A variational problem in the mechanics of complex materials | Zendy

Mariano Giaquinta | Zendy; Paolo Maria Mariano | Zendy; Giuseppe Modica | Zendy

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A variational problem in the mechanics of complex materials

Author(s) -

Mariano Giaquinta,

Paolo Maria Mariano,

Giuseppe Modica

Publication year - 2010

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2010.28.519

Subject(s) - curvature , microstructure , nucleation , mean curvature , boundary (topology) , texture (cosmology) , mathematics , geometry , boundary value problem , classical mechanics , mathematical analysis , materials science , physics , computer science , composite material , thermodynamics , artificial intelligence , image (mathematics)

We analyze the possible nucleation of cracked surfaces in materials in which changes in the material texture have a prominent influence on the macroscopic mechanical behavior. The geometry of crack patterns is described by means of stratified families of curvature varifolds with boundary. Possible non-local actions of the microstructures are accounted for. We prove existence of ground states of the energy in terms of deformation, descriptors of the microstructure and varifolds.

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