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Multi-scale and multi-order singularity approach to non-equilibrium mechanics: Coupling of atomic-micro-macro damage

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Abstract

Offered in this work is the development of a macro/meso/micro model that covers the lineal scale of 10−11 to 100 by application of the volume energy density function. Boundary constraints and defect geometries are shown to play a role at the smaller scale in the same way as those at the macroscopic scale. Different orders of stress (or energy density) singularities are used to describe the defect geometry and prevailing constraint via the boundary conditions in a way similar to singularity adopted in classical fracture mechanics. Two classes of singularities have been identified in addition to classical one without violating the finiteness conditions of the local displacement and energy density. Still the connection of results from the different scales is no small task and is made possible by application of a scale multiplier. It is determined by considering the interactive effects of the parameters at the different scales from the atomic to the macroscopic. Unlike the classical boundary value problem approach, application of the scale multiplier has led to closed-form asymptotic multiscale solutions that otherwise would not have been made possible. The procedure is demonstrated for the anti-plane shear of a macro-micro-atomic model that accounts for imperfection at the different scales

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Authors and Affiliations

  1. School of Mechanical Engineering, East China University of Science and Technology, Shanghai, China

    G. C. Sih

  2. Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, USA

    G. C. Sih

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  1. G. C. Sih
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Published in Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 3–22, January 2006.

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Sih, G.C. Multi-scale and multi-order singularity approach to non-equilibrium mechanics: Coupling of atomic-micro-macro damage. Int Appl Mech 42, 1–18 (2006). https://doi.org/10.1007/s10778-006-0054-7

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  • DOI: https://doi.org/10.1007/s10778-006-0054-7

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