Discrete and continuum elastic properties of interfaces
Abstract
The microstructure of defects in solids, e.g. interfaces, is heterogeneous and, consequently, so are the elastic properties. The complete anisotropic fourth-order tensors of both the discrete and the effective elastic moduli are defined in the interfacial region. To examine the meaning of discrete elastic constants, (i) a piecewise-continuous medium is considered where individual phases occupy the Voronoi polyhedra and have the elastic moduli associated with individual atoms, and (ii) the relationship between natural vibrations of the discrete systems and continuum waves is explored. Questions of local energy changes and stability are addressed in terms of continuum properties of the moduli, particularly positive definiteness and strong ellipticity. Comparisons between the atomistic results (exact effective moduli) and those for the continuum analog (bounds) establish the validity of the definition of elastic properties for heterogeneous structures at atomic scales and lead to criteria to assess the stability of a given microstructure. Homogenization of interfacial properties gives heterogeneous transition zone (or interphase) model. Interface phenomena in macrosystems (composites) and microsystems (grain boundaries) is explained by inner layer conditions between homogeneous bulk regions. Dynamical membrane and spring models of the imperfect interfaces are shown to be limiting models (similar to Reuss and Voigt bounding approximations in multiphase composite mechanics) for asymptotic expansions of stress and strain fields, respectively. Asymptotic expansion of both fields (in terms of small parameter h-thickness of the layer) produces mixed-type, exact approximation of the first order in h. Derived models of imperfect interface are used for investigation of interface waves in anisotropic bicrystals and for comparison with corresponding acoustical modes in phonon spectra. Localized interface waves are explained as general inhomogeneous plane waves in subsonic, transonic and supersonic regions of the solid. Velocities for subsonic, transonic and supersonic ranges are calculated by complex variable techniques using Stroh's formalism. The dispersion curves are obtained for each model of imperfect interface. Dispersion at the interface is demonstrated to be result of dispersive boundary conditions contrary to the dispersion in nonlinear elastic medium.
Recommended Citation
Elliott Solomon Alber,
"Discrete and continuum elastic properties of interfaces"
(January 1, 1993).
Dissertations available from ProQuest.
Paper AAI9413790.
http://repository.upenn.edu/dissertations/AAI9413790
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