From atomistics to continuum: Effects of a free surface and determination of surface elasticity properties

TY - JOUR

T1 - From atomistics to continuum

T2 - Effects of a free surface and determination of surface elasticity properties

AU - Hu, Lixin

AU - Liu, Liping

N1 - Funding Information: The authors gratefully acknowledge the support of NSF CMMI-1238835, CMMI-135156, DMS-1410273 and AFOSR YIP-12. Publisher Copyright: © 2015 Elsevier Ltd. All rights reserved.

PY - 2015/11/1

Y1 - 2015/11/1

N2 - We present an analysis of surface elasticity from the Born-Oppenheimer approximation for monatomic crystals. The analysis shows that the relaxations of crystal planes parallel to a free surface can be sufficiently determined by a low-rank algebraic Riccati equation instead of a full-scale molecular dynamic (MD) simulation, and gives new restrictions on physically reasonable atomistic models and simple criteria for surface reconstructions. In the case of surface relaxations, we calculate surface elasticity properties, i.e., surface tension, residual surface stress and surface elastic stiffness tensor, from atomistic models which are compared with experimental data and prior simulation results. The formulation also proves that surface relaxations always lower surface tension and surface elastic stiffness tensor. Together with the proposed algorithm, the formulation may be useful for investigating a variety of size-dependent phenomena of nano-structures.

AB - We present an analysis of surface elasticity from the Born-Oppenheimer approximation for monatomic crystals. The analysis shows that the relaxations of crystal planes parallel to a free surface can be sufficiently determined by a low-rank algebraic Riccati equation instead of a full-scale molecular dynamic (MD) simulation, and gives new restrictions on physically reasonable atomistic models and simple criteria for surface reconstructions. In the case of surface relaxations, we calculate surface elasticity properties, i.e., surface tension, residual surface stress and surface elastic stiffness tensor, from atomistic models which are compared with experimental data and prior simulation results. The formulation also proves that surface relaxations always lower surface tension and surface elastic stiffness tensor. Together with the proposed algorithm, the formulation may be useful for investigating a variety of size-dependent phenomena of nano-structures.

KW - Atomistic-to-continuum

KW - Size-dependent effects

KW - Surface elasticity

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U2 - https://doi.org/10.1016/j.mechmat.2015.03.012

DO - https://doi.org/10.1016/j.mechmat.2015.03.012

M3 - Article

VL - 90

SP - 202

EP - 211

JO - Mechanics of Materials

JF - Mechanics of Materials

SN - 0167-6636

ER -