International Journal for Multiscale Computational Engineering

ISSN for PRINT: 1543-1649

For Online Access

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2004, Volume2

Issue 2

157 pages

DOI: 10.1615/IntJMultCompEng.v2.i2

Issue price - $178.00

Dong Qian
Department of Mechanical, Industrial and Nuclear Engineering University of Cincinnati, Cincinnati, OH 45221-0072

Rohit H. Gondhalekar
Department of Mechanical, Industrial and Nuclear Engineering University of Cincinnati, Cincinnati, OH 45221-0072

A virtual atom cluster (VAC) model that represents the effect of interatomic bonding is developed as the constitutive model for crystal systems. In contrast with the crystal elasticity model, the proposed VAC model is distinguished by the following features: i) It does not build any constitutive relations that involve any stress concept, and ii) it does not use the homogeneous deformation assumption, or equivalently, the Born hypothesis. As a consequence of these attributes, the energy density of the system is embedded in the VAC model and directly related to the deformation mapping. The deformation mapping is constructed through the use of meshfree or finite element shape functions. The high-order continuity property of the meshfree shape functions guarantees the accuracy in describing the geometry and thus the energy of the atomic bond. The resulting formulation computationally more efficient than the continuum-based approach. Finally, the robustness of the method is illustrated through example problems involving various nanostructures.

DOI: 10.1615/IntJMultCompEng.v2.i2.70 Download article, 15 pages

Article price - $35.00

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