A variational problem in the mechanics of complex materials

Mariano Giaquinta; Paolo Maria Mariano; Giuseppe Modica

doi:10.3934/dcds.2010.28.519

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2010, Volume 28, Issue 2: 519-537. Doi: 10.3934/dcds.2010.28.519 open access

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A variational problem in the mechanics of complex materials

1.
Scuola Normale Superiore, Piazza dei Cavalieri, I-56100 Pisa
2.
DICeA, University of Florence, via Santa Marta 3, I-50139 Firenze
3.
Dipartimento di Matematica Applicata "G. Sansone”, University of Florence, via Santa Marta 3, I-50139 Firenze

Received: November 30, 2009

Revised: March 31, 2010

Published: June 2010

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Abstract

We analyze the possible nucleation of cracked surfaces in materials in whichchanges in the material texture have a prominent influence on themacroscopic mechanical behavior. The geometry of crackpatterns is described by means of stratified families of curvature varifoldswith boundary. Possible non-local actions of the microstructures areaccounted for. We prove existence of ground states of the energy in terms ofdeformation, descriptors of the microstructure and varifolds.

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Mathematics Subject Classification: Primary: 49J45, 49Q15, 74A30, 74A45, 74A60.

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