Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy | Zendy

Andrea Braides | Zendy; Caterina Ida Zeppieri | Zendy

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Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy

Author(s) -

Andrea Braides,

Caterina Ida Zeppieri

Publication year - 2009

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/204

Subject(s) - microstructure , surface (topology) , surface energy , energy (signal processing) , materials science , statistical physics , computer science , physics , mathematics , metallurgy , composite material , geometry , statistics

The combined effect of fine heterogeneities and small gradient perturbations is analyzed by means of an asymptotic development by -convergence for a family of energies related to (one- dimensional) phase transformations. We show that multi-scale effects add up to the usual sharp-interface limit, due to the homogenization of microscopic interfaces, internal and external boundary layers, optimal arrangements of microscopic oscillations, etc. Several regimes are analyzed depending on the "size" of the heterogeneity (small or large perturbations of a homogeneous situation) and their relative period as compared with the characteristic length of the phase transitions (slow or fast oscillations).

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