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We study the $\Gamma$-convergence of damage to fracture energy functionals in the presence of low-order nonlinear potentials that allows us to model physical phenomena such as fluid-driven fracturing, plastic slip, and the satisfaction of kinematical constraints such as crack non-interpenetration.
Functions of bounded deformation
R. Temam and G. Strang · 1980
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Sur les équations de la plasticité: existence et régularité des solutions
P.-M Suquet · 1981
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Integral representation and relaxation of local functionals
G. Buttazzo and G. Dal Maso · 1985
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Semicontinuity, relaxation, and integral representation in the calculus of variations
G. Buttazzo · 1989
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Approximation of functionals depending on jumps by elliptic functionals via Γ \Gamma -convergence
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Revisiting brittle fracture as an energy minimization problem
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G. Cortesani and R. Toader · 1999
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L. Ambrosio, N. Fusco, and D. Pallara · 2000
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M. Focardi · 2002
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B. Bourdin, G. A. Francfort, and J. J. Marigo · 2008
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G. Allaire, F. Jouve, and N. Van Goethem · 2011
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Fracture models as Γ \Gamma -limits of damage models
G. Dal Maso and F. Iurlano · 2013
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Fracture and plastic models as γ \gamma -limits of damage models under different regimes
F. Iurlano · 2013
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Asymptotic analysis of ambrosio–tortorelli energies in linearized elasticity
M. Focardi and F. Iurlano · 2014
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Korn-poincaré inequalities for functions with a small jump set
A. Chambolle, S. Conti, and G. Francfort · 2016
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Approximation of functions with small jump sets and existence of strong minimizers of Griffith’s energy
A. Chambolle, S. Conti, and F. Iurlano · 2017
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