  Jiun-Shyan Chen,et al.  A stabilized conforming nodal integration for Galerkin mesh-free methods , 2001 .

[45]  D. H. Tsai The virial theorem and stress calculation in molecular dynamics , 1979 .

[46]  T. J. Delph,et al.  Stress calculation in atomistic simulations of perfect and imperfect solids , 2001 .

[47]  S. Jun,et al.  Multiresolution reproducing kernel particle methods , 1997 .