Volume 18, Number 1, January-March 2012
|Page(s)||91 - 123|
|Published online||23 December 2010|
- R.A. Adams and J.J.F. Fournier, Sobolev spaces, Pure and Applied Mathematics (Amsterdam) 140. Elsevier/Academic Press, Amsterdam, 2nd edition (2003).
- L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs, Oxford University Press, Oxford (2000).
- M. Barchiesi and G. Dal Maso, Homogenization of fiber reinforced brittle materials : the extremal cases. SIAM J. Math. Anal. 41 (2009) 1874–1889. [CrossRef] [MathSciNet]
- A. Braides, Γ-convergence for beginners, Oxford Lecture Series in Mathematics and its Applications 22. Oxford University Press, Oxford (2002).
- A. Braides, and V. Chiadò Piat, Another brick in the wall, in Variational problems in materials science, Progr. Nonlinear Differential Equation Appl. 68, Birkhäuser, Basel (2006) 13–24.
- A. Braides, A. Defranceschi and E. Vitali, Homogenization of free discontinuity problems. Arch. Rational Mech. Anal. 135 (1996) 297–356. [CrossRef] [MathSciNet]
- P.G. Ciarlet, Mathematical elasticity. Three-dimensional elasticity I, Studies in Mathematics and its Applications 20. North-Holland Publishing Co., Amsterdam (1988).
- P.G. Ciarlet and J. Nečas, Injectivity and self-contact in nonlinear elasticity. Arch. Rational Mech. Anal. 97 (1987) 171–188. [CrossRef] [MathSciNet]
- G. Cortesani and R. Toader, A density result in SBV with respect to non-isotropic energies. Nonlinear Anal. 38 (1999) 585–604. [CrossRef] [MathSciNet]
- G. Dal Maso, An introduction to Γ-convergence, Progress in Nonlinear Differential Equations and their Applications 8. Birkhäuser Boston Inc., Boston, MA (1993).
- G. Dal Maso and G. Lazzaroni, Quasistatic crack growth in finite elasticity with non-interpenetration. Ann. Inst. Henri Poincaré Anal. Non Linéaire 27 (2010) 257–290. [CrossRef]
- G. Dal Maso and C.I. Zeppieri, Homogenization of fiber reinforced brittle materials : the intermediate case. Adv. Calc. Var. 3 (2010) 345–370. [CrossRef] [MathSciNet]
- L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. Studies in Advanced Mathematics, CRC Press, Boca Raton, FL (1992).
- G.A. Francfort and C.J. Larsen, Existence and convergence for quasi-static evolution in brittle fracture. Commun. Pure Appl. Math. 56 (2003) 1465–1500. [CrossRef] [MathSciNet]
- A. Giacomini and M. Ponsiglione, Non-interpenetration of matter for SBV deformations of hyperelastic brittle materials. Proc. R. Soc. Edinb. Sect. A 138 (2008) 1019–1041. [CrossRef]
- G.A. Iosifýan, Homogenization of problems in the theory of elasticity with Signorini boundary conditions. Mat. Zametki 75 (2004) 818–833.
- N. Kikuchi and J.T. Oden, Contact problems in elasticity : a study of variational inequalities and finite element methods, SIAM Studies in Applied Mathematics 8. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1988).
- D. Lukkassen, G. Nguetseng and P. Wall, Two-scale convergence. Int. J. Pure Appl. Math. 2 (2002) 35–86.
- A. Mikelić, M. Shillor and R. Tapiéro, Homogenization of an elastic material with inclusions in frictionless contact. Math. Comput. Model. 28 (1998) 287–307. [CrossRef]
- O. Pantz, The modeling of deformable bodies with frictionless (self-)contacts. Arch. Ration. Mech. Anal. 188 (2008) 183–212. [CrossRef] [MathSciNet]
- L. Scardia, Damage as Γ-limit of microfractures in anti-plane linearized elasticity. Math. Models Methods Appl. Sci. 18 (2008) 1703–1740. [CrossRef] [MathSciNet] [PubMed]
- L. Scardia, Damage as the Γ-limit of microfractures in linearized elasticity under the non-interpenetration constraint. Adv. Calc. Var. 3 (2010) 423–458. [CrossRef] [MathSciNet]
- A. Signorini, Sopra alcune questioni di statica dei sistemi continui. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2 (1933) 231–251. [MathSciNet]
- P.E. Stelzig, Homogenization of many-body structures subject to large deformations and noninterpenetration. Ph.D. Thesis, Technische Universität München (2009). Available electronically at http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:91-diss-20091214-797081-1-9.
- J.Y. Wong, Theory of ground vehicles. John Wiley & Sons Inc., New York (2001).
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