# American Institute of Mathematical Sciences

June  2010, 28(2): 519-537. doi: 10.3934/dcds.2010.28.519

## A variational problem in the mechanics of complex materials

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

Received  December 2009 Revised  April 2010 Published  April 2010

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.
Citation: Mariano Giaquinta, Paolo Maria Mariano, Giuseppe Modica. A variational problem in the mechanics of complex materials. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 519-537. doi: 10.3934/dcds.2010.28.519
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