Multi-Scale Free-Discontinuity Problems with Soft Inclusions

Andrea Braides; Margherita Solci

Bollettino dell'Unione Matematica Italiana (2013)

  • Volume: 6, Issue: 1, page 29-51
  • ISSN: 0392-4041

How to cite

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Braides, Andrea, and Solci, Margherita. "Multi-Scale Free-Discontinuity Problems with Soft Inclusions." Bollettino dell'Unione Matematica Italiana 6.1 (2013): 29-51. <http://eudml.org/doc/294037>.

@article{Braides2013,
author = {Braides, Andrea, Solci, Margherita},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {29-51},
publisher = {Unione Matematica Italiana},
title = {Multi-Scale Free-Discontinuity Problems with Soft Inclusions},
url = {http://eudml.org/doc/294037},
volume = {6},
year = {2013},
}

TY - JOUR
AU - Braides, Andrea
AU - Solci, Margherita
TI - Multi-Scale Free-Discontinuity Problems with Soft Inclusions
JO - Bollettino dell'Unione Matematica Italiana
DA - 2013/2//
PB - Unione Matematica Italiana
VL - 6
IS - 1
SP - 29
EP - 51
LA - eng
UR - http://eudml.org/doc/294037
ER -

References

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  2. AMBROSIO, L. - FUSCO, N. - PALLARA, D., Functions of Bounded Variation and Free Discontinuity Problems, Oxford University Press, Oxford, 2000. Zbl0957.49001MR1857292
  3. BABUŠKA, I. - ANDERSSON, B. - SMITH, P. J. - LEVIN, K., Damage analysis of fiber composites Part I: Statistical analysis on fiber scale. Computer Methods in Applied Mechanics and Engineering172 (1999), 27-77. Zbl0956.74048MR1685902DOI10.1016/S0045-7825(98)00225-4
  4. BOURDIN, B. - FRANCFORT, G. A. - MARIGO, J.-J., The Variational Approach to Fracture. Journal of Elasticity, 91 (2008), 5-148. Zbl1176.74018MR2390547DOI10.1007/s10659-007-9107-3
  5. BRAIDES, A., Approximation of Free-Discontinuity Problems. Lecture Notes in Math.1694, Springer Verlag, Berlin, 1998. Zbl0909.49001MR1651773DOI10.1007/BFb0097344
  6. BRAIDES, A., Γ -convergence for Beginners, Oxford University Press, Oxford, 2002. MR1968440DOI10.1093/acprof:oso/9780198507840.001.0001
  7. BRAIDES, A., A handbook of Γ -convergence. In Handbook of Differential Equations. Stationary Partial Differential Equations, Volume 3 (M. Chipot and P. Quittner, eds.), Elsevier, 2006. Zbl1195.35002MR2569337
  8. BRAIDES, A. - CHIADÒ PIAT, V. - PIATNITSKI, A., A variational approach to double-porosity problems. Asymptotic Anal.39 (2004), 281-308. Zbl1113.35014MR2097996
  9. BRAIDES, A. - DEFRANCESCHI, A., Homogenization of Multiple Integrals. Oxford University Press, Oxford, 1998. Zbl0911.49010MR1684713
  10. BRAIDES, A. - DEFRANCESCHI, A. - VITALI, E., Homogenization of free discontinuity problems. Arch. Rational Mech. Anal.135 (1996), 297-356. Zbl0924.35015MR1423000DOI10.1007/BF02198476
  11. BRAIDES, A. - GARRONI, A., Homogenization of periodic nonlinear media with soft and stiff inclusions. Math. Meth. Mod. Appl. Sci.5 (1995), 543-564. Zbl0836.73003MR1335833DOI10.1142/S0218202595000322
  12. CAGNETTI, F. - SCARDIA, L., An extension theorem in SBV and an application to the homogenization of the Mumford-Shah functional in perforated domains. J. Math. Pures Appl.95 (2011), 349-381. Zbl1217.49036MR2776374DOI10.1016/j.matpur.2010.03.002
  13. DAL MASO, G., An Introduction to Γ -convergence, Birkhauser, Boston, 1993. Zbl0816.49001MR1201152DOI10.1007/978-1-4612-0327-8
  14. DESIMONE, A. - MARIGO, J. J. - TERESI, L., A damage mechanics approach to stress softening and its application to rubber. European Journal of Mechanics A, 20 (2001), 873-892. Zbl1008.74005MR1871955DOI10.1016/S0997-7538(01)01171-8
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