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Kral ER, Komvopoulos K, Bogy DB. Elastic–plastic finite element analysis of repeated indentation of a half-space by a rigid sphere. J. Appl. Mech. 1993; 75: 829–841.

has been cited by the following article:

• TITLE: Characterizing and Modeling Mechanical Properties of Nanocomposites-Review and Evaluation

  AUTHORS: Hurang Hu, Landon Onyebueke, Ayo Abatan

  KEYWORDS: Nanocomposites; Mechanical properties; Multiscale modeling; Finite elementanalysis (FEA); Object-oriented modeling.

  JOURNAL NAME: Journal of Minerals and Materials Characterization and Engineering, Vol.9 No.4, April 20, 2010

  ABSTRACT: This paper presents a critical review of the current work of experiment, theory of micro-nanomechanics, and numerical analysis on characterizing mechanical properties of nanocomposites. First, the classifications of nanomaterials are presented. Then nanoindentation testing and the corresponding finite element modeling are discussed, followed by analytical modeling stiffness of nanocomposites. The analytical models discussed include Voigt and Reuss bounds, Hashin and Shtrikman bounds, Halpin–Tsai model, Cox model, and various Mori and Tanaka models. These micromechanics models predict stiffness of nanocomposites with both aligned and randomly oriented fibers. The emphasis is on numerical modeling includes molecular dynamics modeling and finite element modeling. Three different approaches are discussed in finite element modeling, i.e. multiscale representative volume element (RVE) modeling, unit cell modeling, and object-oriented modeling. Finally, the mechanism of nanocomposite mechanical property enhancement and the ways to improve stiffness and fracture toughness for nanocomposites are discussed.