Atomistic formulation of a multiscale field theory for nano/micro solids

References

• Rudd , RE and Broughton , JQ . 1998 . Phys. Rev B , 58 : R5893
   Web of Science ®Google Scholar
• Rudd , RE and Broughton , JQ . 1999 . J. Model. Simul. Microsyst. , 1 : 26
   Google Scholar
• Abraham , FE , Broughton , JQ Bernsten , N . 1998 . Comput. Phys. , 12 : 538
   Google Scholar
• Abraham , FE , Bernstein , N Broughton , JQ . 2000 . MRS Bull. , 25 : 27
   Google Scholar
• Cuitino , AM , Stainier , L Wang , G . 2001 . A Multiscale Approach for Modeling Crystalline Solids , cond-mat/0104381
   Google Scholar
• Strachan , A , Cagin , T Gulseren , O . 2002 . First Principles Force Field for Metallic Tantalum , cond-mat/0208027
   Google Scholar
• Eringen , AC and Suhubi , ES . 1964 . Int. J. Eng. Sci. , 2 : 189
   Google Scholar
• Mindlin , RO . 1964 . Arch Rat. Mech. Anal. , 16 : 51
   Web of Science ®Google Scholar
• Eringen , AC . 1965 . Developments in Mechanics, Vol. 3 , Edited by: Huang , TC and Johnson , MW Jr . New York : Wiley .
   Google Scholar
• Cosserat , E and Cosserat , F . 1909 . Theorie des Corps Deformable , Paris : Hermann .
   Google Scholar
• Toupin , RA . 1962 . Arch. Rational Mech. Anal. , 11 : 385
   Web of Science ®Google Scholar
• Chen , Y , Lee , JD and Eskandarian , A . 2004 . Comput. Model. Eng. Sci. , 5 : 35
   Web of Science ®Google Scholar
• Chen , Y , Lee , JD and Eskandarian , A . 2004 . Int. Solids J Struct. , 41 : 2085
   Web of Science ®Google Scholar
• Chen , Y , Lee , JD and Eskandarian , A . 2004 . Int. J. Eng. Sci. , 42 : 987
   Google Scholar
• Chen , Y , Lee , JD and Eskandarian , A . 2003 . Int. J. Eng. Sci. , 41 : 61
   Google Scholar
• Chen , Y and Lee , JD . 2003 . Int. J. Eng. Sci. , 4 : 871
   Google Scholar
• Dove , MT . 1993 . Introduction to Lattice Dynamics , Cambridge : Cambridge University Press .
   Google Scholar
• Cochran , W . 1973 . The Dynamics of Atoms in Crystals , London : Edward Arnold .
   Google Scholar
• Ehrenfest , P . 1927 . Z. Phys. , 45 : 455
   Google Scholar
• Hellmann , H . 1937 . Einfüuhrung in die Quantenchemie , 61 – 285 . Leipzig : Deuticke .
   Google Scholar
• Feynman , RP . 1939 . Phys. Rev. , 56 : 340
   Google Scholar
• Born , M , Heisenberg , W and Jordan , P . 1926 . Z. Phys. , 35 : 557
   Google Scholar
• Nielsen , OH and Martin , RM . 1985 . Phys. Rev. B , 32 : 3780
   PubMed Web of Science ®Google Scholar
• Hoover , WG . 1986 . Molecular Dynamics , Berlin : Springer .
   Google Scholar
• Hoover , WG . 1991 . Computational Statistical Mechanics , Amsterdam : Elsevier .
   Google Scholar
• Chen , Y and Lee , JD . 2003 . Physica A , 322 : 359
   Web of Science ®Google Scholar
• Chen , Y and Lee , JD . 2003 . Physica A , 322 : 377
   Google Scholar
• Chen , Y , Lee , JD and Eskandarian , A . 2003 . Acta Mech, , 161 : 81
   Google Scholar
• Huang , K . 1967 . Statistical Mechanics , New York : Wiley .
   Google Scholar
• Kreuzer , HJ . 1981 . Nonequilibrium Thermodynamics and its Statistical Foundations , London : Clarendon Press .
   Google Scholar
• Kittel , C . 1967 . Introduction to Solid State Physics , New York : Wiley .
   Google Scholar
• Cochran , W and Cowley , RA . 1967 . Encyclopedia of Physics , Vol. 25/2a , Berlin : Springer .
   Google Scholar
• Bruesch , P . 1982 . Phonons: Theory and Experiments. Lattice I. Dynamics and Models of Interatomic Forces , New York : Springer .
   Google Scholar
• Dick , BG and Overhauser , AW . 1958 . Phys. Rev. , 112 : 90
   Web of Science ®Google Scholar
• Cochran , W . 1966 . Theory of Phonon Dispersion Curves. Phonons in Perfect Lattice and in Lattice with Point Imperfections , Edited by: Stevenson , RWH . 53 – 72 . New York : Plenum Press .
   Google Scholar
• Chen , Y and Lee , JD . 2005 . Int. J. Eng. Sci. , accepted for publication
   Google Scholar
• Eringen , AC . 1999 . Microcontinuum Field Theories I: Foundations and Solids , New York : Springer .
   Google Scholar
• Hardy , RJ . 1963 . Phys. Rev. , 132 : 168
   Google Scholar
• Kunc , K . 1985 . Electronic Structure, Dynamics and Quantum Structural Properties of Condensed Matter , Edited by: Devreese , JT and Van Camp , P . 227 New York : Plenum Press .
   Google Scholar