A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (Ir) relevance for nanotechnologies

被引:266
作者
Maranganti, R.
Sharma, P. [1 ]
机构
[1] Univ Houston, Dept Mech Engn, Houston, TX 77204 USA
[2] Univ Houston, Dept Phys, Houston, TX 77204 USA
关键词
strain gradient elasticity; nonlocal elasticity; sign paradox; atomistic method; phonon dispersion;
D O I
10.1016/j.jmps.2007.02.011
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
Strain-gradient elasticity is widely used as a suitable alternative to size-independent classical continuum elasticity to, at least partially, capture elastic size effects at the nanoscale. In this work, borrowing methods from statistical mechanics, we present mathematical derivations that relate the strain-gradient material constants to atomic displacement correlations in a molecular dynamics computational ensemble. Using the developed relations and numerical atomistic calculations, the strain-gradient constants are explicitly determined for some representative semiconductor, metallic, amorphous and polymeric materials. This method has the distinct advantage that amorphous materials can be tackled in a straightforward manner. For crystalline materials we also employ and compare results from both empirical and ab initio based lattice dynamics. Apart from carrying out a systematic tabulation of the relevant material parameters for various materials, we also discuss certain subtleties of strain-gradient elasticity, including: the paradox associated with the sign of the strain-gradient constants, physical reasons for low or high characteristic length scales associated with the strain-gradient constants, and finally the relevance (or the lack thereof) of strain-gradient elasticity for nano technologies. (C) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1823 / 1852
页数:30
相关论文
共 100 条
[1]   Strain gradient interpretation of size effects [J].
Aifantis, EC .
INTERNATIONAL JOURNAL OF FRACTURE, 1999, 95 (1-4) :299-314
[2]  
[Anonymous], COURSE THEORETICAL P
[3]   A classification of higher-order strain-gradient models - linear analysis [J].
Askes, H ;
Suiker, ASJ ;
Sluys, LJ .
ARCHIVE OF APPLIED MECHANICS, 2002, 72 (2-3) :171-188
[4]   Gradient elasticity theories in statics and dynamics a unification of approaches [J].
Askes, Harm ;
Aifantis, Elias C. .
INTERNATIONAL JOURNAL OF FRACTURE, 2006, 139 (02) :297-304
[5]   THE ROLE OF SINGLE-PARTICLE DENSITY IN CHEMISTRY [J].
BAMZAI, AS ;
DEB, BM .
REVIEWS OF MODERN PHYSICS, 1981, 53 (01) :95-126
[6]   Phonons and related crystal properties from density-functional perturbation theory [J].
Baroni, S ;
de Gironcoli, S ;
Dal Corso, A ;
Giannozzi, P .
REVIEWS OF MODERN PHYSICS, 2001, 73 (02) :515-562
[7]   Paper: "Higher-order strain/higher-order stress gradient models derived from a discrete microstructure, with application to fracture", by C.S Chang, H. Askes and L.J. Sluys; Engineering Fracture Mechanics 69 (2002), 1907-1924 [J].
Borino, G ;
Polizzotto, C .
ENGINEERING FRACTURE MECHANICS, 2003, 70 (09) :1219-1221
[8]   A micromechanically based couple-stress model of an elastic two-phase composite [J].
Bouyge, F ;
Jasiuk, I ;
Ostoja-Starzewski, M .
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2001, 38 (10-13) :1721-1735
[9]  
BRATKOVSKII AM, 1984, FIZ TVERD TELA+, V26, P2561
[10]   3RD-ORDER ELASTIC-CONSTANTS FROM MOLECULAR-DYNAMICS - THEORY AND AN EXAMPLE CALCULATION [J].
CAGIN, T ;
RAY, JR .
PHYSICAL REVIEW B, 1988, 38 (12) :7940-7946