Elastic interaction between inclusions and tunable periodicity of superlattice structure in nanowires
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2654-6
Elastic interaction between inclusions and tunable periodicity of superlattice structure in nanowires∗ Yang YANG,
Yong NI†
CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Anhui 230026, China (Received Mar. 19, 2020 / Revised Jun. 19, 2020)
Abstract The elastic stress distribution and the variation of the elastic energy with spacing between two inclusions of arbitrary sizes in an infinite isotropic cylindrical rod are obtained by an analytical approach and the phase field microelasticity (PFM) simulation. The results show a near-attraction and far-repulsion elastic interaction between two inclusions with hydrostatic dilatation. The critical spacing, at which the interaction changes from attraction to repulsion, is on the order of the radius of the rod, dependent on the length and Poisson’s ratio of inclusions. Furthermore, the elastic energy calculations and PFM simulation results indicate that applying the local radial stress on the rod surface can modulate the elastic interaction between inclusions and adjust the periodicity of the superlattice nanowire structure. This can provide some guidelines for the tunable construction of superlattice nanowire structures. Key words
elastic interaction, inclusion, critical spacing, superlattice structure
Chinese Library Classification O302, O33, O34, O39 2010 Mathematics Subject Classification 35Q74, 37N15, 82C05
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Introduction
When elastic uniformity is disturbed by a region within it, and the region undergoes a change of form or the elastic constants of the region are different from those of the remainder, this region is called inclusion[1] . When two or more inclusions coexist in the matrix, the overlap of the elastic field induced by individual inclusions may generate an elastic interaction between them[2] . Such interaction is known to provide a thermodynamic driving force for the formation of various ordered heterostructure patterns[3–5] . The elastic interaction between two homogeneous inclusions with hydrostatic dilatation in a homogeneously isotropic infinite matrix usually vanishes for the special case[2] , and can appear when the elastic stress field of the inclusion is modified by various factors including, but not limited to, the surface or the interface[6–12] , the ∗ Citation: YANG, Y. and NI, Y. Elastic interaction between inclusions and tunable periodicity of superlattice structure in nanowires. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-020-2654-6 † Corresponding author, E-mail: [email protected] Project supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB22040502), the National Natural Science Foundation of China (No. 11672285), and the Fundamental Research Funds for the Central Universities of China (No. WK2090050043) c
Shanghai University and Springer-Verlag GmbH Germany
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